Physiotherapy is the means of treating disorders by physical means. Electrotherapy is an integral part of physiotherapy. The use of electricity for therapeutic purposes has grown up in recent years and now includes a wide variety of apparatus and equipments. A large number of therapeutic modalities for treating several disorders are now in use.
The evolution of electricity for therapeutic uses starts way back in 1646 when Thomas Rown coined the term Electricity. After this period there was a rapid development in the field of electricity. It became possible to store electricity for experiments. The important names during this period that contributed to these achievements included Pieter Van Musschenvoroek of Leyden, Benjamin Franklin of Philadelphia and Luigi Galavani of Bologna (Cherington et al. 1994). Benjamin Franklin was a great thinker and statesman at the time of the American revolution. In 1752, he conducted his famous kite experiment. It is possible that his kite was not actually struck by lightening but was electrified due to induction because of the presence of a highly charged electrical field. Franklin charged his Leyden jar by using a kite during electrical storms. During this period, electricity has become a source of Astonishment and Amusement.
Franklin's analysis of Leyden jar lead to the discovery of the law of electrostatic induction. He postulated the two opposing forces of electricity-positive and negative. Luigi Galvani a professor of Anatomy at University of Bologna proceeded his work on animal electricity. Galvani discovered that the nerves were a good conductor of electricity. This serendipitous discovery was made, when Galvani stimulated nerve of a frog with a knife during an experiment. This study revealed the relationship between electrical stimulation of nerve and contraction of its muscle.
Carlo Matteucci (1844) Professor of Physics in Pisa, Italy, investigated the localization of electricity in a muscle nerve preparation and proposed the concept of electrophysiologically based functioning of the nerve system. Matteucci also demonstrated that the electrical activity originates from a contracting muscle.
Dechenne (1833) demonstrated that the muscle can be stimulated percutaneously. He was the first to systematically study the neuromuscular diseases and was first to study the muscular dystrophies. Dechenne considered himself as the inventor of muscle nerve electricity or “localized faradizations”.
Remak (1858) discovered that the points where the nerve entered into the muscle were easy to stimulate.
Weiss (1892) first attempted to produce a rectangular pulse using ballistic rheotome. The important role of duration of current in eliciting the muscle contraction was reported by Keningsberg (1864). He developed a mechanical device which could rapidly interrupt the current; if the rate of interruption exceeded the limit, there was no muscle contraction. It was reported by Baierlacher (1859) that a paralysed muscle responded to galvanic but not faradic current.
Lapicque (1907) defined rheobase as minimal continuous current intensity required for muscle excitation. He also defined chronaxie which is the minimal current duration required at an intensity twice the rheobase.
Adrian (1916) was the first to demonstrate strength duration curve. He noted that healthy muscles showed a fairly constant curve. There was a predictable shift of the curves during muscle degeneration as well as in different phases of recovery.
Erb (1861) introduced the method of electro-diagnosis based on faradic and galvanic current. Erb was the first to demonstrate increase electrical irritability of motor nerves in tetany which in known as Erb's phenomenon. He was also the first to electrically stimulate the brachial plexus. This is how evolution of electricity in the use of nerve muscle stimulation has taken place.
THE STRUCTURE OF AN ATOM
The structure of matter that shapes the world around us has been a subject of study since long. The first contribution came from John Dalton, who postulated that matter is composed of atoms. The structure of atom was first described by J J Thompson and later modified by Rutherford and Neil Bohr. Historically they were described as minute individual particles but the quantum physics has explained the existence of many subatomic particles.
An atom can be described as the smallest particle of an element. It contains the central nucleus in which two particles protons and neutrons are held together by strong nuclear forces and are surrounded by negatively charged particles called electrons. The diameter of the atom is of the order of 10−10m.
The whole mass of an atom is concentrated in the central part called the nucleus. Its diameter ranges from 10−15 m to 10−14m. It consists of positively charged protons and neutral charged neutrons. The proton and neutron are regarded as two different charge state of same particle called neucleon. As the atom is electrically neutral, the number of electrons in the atom is equal to the number of protons inside the nucleus.
Protons were discovered by Gold stein. They are comparatively larger in size and bears a positive charge. It is the positive charge of proton which gives the nucleus of an atom and over all positive charge. Number of protons in the nucleus determines the element of which it is an atom and is called the atomic number. For example, the atomic number of hydrogen is 1.
Neutrons were discovered by James Chadwick (1932). The neutrons possess no charge and are therefore electrically neutral. Usually the number of neutrons approximately equals a number of protons but in larger elements there are more neutrons than protons. The sum of protons and neutrons in the nucleus gives rise to the atomic mass.
In certain elements it is possible for different atoms to have different number of neutrons in there nuclei with the same number of protons. These are called Isotopes of an element. For example, carbon with atomic number 6 may have atomic masses 12,13 or 14. So an isotope is an atom of an element with same number of protons but different number of neutrons.
Electrons were discovered by J. J. Thomson. Electrons are negatively charged particles found revolving around the nucleus in fixed orbits. Although electrons are very small (1/1837 mass of a proton) they are responsible for various physical and chemical activities of an atom.
A force of attraction between nucleus and electron is very strong. Therefore, these electrons are tightly bound with the nucleus. These electrons lie close to nucleus, and are called bound electrons. As the distance between the nucleus and electrons increases, force of attraction decreases. It means that there is an inverse relation between force of attraction and the distance between the two.
As the number of orbits increasees, the force of attraction between nucleus and electron weakens and therefore, the last orbit electrons are bounded by weak force and as a result of which these electrons remain free and are known as free electrons. Transfer of these free electrons makes the body charged.
THE FORMATION OF COMPOUNDS
A compound is a substance formed by the union of two or more elements via the electrons of the atoms involved to form a molecule of the compound. Compounds may be either electrovalent or covalent.
- Covalent compounds: These are formed when the outer shells of atoms of the elements share a number of common or bonding electrons so that each atom has a complete outer shell. For example, Methane.
The Conductors and Non- conductors of Electricity
Conductors: Conductors are elements whose atoms have few electrons in their outer orbit. For example, Copper has a single loosely held electron in its outer orbit. It is such conducting electrons which facilitate the passage of an electric current.
Non-conductors (Insulators): are materials made of atoms in which the electrons in the outer shell are firmly held in their orbits and do not leave the atom in order to conduct the current.
States of Matter
Matter can be solid, liquid or gaseous. The molecules of a substance are attracted by cohesive forces (force of attraction in molecules of same substance) and kinetic forces (force of movement of molecules).
In Solids: There is a strong cohesive force which holds them in a rigid lattice formation so that shape remains same or constant. The kinetic force produces vibration of molecules about a mean position.
In Liquids: When considerable amount of energy is applied to solids, cohesive force decreases and kinetic force increases so that rigid structure collapses and liquid state is reached.
In Gases: If even more heat is applied, there comes a point when, kinetic force is greater than cohesive force. Then molecules fly apart and form a gas. The molecules collide with each other and with the walls of the container, so that the pressure increases. As a result, temperature increases.
Latent heat: It is the energy required for (or released by) a change of state.
Latent heat of fusion is the amount of heat required to convert 1 gm of ice at 0 degree Celsius to 1 gm of water at 0 degree Celsius.(Value is 336 joules).
Latent heat of vaporization is the amount of heat required to convert 1 gm of water at 100 degree Celsius to1 gm of steam at 100 degree Celsius.(Value is 2268 joules).
Transmission of Heat
Conduction: If one end of a solid metal rod is heated, the energy added causes an increased vibration of molecules. This is transmitted and thus, heat is conducted from area of high temperature to area of low temperature. For example, metals.
Convection: It takes place in fluids. If one part of a fluid is heated, the kinetic energy of the molecules in that part is increased, they move further apart and this part becomes less dense. As a result it rises, displacing the more dense fluid above which descends to take its place. The current produced is called convection current.
Radiation: Heat may be transmitted by infra-red electromagnetic radiation. As a substance is heated, it causes the electron to move to the higher-energy shell. As it returns to its normal shell, the energy is released as a pulse of infra-red electromagnetic energy.
TYPES OF ELECTRICITY
- Static Electricity:When the charges on a body do not flow, then it is called static electricity.
- Current Electricity:When charges flow through a conductor it is known as current electricity.Charges: There are two types of charges – positive and negative.
The simplest way of producing a static electric charge is to rub two materials together. If the materials involved are insulators, the charges are held on the surfaces of objects and spread themselves evenly over the surfaces unless there are points or corners, at which charges tend to concentrate.
Experiments to prove the existence of charge:
Experiment-1: Take a glass rod and a silk cloth. Rub glass rod on silk cloth. After rubbing hang it with the help of non-metallic string. Take another ebonite rod and repeat this experiment. Bring it close to hanged rod; we see force of repulsion between them.
Experiment-2: Take ebonite rod and a woolen cloth. Rub the rod on woolen cloth and hang it with the help of non-metallic string. Take another ebonite rod and repeat the above process. Bring it close to first hang rod we observe the property of force of repulsion.
Experiment-3: Take a glass rod and a silk cloth. Rub the rod on the silk cloth. Hand it with the help of a non-metallic string. Now take an ebonite rod and a woolen cloth. Rub these with each other and bring this rod close to the glass rod, we observe the property of force of attraction.
Conclusion: On the basis of these experiments, we conclude that charge is produced on glass rod. Later, American scientist Benjamin Franklin (1706–1790) confirms these charges as positive and negative charges. When glass rod is rubbed with silk, charge produced on glass rod is known as positive charge. When ebonite rod is rubbed on woolen cloth, charge produced on ebonite rod is known as negative charge.
We may conclude that like charges repel each other but unlike charges attract each other.
Other Methods of Producing Electricity
According to the law of conservation of energy, energy can neither be created nor be destroyed, but can be converted from one form to another. When it is produced by friction, mechanical energy is converted into electrical energy. When it is produced in dry cells, chemical energy is converted into electrical energy, etc.
Quantization of Electric Charge
The quantization of electric charge is the property by virtue of which any charge exists only in discrete lumps or packets or bundles of certain minimum charge ±e, where –e is the charge of an electron and +e is the charge of a proton. The least charge found on any body is equal to the charge of electron or proton.
Also, charge on any body can only be the integral multiple of the charge of electron i.e.
where n is an integer 1,2,3,….
According to this law, the force of interaction between any two point charges is directly proportional to the product of charges and inversely proportional to the square of distance between them.
Suppose two bodies having charges q1 and q2 are separated in vacuum by a distance r. Let their linear dimensions be much smaller than the distance r so that they act as point charges.
According to Coulomb's law
Where, k is electrostatic force constant.
Coulomb's Law of electrostatic force between two charges corresponds to the Newton's Law of Gravitational force between two masses i.e.,
A unit charge is that much charge which when placed in vacuum at a distance of one meter from an equal and similar charge would repel it with a force of 9 × 109 Newton.
Electric Field Intensity due to a Group of Charges
The electric field intensity at any point due to a group of point charges is equal to the vector sum of the electrical field intensities due to the individual charges at the same point.
Electric Lines of Forces
Michael Faraday invented the idea of electric lines of force. They give us partial qualitative information about an electric field. We may define an electric line of force as a path, straight or curved, such that tangent to it at any point gives the direction of electric field intensity at that point. Infact, it is the path along which a unit positive charge actually moves in the electrostatic field, if free to do so.
In Figure 1.1, AB is an electrostatic line of force. The tangent to the line at any point P gives us the direction of electric intensity
p at P. Similarly, tangent to AB at Q gives us the direction of
q, Fig. 1.1
It is important to note here that the lines of force do not actually exist, but what they represent is a reality.
Figure 1.2 shows some lines of force due to single positive point charge. These are directed radially outwards. The lines of force extend to infinity.
On the contrary, lines of force due to singly negative point charge are directed radially inwards, Figure 1.3.
Figure 1.4 shows lines of force due to a pair of equal and opposite charges. The lines of force due to two equal positive point charges of different strength are shown in Figures 1.5 and 1.6
When the charges are equal, P lies at the centre of the line joining the charges. However, when the charges are unequal, the neutral point P is closer to the smaller charge. Figure 1.7 shows lines of force for a section of an infinitely large sheet of positive charge.
Properties of Electric Lines of Forces
Electric lines of force are discontinuous curves. They start form a positively charged body and end at a negatively charged body. No electric lines of force exit inside the charged body.
- Tangent to the line of force at any point gives the direction of electric intensity at that point.
- No two electric lines of force can intersect each other. This is because at the point of intersection P, we can draw two tangents PA and PB to the two lines of force, Fig. 1.8 This would mean two directions of electric intensity at the same point, which is not possible. Hence no two lines of force can cross each other.
- The electric lines of force are always normal to the surface of a conductor, both while starting and ending on the conductor. Therefore, there is no component of electric field intensity parallel to the surface of the conductor.
- The electric lines of force contract longitudinally, on account of attraction between unlike changes.
- The electric lines of force exert a lateral pressure on account of repulsion between like charges.
Electric Dipole: An electric dipole consists of a pair of equal and opposite point charges separated by a very small distance. Atoms or molecules of ammonia, water, alcohol, carbon dioxide, HCI, etc. are some of the examples of electric dipoles, because in their cases, the centres of positive and negative charge distributions are separated by some small distance. Figure 1.9 shows an electric dipole consisting of two equal and opposite point charges (±q) separated by a small distance ‘2a’.
Dipole moment: Dipole moment
is a measure of the strength of electric dipole. It is a Vector quantity whose magnitude is equal to product to the magnitude of either charge or the distance between them.
The direction of
is from negative charge to positive charge. The S.I. unit of dipole moment is Coulomb-metre. (C-m).
If charge q gets larger; and the distance 2a gets smaller and smaller, keeping the product
, we get what is called an ideal dipole. Thus an ideal dipole is the smallest dipole having almost no size.
Dipole Field: The dipole field is the electric field produced by an electric dipole. It is the space around the dipole in which the electric effect of the dipole can be experienced. To calculate dipole field intensity at any point, we imagine a unit positive charge held at that point. We calculate force on this charge due to each charge of the dipole and take vector sum of the two forces. This gives us dipole field intensity at that point.
The capacitance of an object is the ability of the body to hold an electrical charge. Its units are farad.
A farad is the capacity of an object which is charged to a potential of 1 volt by 1 coulomb of electricity.
In practice, microfarad is used most commonly. (1 microfarad = 1/1000000 farad).
At any stage, if q is the charge on the conductor and V is the potential of the conductor, then
where C is a constant of proportionality and is called capacity or capacitance of the conductor. The value of C depends on the shape and size of the conductor and also on the nature of the medium in which the capacitance is located.
Factors affecting capacity of a conductor
- Area of conductor: It is inversely related to capacity.
- Presence of any conductor nearby: In this case, potential decreases, so capacity increases.
- Medium around conductor: The capacity increases when any other medium is placed around conductor.
Parallel plate capacitor is the capacitor which is used most commonly. It consists of two thin conducting plates of area A, held parallel to each other, suitable distance d apart. The plates are separated by an insulating medium like air, paper, mica, glass, etc or dielectric constant k (Fig. 1.10).
Spherical capacitor consists of a hollow conducting sphere A of radius Ra surrounded by another concentric conducting spherical shell B of radius Rb (Fig. 1.11).
Variable capacitor consists of two sets of plates interleaving with one another, constructed in such a way that one set of plates can be moved relative to the other, thus varying the surface area of the plates facing each other. When all the surfaces of both the sets of plates are fully interleaved, the capacitance is maximum. Variable sets are found in radio sets and short wave diathermy machine.
Grouping of Capacitors: In many electrical circuits, capacitors are to be grouped suitably to obtain the desired capacitance. Two most commonly used modes of grouping of capacitors are: Series and parallel.
- Capacitors in Series: A voltage applied across four capacitors in series induces charges of +Q and –Q on the plates of each. As we know:
The potential difference across the row is the sum of the potentials across each capacitor and so, the single capacitance C equivalent to the three capacitors C1, C2, C3 is given by as in Figure 1.12.
- Capacitors in parallel: If capacitors are connected in parallel, the total charge developed on them is the sum of the charges on each of them. The effective capacitance is given by as in Figure 1.13.
Where Q = Q1+Q2+Q3+Q4
When charges flow through a conductor, the study of this is known as Current Electricity.
The flow of charge in a conductor is known as Electric current.
The essentials for the production of electric current are:
- Potential difference
- Pathway along which current can move
Electric Potential: The electric potential of a body is the condition of that body when compared to the neutral potential of the Earth. Its unit is the volt.
Volt is that EMF which when applied to a conductor with a resistance of 1 ohm produces a current of 1 ampere. In simple words, it is the repelling power between the charges.
Potential Gradient: The rate of change of potential with respect to distance is called potential gradient. It is directed from an area of low potential to an area of high potential. It is a vector quantity.
potential of that point
From this equation we conclude that potential gradient can be increased by bringing two plates together.
The Current Carriers
The charged particles whose flow in a definite direction constitutes the electric current are called current carriers.
Current carriers in solid conductors: In solid conductors like metals, the valence electrons of the atoms do not remain attached to individual atoms but are free to move throughout the volume of the conductor. Under the effect of an external electric field, the valence electrons move in a definite direction causing electric current in the conductors. Thus, valence electrons are the current carriers in solid conductors.
Current carriers in liquids: In an electrolyte like CuSO4 NaCl, etc., there are positively and negatively charged ions (like Cu++, SO4− −, Na+, Cl−). These are forced to move in definite directions under the effect of an external electric field, causing electric current. Thus, current carriers in liquids are positive and negative charged ions.
Current carriers in gases: Ordinarily, the gases are insulators of electricity. But they can be ionized by applying a high potential difference at low pressures or by their exposures to X-rays, etc. The ionized gas contains positive ions and electrons. Thus, positive ions and electrons are the current carriers in gases.
It is the force producing the flow of electrons from the more negative to the less negative body, if similar bodies are charged with different quantities of electricity.
If a pathway is provided, the EMF produces a flow of electrons, but if there is no pathway, so that no current can pass, the force still exists. The greater the potential difference the greater is the EMF, and both are measured in the same unit, i.e. the volt.
A volt is that EMF which when applied to a conductor with a resistance of one Ohm produces a current of one Ampere.
Electrons move only so long as a potential difference exists between the ends of the pathway, i.e. so long as the EMF is maintained. A potential difference can be produced by friction, but when a pathway is completed the charges quickly neutralise each other and current ceases to flow. Other methods of producing a potential difference, and so an EMF, are by the chemical action in cells, by electromagnetic induction in dynamo, by heat in a thermocouple and from radiant energy in a photo-electric cell. With all these methods the potential difference is maintained in spite of the electron flow.
As fast as electrons move away from the negative end of the conductor they are replaced by others from the generator, while those which reach the positive end are drawn away by the generator. Thus the potential difference is maintained and current continues to flow.
Electric current: The flow of charge in a definite direction constitutes the electric current and the time rate of flow of charge through any cross section of a conductor is the measure of electric, current i.e.
Unit of electric current: SI unit of electric current is Ampere.
Thus, the current through a wire is said to be 1 ampere, if one coulomb charge is flowing per second through a section of the wire.
Direction of electric current: As a matter of convention, the direction of flow of positive charge gives the direction of current. This is called conventional current. The direction of flow of electrons gives the direction of electronic current. The direction of flow of conventional current is opposite to that of electronic current (Fig. 1.14)
Current Density: Current density at a point is defined as the amount of current flowing per unit are of the conductor around that point provided the area is held in a direction normal to the current.
It is the obstruction to the flow of electrons in a conductor. The unit of electrical resistance is the ohm. It is the resistance offered to current flow by a column of mercury 1.063m long and 1 mm square in cross-section at 0 degree Celsius.
Cause of resistance of a conductor: Resistance of a given conducting wire is due to the collisions of free electrons with the ions or atoms of the conductor while drifting towards the positive end of the conductor which in turn depends upon the arrangement of atoms in the conducting material (silver, copper, etc) as well as on the length and thickness of the conducting wire.
Resistance is directly proportional to length and inversely proportional to area of cross-section, temperature and number of free electrons in a unit volume.
It was given by a German scientist George Siman Ohm, in the year 1828. It states that,
The current flowing through a metallic conductor is proportional to the potential difference across its ends, provided that all physical conditions remain constant.
If V = Potential difference and I = current then,
where R is Resistance and is the constant of proportionality.
So, 1 ohm is defined as the resistance of a body such that 1 volt potential difference across the body results in a current of 1 ampere through it.
Limitations of Ohm's law
- Temperature of the conductor should remain constant.
- The conducting body should not be deformed.
- It takes place in metallic conductors only.
Resistance in Series
If the components of a circuit are connected in series, there is only one possible pathway for the current, i.e. the components carry the same current. The total resistance equals the sum of individual resistances (Fig. 1.15).
Then from Ohm's law, we have,
If potential difference between A and B is V,
So, in series combination, equivalent resistance is equal to sum of individual resistances.
Resistance in Parallel
In this case, there are a number of alternative routes offered to the current. However, potential difference remains the same. It has been found by the application of Ohm's law that the largest resistance carries the smallest current and vice-versa.
If 3 resistances R1, R2, R3 are connected in parallel across points A and B connected to a point C at point A current I gets divided into I1, I2, and I3 (Fig. 1.16).
Potential difference across A and B is V.
Then from Ohm's law,
Hence, in a parallel combination, the reciprocal of equivalent resistance is equal to the sum of reciprocals of individual resistances.
Electric conductivity: The inverse of resistivity of a conductor is called its conductivity.
Rheostat is a device used to regulate current by altering either the resistance of the current or potential in the part of the circuit. It consists of a coil of high resistance wire wound onto an insulating block with each turn insulated from adjacent turns.
Types There are two types of rheostat:
- Series rheostat: In this, the rheostat is wired in series with the apparatus. If all the wires in the rheostat are included in the circuit, resistance is at its maximum and current at its lowest. In the physiotherapy department, it is found in the apparatus where an effect on the degree of heating is required. For example: for wax baths. It is also known as variable rheostat.
- Shunt rheostat: It is wired across a source of potential difference and any other circuit has to be taken off in parallel to it. This apparatus has a current regulating mechanism in which an electric current is applied directly to the patient, as the current intensity can be increased gradually from zero upto maximum. It is also known as potentiometer rheostat.
Those conductors which do not obey the Ohm's Law are called the non-Ohmic conductors. For example, vacuum tubes, semiconductor diode, liquid electrolyte, transistor, etc.
The relation V/I = R is valid for Ohmic and non-Ohmic conductors. The value of R is constant for Ohmic conductors but not so for non-Ohmic conductors.
A thermistor is a heat sensitive device whose resistivity changes very rapidly with the change of temperature. The thermistors are usually prepared from the oxides of nickel, copper, iron, cobalt, etc. These are generally in the form of beads, discs or rods. Pair of platinum leads is attached at the two ends of the electric connections. This arrangement is sealed in a small glass bulb. A thermistor can have a resistance in the range of 0.1 Ohm to 107 Ohm, depending upon its composition. A thermistor can be used over a wide range of temperatures.
Important applications of thermistors:
- Thermistors can be used to detect small temperature changes. A typical thermistor can easily measure a change in temperature of 10¯3 ºC.
- Thermistors are used to safeguard the filament of the picture tube of a television set against the variation of electric current.
- Thermistors are used in temperature control units of industry.
- Thermistors are used for voltage stabilization.
- Thermistors are used in the protection of windings of generators, transformers and motors.
Semiconductors are elements whose conductivity is between conductors and insulators. Elements such as germanium, silicon and carbon are insulators of electricity. But when impurities are added to it they become semiconductors. Semiconductors are insulators at low temperature. The resistance of semiconductors decreases when the temperature increases.
The process of deliberate addition of impurities to a pure semiconductor to enhance conductivity is called doping. The impurity atoms are called dopants.
The semiconductors are thus called n-type or p-type. The n-type is with excess of electrons and p-type is with deficient electron.
Types of Semiconductors
Semiconductors are of two types:
- Intrinsic semiconductors
- Extrinsic semiconductors
Intrinsic semiconductors: A pure semiconductor which is free of every impurity is called intrinsic semiconductor. Germanium and silicon are important examples of intrinsic semiconductors which are widely used in electronics industry.
Extrinsic semiconductors: A doped semiconductor or a semiconductor with suitable impurity atoms added to it is called extrinsic semiconductor.
Extrinsic semiconductor is of two types:
- N- type semiconductor
- P-type semiconductor
N-type semiconductor: When a pure semiconductor of silicon(Si) in which each Si atom has four valence electrons, is doped with a controlled amount of pentavalent atoms, say arsenic or phosphorous or antimony or bismuth, which have five valence electrons, the impurity atoms will replace the silicon atoms. The four of the five valence electrons of the impurity atoms will form covalent bonds by sharing the electrons with the adjoining four atoms of silicon, while the fifth electron is very loosely bound with the parent impurity atom and is comparatively free to move (Fig. 1.17).
Thus each impurity atom added donates one free electron to the crystal structure. These impurity atoms which donate free electrons for the conduction are called donor atoms. Since the conduction of electricity is due to the motion of electrons, i.e. negative charges or n-type carriers, therefore, the resulting semiconductor is called donor-type or n-type semiconductor. On giving up their fifth electron, the donor atoms become positively charged. However, the matter remains electrically neutral as a whole.
P-type semiconductor: When a pure semiconductor of silicon(Si) in which atom has four valence electrons is doped with a controlled amount of trivalent atoms say indium (In) or boron(B) or aluminium (Al) which have three valence electrons, the impurity atoms will replace the silicon atoms (Fig. 1.18).
The three valence electrons of the impurity atom will form covalent bonds by sharing the electrons of the adjoining three atoms of silicon, while there will be one incomplete covalent bond with the neighbouring Si atom, due to the deficiency of an electron. This deficiency is completed by taking an electron from one of the Si-Si bonds, thus completing the In-Si bond. This makes Indium ionized (negatively charged) and creates a hole. An electron moving from a Si-Si bond to fill a hole, leaves a hole behind. That is how, holes move in the semi-conductor structure. The trivalent atoms are called acceptor atoms and the conduction of electricity due to motion of holes, i.e. positive charges or p-type carriers. That is why the resulting semiconductor is called acceptor type or p-type semiconductor.
Prof. K Onnes in 1911 discovered that certain metals and alloys at very low temperature lose their resistance considerably. This phenomenon is known as superconductivity. As the temperature decreases, the resistance of the material also decreases, but when the temperatures reaches a certain critical value (called critical temperature or transition temperature), the resistance of the material completely disappears, i.e. it becomes zero. Then the material behaves as if it is a superconductor and there will be flow of electrons without any resistance what so ever. The critical temperature is different for different materials. It has been found that mercury at critical temperature 4.2K, lead at 7.25K and niobium at critical temperature 9.2K become superconductors.
The cause of superconductivity is that, the free electrons in superconductor are no longer independent but are mutually dependant and coherent when the critical temperature is reached. The ionic vibrations which could deflect free electrons in metals are unable to deflect this coherent or co-operative cloud of electrons in superconductors. It means that coherent cloud of electrons makes no collisions with ions of the superconductor and, as such, there is no resistance offered by the superconductor to the flow of electrons.
Applications of Superconductor
- Superconductors are used for making very strong electromagnets.
- Superconductivity is used to produce very high speed computers.
- Superconductors are used for the transmission of electric power.
THERMAL AND CHEMICAL EFFECTS OF CURRENTS
Thermal Effects of the Electric Current
The thermal effect was discovered by James Prescott Joule, a British scientist in the year 1841. He established the law called Joule's law.
When current is passed through a conductor, some of its energy is converted into thermal energy. The amount of heat produced can be calculated using Joule's Law which states that:
The amount of heat produced in a conductor is directly proportional to the square of current, the resistance, and the time for which the current flows.
This is given by:
current in amperes
resistance in Ohms
time in seconds.
This equation is known as Joule's Law of heating.
Cause of heating effect of current: When a potential difference is applied across the ends of a conductor, an electric field is set up across its ends and the electric current flows through it. The large number of free electrons present in the conductor get accelerated towards the positive end, i.e. in a direction opposite to the electric field developed and acquire kinetic energy in addition to their own kinetic energy due to their thermal motion. Due to which an electric current flows through the conductor. These accelerated electrons on their way suffer frequent collisions with the ions or atoms of the lattice and transfer their gained kinetic energy to them. As a result of this, the average kinetic energy of vibration of the ions or atoms of the conductors, rises and consequently the temperature of the conductor rises. Thus the conductor gets heated due to flow of electric current through it. Obviously the electrical energy supplied by the source of EMF is converted to this heat energy.
Electrical Energy and Power
Energy: Energy is the ability to do work.
According to the Law of conservation of energy, energy can neither be created nor can destroyed. It only be converted from one form to another.
The amount of work done is given by:
E × C
work done in joules.
EMF in volts.
quantity of electricity in coulombs.
Or Electric energy = Power × time
SI unit of electric energy is Joule, where
1 volt × 1 ampere × 1 sec.
1 watt × 1 sec
The commercial unit of electric energy is called a Kilowatt- hour (kWh)
1 kilo watt × 1 hour
1000 watts × 1 hour
Thus, 1kilowatt hour is the total electric energy consumed when an electrical appliance of power 1 kilowatt works for 1 hour.
Number of units of electricity consumed
Power: It is the rate of doing work.
Electric power: The rate at which work is done by the source of EMF in maintaining the current in electric circuit is called the electric power of the circuit.
It is given by:
Also, Power(P) = work/ time
Its unit is the watt.
If an EMF of 1 volt moves 1 coulomb of electrons in one second then the power of system is said to be 1 watt.
Bigger units of power are Kilowatt (103 watts) and Megawatt(106 watts)
Commercial unit of power is Horsepower.
1 Horsepower = 746 watts.
Some aspects of heating effects of currents:
- The wire supplying current to an electric lamp are not practically heated while that of the filament of the lamp becomes white hot. We know that the heat produce due to a current in a conductor is proportional to its resistance. The lamp and the supply wires are in series. The resistance of the wires supplying the current to the lamp is very small as compared to that of the filament of the lamp. Therefore, there is more heating effect in the filament of the lamp than that in the supply wires. Due to it, the filament of the lamp becomes white hot where the wires remain practically unheated.
- Electric iron, electric heater and heating rod are some of the important household electric appliances whose working is based on the heating effect of the electric current. In all such appliances, the heating element used is of a nichrome (an alloy of nickel and chromium) wire. The wire of nichrome is used because:
- It has high melting point and high value of specific resistance
- It can be easily drawn into wires.
- It is not oxidized easily when heated in air.Electric iron, electric heater and heating rod are of high power instruments. As, electric power, P = VI. Therefore, for the given voltage V, P α′ I. Thus, the higher is the power of the electrical appliance, the larger is the current drawn by it. Since the heat produced, H α′ I², hence the heat produced due to current, is high in both of them.It should be noted that electric power, P = V²/R. Therefore, for the given voltage V, P α′ I/R. This shows that the resistance of high electric power instrument is smaller than that of low power.The heater wire must be of high resistivity and of high melting point. Heat produced, H = V² t/R = V² At/ρl. The resistivity is kept high so that the length l, used for the given area of cross section of the wire and heat to be produced, may be small. Nichrome wire is used in heater due to its high resistivity as compared to platinum, tungsten and copper.
- Incandescent electric lamp: It consists of metal filament of fine wire(generally of tungsten) enclosed in a glass bulb with some inert gas at suitable pressure. The metal filament must be of very high melting point. When voltage is applied across the bulb, the current is passes through the filament. The filament gets heated to a very high temperature. It then becomes white hot (Incandescent state) and then starts emitting white light at once.
- Fuse wire: A fuse wire is generally prepared from tin-lead alloy (63% tin +37% lead). It should have high resistance and low melting point. It is used in series with the electrical installations and protects them from the strong currents. All of a sudden, if strong current flows, the fuse wire melt away, causing the breakage in the circuit, thereby saving the main installations from being damaged. Thus very cheap fuse wire is capable of saving very costly appliances.
- Efficiency of an electric device (η)Efficiency of an electric device is defined as the ratio of its output power to the input power, i.e.
In case of an electric motor,
Here, Input electric power = Output mechanical power + Power lost in heat
Efficiency of a battery or cell is maximum when its internal resistance is equal to external resistance of the circuit.
Chemical Effects of the Electric Current
When we pass current through a solid conductor, it gets heated and also a magnetic field is produced around the conductor. It shows that there is a heating effect as well as magnetic effect of current, but there is no chemical effect in a solid conductor. On the other hand if current is passed through a liquid, it may or may not allow the current to pass through it. On the basis of electric behaviour, the liquids can be classified into three categories.
- Insulators: These are those liquids which do not allow current to pass through them. For example, vegetable oil, distilled water, etc.
- Good conductors: These are those liquids which allow the current to pass through them but do not dissociate into ions. For example, mercury (a liquid metal at ordinary temperature).
- Electrolytes: The liquids which allow current to pass through them and also dissociate into ions or passing through them are called electrolytes. For example, the solution of salts, acids and bases in water, alcohol, etc.
Therefore, when current is passed through an electrolyte, it dissociates into positive and negative ions. This is called chemical effect of electric current and was studied in detail by Michael Faraday in 1933.
Commonly used terms are:
Electrolysis: The process of decomposition of electrolyte solution into ions on passing the current through, is called electrolysis.
Electrolyte: The substance which decomposes into positive and negative ions on passing current through, is called electrolyte. For example: acids, basis, salts, dissolved in water, alcohol, etc. are common electrolytes. Pure salt like NaCl, KCl are electrolyte, in there molten state.
Electrodes: These are the two metal plates which are partially dipped in the electrolyte for passing the current through the electrolyte.
Anode: The electrode connected to the positive terminal of the battery, i.e. the electrode at higher potential is called anode.
Cathode: The electrode connected to the negative terminal of the battery, i.e. the electrode at lower potential is called is cathode.
The current flows through the electrolyte from anode to cathode.
Ions: The charged constituents of the electrolyte which are liberated on passing current are called ions.
Anions: The ions which carry negative charge and moves towards the anode during electrolysis are called anions. The ions formed when chemical reaction involves addition of electrons (i.e. reduction) are called anions.
Cations: The ions which carry positive charge and move towards the cathode during electrolysis are called cations. The ions formed when chemical reaction involves removal of electrons (i.e., oxidation) are called cations.
Voltameter: The vessel in which the electrolysis is carried is called a voltameter. It contains two electrodes and a solution electrolyte. It is also known as electrolytic cell.
Faraday's Laws of Electrolysis
Faraday, from his experimental study, arrived at the two laws of electrolysis which are given below.
First Law: The mass of the substance liberated or deposited at an electrode during electrolysis is directly proportional to the quantity of charge passed through the electrolyte.
If m is the mass of a substance deposited or liberated at an electrode during electrolysis when a charge q passes through the electrolyte, then according to Faraday's First Law of electrolysis
Where z is a constant of proportionality and is called Electrochemical equivalent (ECE) of the substance.
If an electric current I flows for a time t to pass the charge q through the electrolyte, then q = It
Hence electrochemical equivalent (ECE) of a substance is defined as the mass of the substance liberated or deposited on an electrode during electrolysis, when one Coulomb of charge (or 1 ampere current for 1 second) is passed through the electrolyte.
Generally ECE of a substance is expressed in gram/Coulomb (g/C). The value of ECE of copper and hydrogen are 0.0003294 g/C and 0.0000105 g/C respectively.
Second Law: When the same amount of charge is made to pass through any number of electrolytes, the masses of the substances liberated or deposited at the electrodes are proportional to their chemical equivalents.
If m1 and m2 are masses of the substances liberated or deposited on various electrodes, when same current is passed for the same time through their electrolytes.
E1 and E2 are the chemical equivalents of the substances liberated or deposited.
Then according to the Faraday's Second Law of electrolysis
Faraday's Second Law of electrolysis also states that the electrochemical equivalent of a substance is directly proportional to its chemical equivalent.
If E1 and E2 are the chemical equivalents of the two substances and z1 and z2 are ECE of those two substances, then according to Faraday's Second Law of electrolysis
From Faraday's Second Law of electrolysis
Where, F is Faraday's constant
Thus, Faraday's constant is
If m = E, then F = q
Hence, Faraday's constant is equal to the amount of charge required to liberate the mass of a substance at an electrode during electrolysis, equal to its chemical equivalent (in grams).
Practical application of electrolysis:
- Electroplating: It is a process of depositing a thin layer of one metal over another metal by the method of electrolysis. The articles of cheaper metals are coated with precious metals like silver and gold to make their looks more attractive. The article to be electroplated is made the cathode and the metal to be deposited is made the anode. A soluble salt of the precious metal is taken as the electrolyte. When current is passed, a thin layer of the metal (made anode) is deposited on the article made (made cathode).
- Extraction of metals from ores: Certain metals like Aluminium, Copper, Zinc, Magnesium, etc. are extracted from their ores by the method of electrolysis.
- Purification of metals: Impure metals are purified by electrolysis. Blister copper is purified by this method.
- Anodising: It is the process of coating aluminium with its oxide electrochemically to protect it against corrosion. It dilute sulphuric acid as electrolyte, the aluminium article is made the anode. To give surface of articles beautiful colours, dyes are mixed in the electrolyte.
- Medical applications: Similar principles of electrolysis are also used in nerve stimulation. Also, similar principles are used for removing unwanted hairs from the body.
In current electricity, cell means an electrochemical cell. Cell is a device by which chemical energy is converted into electrical energy. Electrochemical cells are of two types:
- The primary cells
- The secondary cells
The primary cells are those in which electrical energy is produced due to chemical energy. The chemical reaction in the primary cell is irreversible. The examples of primary cells are Voltaic cell, Daniel cell, Leclanche cell, Dry cell, etc.
The secondary cells are those in which the electrical energy is first stored up as the chemical energy. When current is required to drawn from the secondary cell, then the chemical energy is reconverted into the electrical energy. The chemical reaction in the secondary cell is reversible. The examples of secondary cells are Lead- acid accumulators, alkali accumulators or Edison cell.
The initial cost of a primary cell is low as compared to the secondary cell. But, the running cost of a secondary cell is low as compared to the primary cell.
The Primary Cells
Voltaic cell: Voltaic cell was invented by Allexandro de Volta in 1800. It consist of two rods (called electrodes) one of copper and another of zinc, partly immersed in dilute sulphuric acid (called electrolyte) contained in a glass vessel (Fig. 1.19). The copper rod acts as positive electrode and zinc rod acts as negative electrode.
When the electrodes are connected to an external resistor, the circuit is completed. There will be flow of electrons from the negatively charged zinc rod to the positively charged copper rod through the external resistor. Now the conventional electric current is said to flow from copper to zinc.
Daniel cell: It consists of a copper vessel containing saturated copper sulphate solution. The copper vessel itself acts as the positive electrode or anode. A porous pot containing 10% dilute sulphuric acid (called electrolyte) and amalgamated zinc rod (called cathode), is placed in the copper vessel and is partly immersed in a copper sulphate solution. The porous pot prevents the solution from mixing, but allows the hydrogen ions to pass through it. A perforated shelf containing the copper sulphate crystal is placed at the top of the vessel in order to keep the concentration of the copper sulphate solution same (Fig. 1.20).
In this cell, as the reaction continues, the concentration of copper sulphate solution decreases. Some CuSO4 crystals get dissolved immediately from the perforated shelf into CuSO4 solution. Thus the concentration of CuSO4 is maintained. As the concentration of the copper sulphate solution remains constant, when Daniel cell is in use, therefore, its emf remains constant.
Lechlanche cell: A Lechlanche cell consists of a vessel of glass containing strong solution of ammonium chloride which acts as electrolyte. An amalgamated zinc rod dipping in ammonium chloride acts as negative electrode or cathode. A porous pot is placed inside the glass vessel. The carbon rod placed inside the porous pot acts as positive electrode or anode. The space in the porous pot is filled with manganese dioxide and charcoal powder (Fig. 1.21). The charcoal powder makes the manganese dioxide electrically conducting and manganese dioxide acts as depolarizer. The inner side of glass vessel near the open end is coated with black paint which works as reflector for the ammonium chloride crystal as they have the tendency to creap along the glass wall. This helps in maintaining the proper concentration of ammonium chloride solution. The electrons released are collected by zinc rod, making it at negative potential with respect to electrolyte. The ammonia gas so produced escapes. The hydrogen ions diffuse through the porous pot and interact with manganese dioxide.
The positive charge is transferred to the carbon rod which attains the positive potential with respect to electrolyte. The depolarizer (MnO2) in Leclanche cell is in solid form and is slow in action. Therefore, when the current is drawn from the Leclanche cell, the hydrogen is liberated quickly than MnO2 can use it up. So, after some time, a partial polarization sets due to accumulation of hydrogen on anode and thereby, the current falls off. When the circuit is switched off, the hydrogen gas escapes. The cell regains its original emf and is again ready for use.
The emf of Lechlanche cell is 1.45 V and its internal resistance can vary from 0.1 Ohm to 10 Ohm.
Dry cell: A dry cell is a portable form of Lechlanche cell. It consists of zinc vessel which acts as a negative electrode or cathode. The vessel contains a moist paste of sawdust saturated with a solution of ammonium chloride and zinc chloride. The ammonium chloride acts as an electrolyte and the purpose of zinc chloride is to maintain the moistness of the paste being highly hygroscopic. The carbon rod covered with the brass cap is placed in the middle of the vessel. It acts as positive electrode or anode. It is surrounded by a closely packed mixture of charcoal and manganese dioxide(MnO2) in a muslin bag. Here MnO2 acts as depolarizer. The zinc vessel is sealed at the top with pitch or shellac. A small hole is provided in it to allow the gases formed by the chemical action to escape (Fig. 1.22).
The emf of dry cell is 1.5V. If this cell is used continuously, the polarization defect may develop in this cell but it regains its emf if allowed to rest for a while.
The Secondary Cell
A secondary cell is that cell in which the electrical energy is first stored up as a chemical energy and when the outside circuit is closed to draw the current from the cell, the chemical energy is reconverted into electrical energy. The chemical reactions are reversible in this cell.
The secondary cells are also called storage cells or accumulators because they act in such a way as if they were reservoir of electricity, i.e. the current can be drawn from them whenever required and when they are discharged, they can be recharged. The commonly used secondary cells are Lead-Acid accumulator and Edison cell.
Lead-Acid accumulator: It consists of a glass or hard rubber vessel containing dilute sulphuric acid (20% conc.), which act as electrolyte. There are two sets of perforated lead plates arranged alternately parallel to each other inside the vessel (Fig. 1.23).
These plates are held apart by strips of wood or celluloid. Alternate plates are soldered together to one lead rod forming one electrode while remaining once soldered to another common lead rod forming another electrode. The holes or perforations in the lead plates are filled with red lead or lead oxide (PbO).
Charging: Charging means storing of electrical energy. To charge this accumulator a source of steady current or battery charger is connected across the two terminals of two electrodes. The electrode which is connected to positive terminal of external source serves as anode and the other electrode serves as cathode. The dissociation of H2SO4 gives the H+ and SO42−. When current is passed through the cell by the help of external source, hydrogen ions move to the negative electrode (called cathode) and the sulphate ions go to positive electrode (called anode).
During charging electron moves from the anode to cathode, thus raising the potential difference between the electrodes. In charging process, water is consumed and sulphuric acid is formed. When the specific gravity of sulphuric acid solution becomes 1.25, the cell is fully charged. The emf of the cell at this stage is 2.2 volts.
Discharging: If the cell is connected to the external circuit, the current is drawn from the cell. The sulphuric acid dissociates into hydrogen ions and sulphate ions. After giving their charges, they react with the electrodes and reduce the active material of each plate to lead sulphate.
In discharging process, the electrons moves from the cathode to anode, thus lowering the potential difference between electrodes. Hence, the emf of cell falls. In this process, sulphuric acid is consumed and water is formed. Therefore the specific gravity of sulphuric acid also falls. If the specific gravity of sulphuric acid falls below 1.18, the cell requires recharging.
Alkali accumulator (Ni-Fe) or Edison cell: It is also known as alkaline secondary cell or Edison cell. It consists of a steel vessel containing 20% solution of KOH in distilled water (as electrolyte) and 1% Lithium hydroxide to make it conducting. Here anode is a perforated steel plate in the form of a grid. Its holes are packed with nickel hydrochloride and trace of nickel to make it conducting.
The cathode is also made of a steel grid. Its holes are packed with a iron hydrochloride and trace of mercury oxide for lowering its internal resistance (Fig. 1.24).
Working: Potassium hydroxide solution breaks up into positive potassium ions and negative hydroxyl ions due to ionization.
Charging: On passing the current from an external source, the anode attracts negative hydroxyl ions and cathode attracts positive potassium ions. These ions on reaching the respective electrodes lose their charge and react with them. Thus, when accumulator is charged Ni(OH)4 is formed on the anode and a spongy Fe on the cathode. In this process, electrons moves from anode to cathode, raising the potential difference between the two electrodes of cell. When this potential difference becomes 1.36 V the cell is fully charged.
Discharging: When the two electrodes of the cell are connected together through a resistor, there is discharging of the cell, i.e. the cell is giving the current. Now the anode attracts the potassium ions and cathode attracts hydroxyl ions. These ions on reaching the respective electrodes give their charges and react with them. The electrons moves from cathode to anode, thus lowering the potential difference between two electrodes, due to which emf of the cell falls. When the emf becomes less than 1.1 V, then the cell requires recharging.
The emf of Ni-Fe cell is 1.36 V. Its internal resistance is low but is higher than net storage cell.
- It can withstand rough handling.
- It is lighter, stronger and more durable than the lead accumulator.
- It is not damaged or over recharged.
- It is not spoiled even if left uncharged for a long time.
- Its initial cost is high.
- It absorbs carbon dioxide when exposed to atmosphere and thus its capacity is considerably reduced.
MAGNETIC EFFECTS OF ELECTRIC CURRENT
Oersted (1820) showed that the electric current through the wire deflects the magnetic needle below the wire. The direction of deflection of the magnetic needle is reversed if the deflection of current in the wire is reversed.
An electric current is equivalent to the charges (or electrons) in motion. Such charges produce magnetic interaction. The magnetic field produce by the conductor carrying current thus interacts with the magnetic needle and deflects it (Fig. 1.25).
As a rule, if we imagine a man swimming along the wire in the direction of current with his face always turned towards the needle, so that the current enters at his feet and leaves at his head, then the N-pole of the magnetic needle will be deflected towards his left hand. This rule can be recollected with the help of the word SNOW. It means, current from South to North, in a wire over the magnetic needle, the north pole of the needle is deflected towards West.
A magnetic field is the space around a magnet or a space around a conductor carrying current in which magnetic influence can be experienced. In the later case, the magnetic field disappears as soon as the current is switched off. It suggests that motion of electrons in the wire produces a magnetic field. In general, a moving charge is a source of magnetic field.
Due to the interaction between the magnetic field produced due to a moving charge, i.e. current and the magnetic field applied, the charge q then experiences a force, which depends upon the following factors (Fig. 1.26):
- The magnitude of the force F experienced is directly proportional to the magnitude of the charge, i.e. F × q.
- The magnitude of the force F is directly proportional to the component of velocity acting perpendicular to the direction of magnetic field, i.e. F α ν sin θ.
Thus, combing the above factors we get
Where, k is the constant of proportionality and its value is found to be 1.
It is the equation of a magnetic Lorentz force experienced by a charged particle moving in the magnetic field.
If ν = 1, q = 1 and sin θ = 1
Or θ = 90°, then F = 1 × 1 × B × 1 = B
Thus, the magnetic field induction at any point in the field is equal to the force acting on a unit charge moving with a unit velocity perpendicular to the direction of magnetic field at that point.
In cases where,
- θ = 0° or 180º, then sin θ = 0F = q ν sin θ B = 0Thus, a charged particle moving parallel to the direction of magnetic field, does not experience any force.
- If ν = 0 thenF = q ν sin θ B = 0It means that if a charged particle is at rest in a magnetic field, it experiences no force.
- If θ = 90°, then sin θ = 1F = q ν (1) B = q ν B
The direction of this force is determined by Fleming's Left Hand Rule.
Fleming's Left Hand Rule states that: If we stretch the first finger, the central finger and the thumb of left hand mutually perpendicular to each other such that the first finger points to the direction of magnetic field, the central finger points to the direction of electric current (motion of the positive charge) then the thumb represents the direction of force experienced by the charge particle.
Unit of B in S I units is Tesla (T)
B = F/q ν sin θ
If q = 1 C, ν = 1 m/s, θ = 90°
Or sin θ = 1 and F = 1 N
Then, B = 1/1 × 1 × 1 = 1 T
Thus, the magnetic field induction at a point is said to be one Tesla, if a charge of one coulomb while moving at right angle to a magnetic field, with the velocity of one m/s experiences a force of one N, at that point.
Biot–Savart's Law is an experimental law predicted by Biot and Savart in the year 1820. This law deals with the magnetic field induction at a point due to a small current element (a part of any conductor carrying current).
Let AB is a small element of length dl of the conductor XY which is carrying I. Let r be the position vector of the point P from the current element dl (The current element dl is a vector which is tangent to the element and is in the direction of current flow in the conductor) and be the angle dl and r (Fig. 1.28).
According to Biot – Savart's law, the magnetic field induction dB (also called magnetic flux density) at a point P due to current element depends the factors as stated below:
- dB α I
- dB α dl
- dB α sin θ
- dB α 1/r 2On combining these factors, we get
where, K is the constant of proportionality.
Important features of Biot – Savart's Law:
- This law is applicable only to very small length conductor carrying current.
- This law cannot be easily verified experimentally as the conductor of very small length cannot be obtained practically.
- This law is analogous to Coulomb's Law in electrostatics.
- is perpendicular to bothand.
- If θ = 0°, i.e., the point P lies on the conductor itself, then dB = K I l sin θ/r2dB = 0 (sin θ = 0). Thus there is no magnetic field induction at any point on the conductor.
- If θ = 90° dB is maximum. Then, dB = K I l sin θ/r2
A magnetic field at the centre of the circular coil carrying current:
Consider a circular coil of radius r with centre O, lying with its plane in the plane of paper. Let I be the current flowing in the circular coil in a particular direction (Fig. 1.29). Suppose the circular coil is made up of a large number of current elements each of length dl.
According to Biot – Savart's Law, the magnetic field at the centre of the circular coil due to the current element dl is given by:
The magnetic lines of force due to circular coil carrying current are perpendicular to the plane of the wire loop and are circular near the wire and practically straight near the centre of the wire loop. If the radius of the current loop is very large, the magnetic field near the centre of the current loop is almost uniform (Fig. 1.30). The magnetic field at the centre of circular current loop is given by Right hand palm rule.
Right hand palm rule: According to this rule, if we hold the thumb of right hand mutually perpendicular to the grip of the fingers such that the curvature of the finger represents the direction of current in the wire loop, then the thumb of the right hand will point in a direction of magnetic field near the centre of the current loop.
Magnetic field due to a straight conductor carrying current:
Consider a long straight conductor XY lying in a plane of paper carrying current I in the direction X to Y (Fig. 1.31).
Let P be a point at a perpendicular distance from the straight conductor. Clearly, PC = a. Consider a small current element of length dl of the straight conductor at O. Let
be the position vector of P with respect to current element and θ be the angle between
and CO = l.
According to Biot-Savart's law, the magnetic field induction, i.e. magnetic flux density at a point P due to current element dl is given by
In rt. angled triangle POC, θ + ϕ = 90°
The direction of dB, according to right hand thumb rule, will be perpendicular to the plane of paper and directed inwards. As all the current elements of the conductor will also produce magnetic field in the same direction, therefore, the total magnetic field at point P due to current through the whole straight conductor XY can be obtained.
Direction of magnetic field: The magnetic lines of force due to straight conductor carrying current are in the form of concentric circles with the conductor as centre, lying in a plane perpendicular to the straight conductor. The direction of magnetic lines of force is anticlockwise, if the current flows from A to B in the straight conductor and is clockwise if the current flows from B to A in the straight conductor (Fig. 1.32).
The direction of magnetic lines of force can be given by right hand thumb rule or Maxwell's cork screw rule.
Right hand thumb rule: According to this rule, if we imagine the linear conductor to be held in the grip of the right hand so that the thumb points in the direction of current, then the curvature of the fingers around the conductor will represent the direction of magnetic lines of force (Fig. 1.33).
Maxwell's cork screw rule: According to this rule, if we imagine a right handed screw placed along the current carrying linear conductor, be rotated such that the screw moves in a direction of flow of current, then the direction of rotation of the thumb gives the direction of magnetic lines of force (Fig. 1.34).
Ampere's circuital law: Ampere's circuital law states that the line integral of magnetic field induction
around any closed path in vacuum is equal toµ0 times the total current threading the closed path, i.e.
This is independent of the size and shape of the closed curve enclosing a current.
Lorentz force: The force experienced by a charged particle moving in space where both electric and magnetic fields exist is called Lorentz force.
Force due to electric field: when a charged particle carrying charge +q is subjected to an electric field of strength E, it experiences a force given by
Whose direction is the same as that of
Force due to magnetic field: If the charged particle is moving in a magnetic field
, with a velocity
it experiences a force given by
The direction of this force is in the direction of
, i.e. perpendicular to the plane containing
and is directed as given by Right hand screw rule.
Due to both the electric and magnetic fields, the total force experienced by the charged particle will be given by
This is called Lorentz force.
Moving coil Galvanometer
Moving coil galvanometer is an instrument used for detection and measurement of small electric currents (Fig. 1.35).
Principle: Its working is based on the fact that when a current carrying coil is placed in a magnetic field, it experiences a torque. It means, the deflection produced is proportional to the current flowing through the galvanometer.
Current sensitivity of a galvanometer is defined as the deflection produced in the galvanometer, when a unit current flows through it.
Voltage sensitivity of a galvanometer is defined as the deflection produced in the galvanometer when a unit voltage is applied across the two terminals of the galvanometer.
Conditions for a Sensitive Galvanometer
A galvanometer is said to be very sensitive if it shows large deflection even when a small current is passed through it.
From the theory of galvanometer
For a given value of I, θ will be large if nBA/k is large. It is so if
- n is large
- B is large
- A is large
- k is small
- The value of n cannot be increased beyond a certain limit because it results in an increase of the resistance of the galvanometer and also makes the galvanometer bulky. This tends to decrease the sensitivity. Hence n cannot be increased beyond a certain limit.
- The value of B can be increased by using a strong horse shoe magnet.
- The value of A cannot be increased beyond a certain limit because in that case the coil will not be in a uniform magnetic field. Moreover, it will make the galvanometer bulky and unmanageable.
- The value of k can be decreased. The value of k depends upon the nature of the material used as suspension strip. The value of k is very small for quartz or phosphor bronze. That is why, in sensitive galvanometer, quartz or phosphor bronze is used as a suspension strip.
Shunt: Shunt is a low resistance connected in parallel with the galvanometer or ammeter. It protects the galvanometer or ammeter from the strong currents.
If the current flowing in a circuit is strong, a galvanometer or ammeter cannot be put directly in it because the instrument may be damaged. To overcome this difficulty, a low resistance (i.e. shunt) is connected in parallel with the instrument. Then a major portion of the current passes through this low resistance (i.e. shunt) and only a small portion passes through the instrument. Due to it the galvanometer or ammeter remains same (Fig. 1.36).
Uses of Shunt
- A shunt is used for converting a galvanometer into an ammeter.
- A shunt may be used for increasing the range of ammeter.
Ammeter: An ammeter is a low resistance galvanometer. It is used to measure the current in a circuit in amperes. A galvanometer can be converted into an ammeter by using a low resistance wire in parallel with the galvanometer (Fig. 1.37). The resistance of the wire (called the shunt wire) depends upon the range of the ammeter. As the shunt resistance is small, the combined resistance of the galvanometer and the shunt is very low and hence ammeter has a much lower resistance than galvanometer. An ideal ammeter has zero resistance.
Voltmeter: A voltmeter is a high resistance galvanometer. It is used to measure the potential difference between two points of a circuit in volt. A galvanometer can be converted into a voltmeter by using a high resistance in parallel in series with the galvanometer. The value of the resistance depends upon the range of the voltmeter. For voltmeter, a high resistance R is connected in series with the galvanometer, therefore, the resistance of voltmeter is very large as compared to that of galvanometer. The resistance of an ideal voltmeter is infinity (Fig. 1.38).
MAGNETS AND EARTH MAGNETISM
A Greek Philosopher, Thales of Melitus had observed as long back as 600 B C that a naturally occurring ore of iron attracted small pieces of iron towards it. This ore was found in the district of Magnesia in Asia Minor in Greece. Hence the ore was named magnetite. The phenomenon of attraction of small bits of iron, steel, cobalt, nickel, etc. towards the ore was called magnetism. The iron ore showing this effect was called a natural magnet.
The Chinese discovered that a piece of magnetite, when suspended freely, always points out roughly in the North-South direction. Thus a natural magnet has attractive and directive properties. A magnetic compass based on directive property of magnets was used by navigators to find their way in steering the ships.
That is why magnetite was called the ‘load stone’ in the sense of leading stone.
The natural magnets have often irregular shape and they are weak. It is found that a piece of iron or steel can acquire magnetic properties, on rubbing with a magnet. Such magnets made out of iron and steel are called artificial magnets. Artificial magnets can have desired shape and desired strength. A bar magnet, a horse shoe magnet, magnetic needle, compass needle, etc. all are artificial magnets.
Basic Properties of Magnets
Following are some basic properties of magnets:
- A magnet attracts magnetic substances like iron, steel, cobalt, nickel towards it. When a magnet is put in a heap of iron fillings, they cling to the magnet. The attraction appears to be maximum at the ends of the magnet (Fig. 1.39). These ends are called poles of the magnet.
- When a magnet is suspended freely with the help of a unspun thread, it comes to rest along the North-South direction. If it is turned from this direction and left, it again returns to this direction. The pole which points towards the geographic north is called North-pole and the pole which points towards geographic south is called South-pole (Fig. 1.40).It should be clearly understood that poles exist always in pairs; two poles of a magnet are always of equal strength. Further, poles N and S are situated a little inwards from the geometrical ends A and B of the magnet. The magnetic length (NS) of magnet is roughly 6/7 of its geometric length (AB). We represent NS by 2l (and not l), this is done for simplification of calculations.The straight line passing through North-and-South poles of a magnet, is called axial line of the magnet. The line passing through centre of a magnet in a direction perpendicular to the length of the magnet is called equatorial line of the magnet.The straight line joining north and south poles of a freely suspended magnet represents magnetic N-S direction. A vertical plane passing through N-S line of a freely suspended magnet is called magnetic meridian.
- Like poles repel each other and unlike poles attract each other.To show this, we suspend a bar magnet with the help of a thread. When we bring N pole of another magnet near the N pole of suspended magnet, we observe repulsion. Similarly, South-pole of one magnet repels South-pole of the other. However, when S pole of one is brought near N pole of suspended magnet, there is attraction (Fig. 1.41).
- The force of attraction or repulsion F between two magnetic poles of strengths m1 and m2 separated by a distance r is directly proportional to the product of pole strengths and inversely proportional to the square of the distance between their centers, i.e.where µ0 is absolute magnetic permeability of free space (air/vacuum).This is called Coulomb's law of magnetic force. However in c.g.s. system, the value of K =1.
- The magnetic poles always exist in pairs, i.e. magnetic monopoles do not exist. In an attempt to separate the magnetic poles, if we break a magnet, we find new poles formed at the broken ends. If the two pieces are broken again, we find the broken ends contain new poles. Thus each piece, howsoever small, is a complete magnet in itself. Even if a magnet is broken into molecules, each molecule shall be a complete magnet. Note that pole strength (m) of each piece broken lengthwise, remains unchanged, although dipole moment M = m × 2l goes on decreasing, with decreasing length.
Atomic/Molecular Theory of Magnetism
The molecular theory of magnetism was given by Weber and modified later by Ewing. According to this theory:
- Every molecule of a magnetic substance (whether magnetized or not) is a complete in itself, having a north pole and a south pole of equal strength.
- In an unmagnetised substance, the molecular magnets are randomly oriented such that they form closed chains (Fig. 1.42). The North-pole of one molecular magnet cancels the effect of South-pole of the other so that the resultant magnetism of the unmagnetised specimen is zero.
- On magnetising the substance, the molecular magnets are realigned so that North-poles of all molecular magnets point in one direction and South-poles of all molecular magnets point in opposite direction (Fig. 1.43).The extent of magnetization of the specimen is the extent of realignment of the molecular magnets.
- When all the molecular magnets are fully aligned, the substance is said to be saturated with magnetism.
- At all stages, the strengths of the two poles developed will always be equal.
- On heating the magnetised specimen, molecular magnets acquire some kinetic energy. Some of the molecules may get back to the closed chain arrangement. That is why magnetism of the specimen would reduce on heating.
Magnetic lines of force: The concept of magnetic lines of force or simply the field lines was developed to visualize the effect of the magnetic field. The magnetic field lines represent the magnetic field in the same way as the electric field lines represent an electric field.
The magnetic lines of force do not exist in reality. They are only hypothetical lines, which enable us to understand certain phenomena in magnetism. To draw these lines, we have to take a test object which is a magnetic dipole such as a small compass needle.
If we imagine a number of small compass needles around a magnet, each compass needle experiences a torque due to the field of the magnet. The torque acting on a compass needle aligns it in the direction of the magnetic field. The path along which the compass needles are aligned is known as magnetic lines of force. It should be clearly understood that tangent to a field line at any point P gives the direction of magnetic field B at that point (Fig. 1.44).
Properties of magnetic lines: Following are some of the important properties of the magnetic lines of force:
- Magnetic lines of force are closed continuous curves; we may imagine them to be extending through the body of the magnet.
- Outside the body of the magnet, the direction of magnetic lines of force, is from North-pole to South-pole (Fig. 1.45).
- The tangent to magnetic lines of force at any point gives the direction of magnetic field at that point.
- No two magnetic lines of force can intersect each other (Fig. 1.46).
- Magnetic lines of force contract longitudinally and they dilate laterally.
- Crowding of magnetic lines of force represents stronger magnetic field and vice-versa (Fig. 1.47).
It should be clearly understood that there is one fundamental difference between electricity and magnetism. Where as in electricity, an isolated charge can exist, in magnetism, an isolated pole does not exist. The simplest magnetic structure that can exist is only a magnetic dipole, characterized by magnetic dipole moment
. Thus for mapping magnetic field, the simplest test object is a dipole. That is why in the definition of
above, we have used the word ‘hypothetical’ isolated north pole. However, this definition of
(corresponding to definition of
) enables us to simplify some calculations.
Thus magnetic dipole is characterized by a vector
in place of a scalar charge q in electricity. We shall show that in an external magnetic field, the dipole experiences a torque (unlike the force experienced by charge q in electric field). The effect of torque is to align the dipole along the external magnetic field. The directive property of a magnet is attributed to the torque acting on the magnetic dipole due to earth's magnetic field.
Each electric line of force starts from a positive charge and ends at a negative charge. It should be clearly understood that the electric lines are discontinuous only in the sense that no such lines exist inside a charged body. However, from a positively charged body to a negatively charged body, there is no discontinuity in the electric lines of force. In magnetism, as there are no monopoles, therefore, the magnetic field lines will be along closed loops with no starting or ending. The magnetic lines of force would pass through body of the magnet. At very far off points, the field lines due to an electric dipole and a magnetic dipole will appear identical.
Remember that electric lines of force are discontinuous, whereas magnetic lines of force are closed continuous curves.
Magnetic dipole: A magnetic dipole consists of two unlike poles of equal strength and separated by a small distance. For example, a bar magnet, a compass needle, etc. are magnetic dipoles. An atom of a magnetic material behaves as a dipole due to electrons revolving around the nucleus. Magnetic dipole moment is defined as the product of pole strength and the distance between the two poles. This distance between the poles is called magnetic length and is represented by 2l. If m is the strength of each pole, then magnetic dipole moment (M) is
Magnetic dipole moment is a vector quantity directed from South-to-North-pole. The S.I. units of M are joule/tesla or ampere metre2 (Fig. 1.48).
The direction of magnetic moment (M) is from south to north. This corresponds to the electric dipole moment (p) of an electric dipole from negative charge to positive charge.
Gauss's theorem (or Gauss's law) in magnetism: According to Gauss's theorem, the surface integral of electrostatic field E over a closed surface S is equal to 1/εo times the total charge q inside the surface, where εo is absolute electrical permittivity of free space, i.e.
If an electric dipole were enclosed by the surface, equal and opposite charges in the dipole add up to zero. Therefore, surface integral of electric field of a dipole over a closed surface enclosing an electric dipole is zero, i.e.
Whereas, electric field can be produced by isolated charge, the magnetic field is produced only by a magnetic dipole. This is because isolated magnetic poles do not exist. Hence magnetic analogue equation is as follows:
i.e., surface integral of magnetic field over a surface (closed or open) is always zero, i.e. the net magnetic flux ψB through any surface S is always zero. This is called Gauss's law in magnetism. In terms of magnetic field lines, the law means that there are as many lines entering S, as are leaving it (Fig. 1.49).
Magnetic field of earth: Sir William Gilbert was the first to suggest in the year 1600, that earth itself is a huge magnet. His statement was based on the following evidence:
- A magnet suspended from a thread and free to rotate in a horizontal plane comes to rest along the north-south direction. On disturbing, the magnet returns quickly to its north-south direction again this is as if huge bar magnet lies along the diameter of the earth. The North pole of this fictitious magnet must be towards geographic south so as to attract South pole of the suspended magnet and vice-versa.
- When a soft iron piece is buried under the surface of earth in the north south direction, it is found to acquire the properties of a magnet after sometime.
- When we draw field lines of a magnet, we come across neutral points. At these points, magnetic field due to the magnet is neutralized or cancelled exactly by the magnetic field of earth. If earth had no magnetism of its own, we would never observe neutral points.
The branch of physics which deals with the study of magnetism of earth is called terrestrial magnetism or geomagnetism.
It has been established that earth's magnetic field is fairly uniform. The strength of this field is approximately 10−4 tesla or 1 gauss. The field is not confined only to earth's surface. It extends upto a height nearly 5 times the radius of the earth.
Cause of earth's magnetism: The exact cause of earth's magnetism is not yet known. However, some important postulates in this respect are as follows:
- The earth's magnetism may be due to molten charged metallic fluid in the core of earth. The radius of this core is about 3500 km with the rotation of earth, the fluid also rotates resulting in the development of currents in the core of earth. These currents magnetise the earth.
- According to Prof Brackett, earth's magnetism may be due to rotation of earth about its axis. This is because every substance is made of charged particles (protons and electrons). Therefore, a substance rotating about an axis is equivalent to circulating currents, which are responsible for its magnetisation.
- In the outer layers of earth's atmosphere, gases are in the ionised state, primarily on account of cosmic rays. As earth rotates, strong electric currents are set up due to movement of (charged) ions. These currents might be magnetising the earth.
Michael Faraday in UK and Joseph Henry in USA observed that an emf is produced across the ends of a conductor when the number of magnetic lines of force associated with the conductor changes. The emf lasts so long as this change continues. This phenomenon of generating an emf by changing the number of magnetic lines of force associated with the conductor is called Electromagnetic Induction (EMI). The emf so developed is called induced emf. If the conductor is in the form of a closed circuit, a current flows in the circuit. This is called induced current.
The phenomenon of EMI is the basis of power generators, dynamos, transformers, etc. and hence it is important.
Magnetic flux: The magnetic flux Φ through any surface held in a magnetic field is measured by the total number of magnetic lines of force crossing the surface. The unit of magnetic flux is weber (Wb). One weber is the amount of magnetic flux over an area of 1 m2 held uniform to a uniform magnetic field of one tesla. Also, magnetic flux is a scalar quantity.
Experiment 1. Figure 1.50 shows a circular insulated wire of one or more turns connected to a sensitive galvanometer G. NS is a bar magnet which can be moved with respect to the coil. Faraday observed the following:
- Whenever there is a relative motion between the coil and the magnet, the galvanometer shows a sudden deflection. This deflection indicates that current is induced in the coil.
- The deflection is temporary. It lasts so long as relative motion between the coil and the magnet continues.
- The direction of deflection is reversed when same pole of magnet is moved in the opposite direction or opposite pole of magnet is moved in the same direction.
The motion of the magnet implies that the number of magnetic lines of force threading the coil is changing.
Experiment II. Figure 1.51 shows the experimental set up. Coil 1 is connected to a battery, a rheostat and a key K. Coil 2 is connected to a sensitive galvanometer G and is held close to coil 1.
When we press K, galvanometer G in coil 2 shows a sudden temporary deflection. This indicates that current is induced in coil 2. This is because current in coil 1 increases from zero to a certain steady value increasing the magnetic field of coil 1 and hence the number of magnetic lines of force entering coil 2. Their direction is shown in the Figure 1.51
On releasing K, galvanometer shows a sudden temporary deflection in the opposite direction. This is because on releasing K, current in coil 1 decreases from maximum to zero value, decreasing thereby the magnetic field of coil 1 and hence the number of magnetic lines of force entering coil 2.
Thus the results of the two experiments are identical.
Note: In both the experiments discussed above, we find that induced emf appears in a coil whenever the amount of magnetic flux linked with the coil changes. Hence we conclude that the cause of emf induced in a coil is change in magnetic flux linked with the coil. It should be clearly understood that mere presence of magnetic flux is not enough. The amount of magnetic flux linked with a coil must change in order to produce any induced emf in the coil.
Faraday's laws of electromagnetic induction: Following are the laws of electromagnetic induction as given by Faraday. Both the laws follow from Faraday's experiments discussed above.
First law: Whenever the amount of magnetic flux linked with a circuit changes, an emf is induced in the circuit. The induced emf lasts so long as the change in magnetic flux continues.
Second law: The magnitude of emf induced in a circuit is directly proportional to the rate of change of magnetic flux linked with a circuit.
First law: In Faraday's experiment, when magnet is moved towards the coil, number of magnetic lines of force linked with the coil increases, i.e. magnetic flux increases. When the magnet is moved away, the magnetic flux linked with the coil decreases. In both the cases, galvanometer shows deflection indicating that emf is induced in the coil.
When there is no relative motion between the magnet and the coil, magnetic flux linked with the coil remains constant. That is why galvanometer shows no deflection. Thus induced emf is produced when magnetic flux changes and induced emf continues so long as the change in magnetic flux continues. This is first law. The same results follow from Faraday's second experiment.
Second law: In Faraday's experiment, when magnet is moved faster, the magnetic flux linked with the coil changes at a faster. Therefore, galvanometer deflection is more. However, when the magnet is moved slowly, rate of change of magnetic flux is smaller. Therefore, galvanometer deflection is smaller. Hence magnitude of emf induced varies directly as the rate of change of magnetic flux linked with the coil. This is second law.
If is amount of magnetic flux linked with the coil at any time and is the magnetic flux linked with the coil after t sec., then
Rate of change of magnetic flux =
According to Faraday's second law, induced emf
where k is a constant of proportionality.
As k =1 (in all systems of units)
If d is small change in magnetic flux in a small time dt, then
Negative sign is taken because induced emf always opposes any change in magnetic flux associated with the circuit.
Lenz's law: This law gives us the direction of current in a circuit. According to this law, the induced current will appear in such a direction that it opposes the change (in magnetic flux) responsible for its production.
The law refers to induced currents, which means that it applies only to closed circuits. When we push the magnet towards the coil (or the loop towards the magnet), an induced current appears. In terms of Lenz's law, induced current will oppose the push when face of the loop towards the magnet becomes a north pole. Therefore, induced current will be anticlockwise, as we see along the magnet towards the loop.
If we pull the magnet away from the coil, the induced current wil oppose the pull by creating a south pole on the face of the loop towards the magnet. Therefore, induced current will be clockwise.
The agent that moves the magnet, either towards the coil or away from it, will always experience a resisting force and will thus be required to do the work.
Experimental verification of Lenz's law (Fig. 1.52): A coil of a few turns is connected to a cell C and a sensitive galvanometer G through a two way key 1, 2, 3.
Put in the plug of key between 1 and 2. Cell sends current through the coil. At the upper face of the coil, the current is anticlockwise, which would produce North Pole on this face. Suppose the galvanometer deflection is to the right. Obviously, if galvanometer deflection were to the left, current would be clockwise at the upper face, which would behave as south pole.
Remove the plug of key from 1 and 2. Insert the plug of key between 2 and 3. Now, move N-pole of a bar magnet towards the coil. The galvanometer shows a sudden deflection to the right indicating that current induced in the coil is anticlockwise and upper end of the coil behaves as north. It opposes the inward motion of N-pole of the bar magnet, which is the cause of induced current.
Similarly when N-pole of the bar magnet is moved away from the coil, the galvanometer shows a sudden deflection to the left, indicating that current induced in the coil is clockwise and upper end of the coil behaves as south. It opposes the outward motion of N-pole of the bar magnet, i.e. cause of induced emf is opposed.
Hence, induced current always opposes the change which produces it. This verifies Lenz's law.
Lenz's law and energy conservation: Lenz's law is in accordance with the law of conservation of energy.
For example, in the experimental verification of Lenz's law, when N-pole of magnet is moved towards the coil, the upper face of the coil acquires north polarity. Therefore, work has to be done against the force of repulsion, in bringing the magnet closer to the coil. Similarly, when N-pole of magnet is moved away, south polarity develops on the upper face of the coil. Therefore, work has to be done against the force of attraction, in taking the magnet away from the coil.
It is this mechanical work done in moving the magnet with respect to the coil that changes into electrical energy producing induced current. Thus energy is being transformed only.
When we do not move the magnet, work done is zero. Therefore, induced current is also not produced.
Hence Lenz's law obeys the principle of energy conservation.
Conversely, Lenz's law can be treated as a consequence of the principle of energy conservation.
Fleming's right hand rule: Fleming's right hand rule also gives the direction of induced emf/current, in a conductor moving in a magnetic field. According to this rule, if we stretch the first finger, central finger and thumb of our right hand in mutually perpendicular directions such that first finger points along the direction of the field and thumb is along the direction of motion of the conductor, then the central finger would give us the direction of induced current (Fig. 1.53).
The direction of induced current given by Lenz's law and Fleming's right hand rule is the same.
Eddy currents: Eddy currents are the currents induced in the body of the conductor when the amount of magnetic flux linked with the conductor changes. These were discovered by Foucault in the year 1895 and hence they are also called Foucault currents.
The magnitude of eddy current is
The direction of eddy currents is given by Lenz's law or Fleming's right hand rule.
Note: Eddy currents are basically the currents induced in the body of a conductor due to change in magnetic flux linked with the conductor.
Experiment 1: Hold a light metallic disc D atop the cross-section of an electromagnet connected to a source of a.c. Figure 1.54. When a.c. is switched on, the disc is thrown up into the air.
This is due to eddy currents developed in the disc. As current through the solenoid increases, the magnetic flux along the axis of the solenoid increases. Therefore, magnetic flux linked with the disc increases. Induced currents or eddy currents develop in the disc and magnetise it. If upper end of solenoid initially acquires north polarity, the lower face of disc also acquires north polarity in accordance with the Lenz's law. The force of repulsion between the two throws the disc up in the air.
Experiment 2: Suspend a flat metallic plate between pole pieces N and S of an electromagnet (Fig. 1.55).
When the magnetic field is off, the metallic plate disturbed once from its equilibrium position and left, oscillates freely for a longer time. But when the electromagnet is switched on, the vibrations of the plate are damped. This is because of eddy currents developed in the vibrating plate.
In the normal position of rest of the plate, magnetic flux linked with the plate is maximum. When it is displaced towards any one extreme position, area of plate in the field decreases. Therefore, magnetic flux through the plate decreases. Eddy currents develop in the plate which, according to Lenz's law, opposes the motion of the plate towards extreme position. Similarly, when plate returns from extreme position to mean position, area of plate in the field increases, magnetic flux linked with the plate increases. Eddy currents are developed which oppose the motion of the plate towards the mean position.
In either case, vibrations of the plate are damped.
Figure 1.56 shows the same metallic plate with slots cut in it. When such a plate is made to oscillate in the magnetic field, the damping effect is there, but it is much smaller compared to the case when no slots were cut.
This means eddy currents are reduced. This is because closed loop of a given area now has a much longer path. As longer path means more resistance, eddy currents will reduce. We can only minimize eddy currents but cannot reduce such currents to zero.
Applications of Eddy Currents
Eddy currents are useful in many ways:
Some of the applications of eddy currents are:
- Electromagnetic damping: This is used in designing dead beat galvanometers.When a steady current is passed through the coil of a galvanometer, it is deflected. Normally, the coil oscillates about its equilibrium position for some time before coming to rest.To avoid delay due to these oscillations, the coil is wound over a metallic frame. As the coil is deflected, eddy currents set up in the metallic frame oppose its motion.Therefore, the coil attains its equilibrium position almost instantly. Thus the motion of coil is damped. This is called electromagnetic damping.
- Induction furnace: It makes use of the heating effect of eddy currents. The substance to be heated/melted is placed in a high frequency magnetic field. The large eddy currents developed in the substance produce so much heat that it melts. Such an arrangement is called induction furnace. It is used for extracting a metal from its ore and also in the preparation of certain alloys.
- Electromagnetic brakes: They are used in controlling the speed of electric trains. A strong magnetic field is applied to a metallic drum rotating with the axle connecting the wheels. Large eddy currents set up in the rotating drum oppose the motion of the drum and tend to stop the train.
- Induction motor: A induction motor or a.c. motor is another important application of eddy currents. A rotating magnetic field produces strong eddy currents in a rotor, which starts rotating in the direction of the rotating magnetic field.
- Speedometers: In speedometers of automobiles and energy meters.
- Eddy currents: They are also used in diathermy, i.e. in deep heat treatment of the human body.Some of the undesirable effects of eddy currents are:
- They oppose the relative motion.
- They involve loss of energy in the form of heat.
- The excessive heating may break the insulation in the appliances and reduce their life.
To minimize the eddy currents, the metal core to be used in an appliance like dynamo, transformer, choke coil, etc. is taken in the form of thin sheets. Each sheet is electrically insulated from the other by insulating varnish. Such a core is called a laminated core. The planes of these sheets are arranged parallel to the magnetic flux.
Large resistance between the thin sheets confines the eddy currents to the individual sheets. Hence the eddy currents are reduced to a large extent.
Self induction is the property of a coil by virtue of which, the coil opposes any change in the strength of current flowing through it by inducing an emf in itself. For this reason, self induction is also called the inertia of electricity.
Suppose there is a coil connected to a cell through a tap key K (Fig. 1.57).
On pressing K, current through the coil increases from zero to a certain maximum value. It takes some time. During this time (of make M), current through the coil is increasing, magnetic flux linked with the coil is increasing. Therefore, a current is induced in the coil. According to Lenz's law, the induced current at make will oppose the growth of current in the coil, by flowing in a direction opposite to the direction of the cell current.
On releasing K, current through the coil decreases from maximum to zero value. It takes some time. During the time (of break B), current through the coil is decreasing. Therefore, magnetic flux linked with the coil is decreasing. A current is induced in the coil. According to Lenz's law, the induced current at break will oppose the decay of current in the coil, by flowing in the direction of the cell current, so as to prolong it.
Coefficient of self induction (L) of a coil is equal to the emf induced in the coil when rate of change of current through the coil is unity.
The SI unit of L is henry. Self inductance of a coil is said to be one henry, when a current change at the rate of one ampere/sec through the coil induces an emf of one volt in the coil.
Mutual induction is the property of two coils by virtue of which each opposes any change in the strength of current flowing through the other by developing an induced emf.
Suppose there are two coils P and S which are held closely. P is connected to a cell through a key K. S is connected to a sensitive galvanometer G (Fig. 1.58).
On pressing or releasing K, galvanometer shows a temporary deflection. This is due to mutual induction as detailed below:
On pressing K, current in P increases from zero to maximum value. It takes some time. During this time (of make M), current in P is increasing. Therefore, magnetic flux linked with P is increasing. As S is close by, magnetic flux associated with S also increases. An emf is induced in S, according to Lenz's law, the induced current in S would oppose increase in current in P by flowing in a direction opposite to the cell current in P.
On releasing K, current in P decreases from maximum to zero value. It takes some time. During this time (of break B), current in P is decreasing. Therefore, magnetic flux linked with P is decreasing. As S is close by, magnetic flux associated with S also decreases. An emf is induced in S. According to Lenz's law, the induced current in S during break flows in the direction of the cell current in P so as to oppose the decrease in current in P, i.e. it prolongs the decay of current.
Coefficient of mutual inductance of two coils is numerically equal to the amount of magnetic flux linked with one coil when unit current flows through the neighboring coil.
Coefficient of mutual induction (M) of two coils is equal to the emf induced in one coil when rate of change of current through the other coil is unity.
The SI unit of M is henry. Coefficient of mutual inductance of two coils is said to be one henry, when a current change at the rate of one ampere/sec in one coil induces an emf of one volt in the other coil.
The mutual inductance of two coils depends on:
- geometry of two coils, i.e. size of coils, their shape, number of turns, nature of material on which two coils are wound.
- distance between two coils.
- relative placement of two coils (i.e. orientation of the coils).
Note: In self induction, change in strength of current in a coil is opposed by the coil itself by inducing an emf in itself. However, in mutual induction, one coil opposes any change in the strength of current in the neighboring coil. It should be clearly understood that mutual induction is over and the self induction of each coil, due to change in magnetic flux in both.
An a.c. generator/dynamo is a machine which produces alternating current energy from mechanical energy. It is one of the most important applications of the phenomenon of electromagnetic induction. The generator was designed by Yugoslav scientist, Nikola Tesla. It is an alternator converting one form of energy into another.
Principle: An a.c. generator/dynamo is based on the phenomenon of electromagnetic induction, i.e. whenever amount of magnetic flux linked with the coil changes, an emf is induced in the coil. It lasts so long as the magnetic flux through the coil continues. The direction of current induced is given by Fleming's right hand rule.
Multiphase AC Generator
- Two phase a.c. generator: In this generator, there are two armature coils held at 90º to each other. Each coil has its own pair of slip rings and brushes. When this pair of coils is rotated in magnetic field, emf is induced in each coil. When emf induced in one coil is maximum, it is minimum in the other coil and vice versa. Thus the emf's induced in the two coils differ in phase by 90º. This is called two phase a.c (Fig. 1.59).
- Three phase a.c. generator: In this generator, there are three armature coils equally inclined to one another at 60º. Each coil has its own pair of slip rings and brushes. When this arrangement of coils is rotated in magnetic field, emf is induced in each coil. Thus we obtain three alternating emf's differing in phase from one another by 60º. This is called three phase a.c (Fig. 1.60).
- In general: When there are a number of separate coils, each having its own pair of slip rings and brushes, the generator is called polyphase generator. The current produced is called polyphase alternating current.
In actual practice one end of each coil is brought to a common point through shaft of the generator. The line wire from this line is called Neutral line. Separate slip rings are provided for other ends of different coils. The line wires from these rings (through these brushes) are called phase lines.
It should be clearly understood that the principle of generator discussed here applies to all the practical devices for the purpose ranging from portable generator to giant hydroelectric and thermal power generators and even nuclear power generators.
In a hydroelectric power station, water is stored to a great height in a dam, from where it falls on to giant turbines (popularly known as water wheels). These turbines are connected to loops of wires in a.c. generator. Thus kinetic energy of falling water is converted into rotational energy of turbines, which leads to the production of electric energy by the generator.
In a thermal power station, superheated steam is produced by boiling water using coal or oil as fuel. The superheated steam pushes past the turbines and rotates them. This leads to the production of electrical energy by the generator.
A d.c. generator/dynamo is device which is used for producing direct current energy from mechanical energy.
The principle of d.c. generator is the same as that of a.c. generator.
Motor starter: A starter is a device which is used for starting a d.c. motor safely. Its function is to introduce a suitable resistance in the circuit at the time of starting of the motor. This resistance decreases gradually and reduces to zero when the motor runs at full speed.
Infact, resistance of armature of d.c. motor is kept low (to reduce the copper losses) and when armature is stationary, there is no back emf. Therefore, when operating voltage is applied, the current through armature coil may become so large (I = V/R) that the motor may burn. A starter is needed to avoid this.
A transformer is an electric device which is used for changing the a.c. voltages.
A transformer which increases the a.c. voltages is called a step up transformer. A transformer which decreases the a.c. voltages is called a step down transformer.
Principle: A transformer is based on the principle of mutual induction, i.e. whenever the amount of magnetic flux linked with the coil changes, an emf is induced in the neighbouring coil.
Construction: The transformer consists of two coils of insulated wire wound onto a laminated soft-iron frame. The two coils may be wound on top of one another or on opposite sides of the frame.
Working: An alternating current is passed through the primary coil and this sets up a varying magnetic field which cuts the secondary coil. By electromagnetic induction, an EMF is induced into the secondary circuit.
Step up transformer: In this, the number of turns in the primary coil is less than that in the secondary coil (Fig. 1.61).
The primary coil is made up of thick insulated copper wire, with less number of turns, while the secondary coil is made up of thin insulated copper wire, with large number of turns. It converts a low voltage at high current into high voltage at low current.
Step down transformer: In this, the number of turns in the primary coil is more than that in the secondary coil (Fig. 1.62).
The primary coil is made up of thin insulated copper wire, with larger number of turns while the secondary coil is made up of thick copper wire with less number of turns. It converts a high voltage at low current into low voltage at high current.
Types of Transformers
- Static transformer: It has been described above.
- Variable transformer: This consists of a primary and a secondary coil and is made so that one of them can be altered in length. The primary coil has a number of tappings and a movable contact can be placed on any one of these by turning a knobs. There is a step up voltage in the secondary coil. In this way a very crude control of voltage is obtained.
- The autotransformer: It consists of a single coil of wire with four contact points coming from it. It works on the principles of electromagnetic induction but it has the disadvantage that it allows only a small step up and does not render the current earth free.
Energy Losses in a Transformer
Following are the major sources of energy loss in transformer:
- Copper loss: It is the energy loss in the form of heat in the copper coils of a transformer. This is due to Joule heating of conducting wires.
- Iron loss: It is the energy loss in the form of heat in the iron core of the transformer. This is due to formation of eddy currents in iron core. It is minimized by taking laminated cores.
- Hysteresis loss: This is the loss of energy due to repeated magnetization and demagnetization of the iron core when a.c. is fed to it.
- Magnetostriction: i.e. humming noise of a transformer.
Therefore, output power in a transformer is roughly 90% of the input power.
Uses of Transformer
A transformer is used in almost all a.c. operations e.g.
- In voltage regulators of TV, refrigerator, computer, air conditioner, etc.
- In the induction furnaces
- A step down transformer is used for welding purposes.
- In the transmission of a.c. over long distances.
History of Electromagnetic Waves
Faraday from his experimental study of electromagnetic induction concluded that a magnetic field changing with time at a point produces an electric field at that point. Maxwell in 1865 from his theoretical study pointed out “there is a great symmetry in nature”, i.e. an electric field changing with time at a point produces a magnetic field there. It means a change in either field (electric or magnetic) with time produces the other field. This idea led Maxwell to conclude that the variation in electric and magnetic field vectors perpendicular to each other leads to the production of electromagnetic disturbances in space. These disturbances have the properties of wave and can travel in space even without any material medium. These waves are called electromagnetic waves.
According to Maxwell, the electromagnetic waves are those waves in which there are sinusoidal variation of electric and magnetic field vectors at right angles to each other as well as at right angles to the direction of wave propagation. Both these fields vary with time and space and have the same frequency.
In Figure 1.63 the electric field vector (E) and magnetic field (B) are vibrating along Y and Z directions and propagation of electromagnetic wave is shown in X-direction.
Maxwell also found that the electromagnetic wave should travel in free space (or vacuum) also.
Maxwell also concluded that electromagnetic wave is transverse in nature and light is electromagnetic wave.
Examples of electromagnetic waves are radiowaves, microwaves, infrared rays, light waves, ultraviolet rays, X-rays and γ-rays.
In 1888, Hertz confirmed experimentally the existence of electromagnetic waves. With the help of his experiment, Hertz produced electromagnetic waves of wavelength about 6 m.
In 1894, an Indian Physicist Jagdish Chander Bose was able to produce electromagnetic waves of wavelength ∼ 5 to 25 mm but his experiment was confined to laboratory only.
In 1899, Guylielmo Marconi was the first to transmit electromagnetic waves up to a few kilometers and established a wireless communication across the English Channel, a distance of about 50 km.
Production of Electromagnetic Waves
We know that an electric charge at rest has electric field in the region around it, but no magnetic field. A moving charge produces both the electric and magnetic fields. If a charge is moving with a constant velocity (i.e. if current is not changing with time), the electric and magnetic fields will not change with time, hence no electromagnetic wave can be produced. But if the charge is moving with a non-zero acceleration (i.e. charge is accelerated) both the magnetic field and electric fields will change with space and time, it then produces electromagnetic wave. This shows that an accelerated charge emits electromagnetic waves.
In an atom, an electron while orbiting around the nucleus in a stable orbit, although accelerating, does not emit electromagnetic waves. Electromagnetic waves are emitted only when it falls from higher energy orbit to lower energy orbit.
Electromagnetic waves (i.e. X-rays) are also produced when fast moving electrons are suddenly stopped by the metal target of high atomic number.
Important Facts About the Electromagnetic Waves
- The electromagnetic waves are produced by accelerated or oscillated charge.
- These waves do not require any material medium for propagation.
- The sinusoidal variation in both electric and magnetic field vectors (E and B) occurs simultaneously. As a result, they attain the maxima and minima at the same place and at the same time.
- The directions of variation of electric and magnetic field vectors are perpendicular to each other as well as perpendicular to the direction of propagation of waves. Therefore, electromagnetic waves are transverse in nature like light waves.
- The velocity of electromagnetic waves depends entirely on the electric and magnetic properties of the medium in which these waves travel and is independent of the amplitude of the field vectors.
- The velocity of electromagnetic waves in dielectric is less than 3 × 108 m/s.
- The energy in electromagnetic waves is equally divided between electric and magnetic vectors.
- The electric vector is responsible for the optical effects of an electromagnetic wave and is called the light vector.
- The electromagnetic waves being uncharged are not deflected by electric and magnetic fields.
Maxwell in 1865 predicted electromagnetic waves from theoretical considerations and their existence was confirmed experimentally by Hertz in 1888.
Hertz experiment was based on the fact that an oscillating electric charge radiates electromagnetic waves and these waves carry energy which is being supplied at the cost of kinetic energy of the oscillating charge. The detailed study revealed that the electromagnetic radiation is significant only if the distance to which the charge oscillates is comparable to the wavelength of radiation.
After the experimental discovery of electromagnetic waves by Hertz, many other electromagnetic waves were discovered by different ways of excitation.
The orderly distribution of electromagnetic radiations according to their wavelength or frequency is called electromagnetic spectrum.
The electromagnetic spectrum has much wider range with wavelength variation of ∼10−14m to 6 × 106m.
The whole electromagnetic spectrum has been classified into different parts or subparts in order of increasing wavelength, according to their type of excitation. There is overlapping in certain parts of the spectrum, showing that the corresponding radiations can be produced by two methods. It maybe noted that the physical properties of electromagnetic waves are decided by their wavelengths and not by the method of their excitation.
The above table shows the various parts of the electromagnetic spectrum with wavelength range, frequency range and the names of the sources of the various electromagnetic radiations.
Wavelength range (m)
Frequency range (Hz)
6 × 10−14 to 1 × 10−11
5 × 1022 to 3 × 1019
1 × 10−11 to 3 × 10−8
3 × 1019 to 1 × 1016
Sudden declaration of high energy electrons
6 × 10−10 to 4 × 10−7
5 × 1017 to 8 × 1014
Excitation of atom, spark and arc lamp
4 × 10−7 to 8 × 10−7
8 × 1014 to 4 × 1014
Excitation of valence electrons
8 × 10−7 to 3 × 10−5
4 × 1014 to 1 × 1013
Excitation of atoms and molecules
10−5 to 10−1
3 × 1013 to 3 × 109
10−3 to 0.3
3 × 1011 to 1 × 109
Oscillating current in special vacuum tube
1 × 10−1 to 1
3 × 109 to 3 × 108
Very high radio frequency
1 to 10
3 × 108 to 3 × 107
10 to 104
3 × 107 to 3 × 104
5 × 106 to 6 × 106
60 to 50
Weak radiations from AC circuits
Uses of Electromagnetic Spectrum
The following are some of the uses of electromagnetic spectrum:
- Radio and microwave radiations are used in radio and TV communication system.
- Infra-red radiations are used
- In revealing the secret writings on the ancient walls.
- In green houses to keep the plants warm.
- In war fare, for looking through haze, fog or mist as these radiations can pass through them.
- In electrotherapy for the heating of soft tissues.
- Ultra-violet radiations are used in the detection of invisible writing, forged documents, finger prints in forensic laboratory and to preserve the food stuffs. Ultra-violet radiations are used in electrotherapy for the treatment of various skin conditions.
- X-rays can pass through soft tissues but not through bones. This property of X-rays is used in medical diagnosis, after X-ray films are made.
- Electromagnetic waves of suitable frequencies are used in medical science for the treatment of various diseases.
Shock: Shock is stage of unconsciousness which could be due to so many causes.
Electric shock: Electric shock is a painful stimulation of sensory nerves caused by:
- Sudden flow of current
- Cessation or pause of flow of current
- Variation of the current passing through the body
Causes of Electric Shock
- Poorly designed electromedical apparatus
- Improper insulation of equipment
- Improper insulation of wires
- Badly serviced medical equipment
- Mishandling of apparatus
- Improper guidance to the patient
- Lack of proper safety measures
Severity of Electric Shock
- In accordance with the Ohm's Law, resistance is inversely proportional to current. Hence, lower the resistance of the skin the greater the current which passes through the body. Therefore, if exposed part of the circuit is touched with wet hands, the shock is more likely to be severe than if the hands are dry.
- The greater the current passing through the body the more severe is the shock.
- The severity also depends upon the path taken by the current. A strong current through the head, neck or heart proves to be more fatal.
- The severity also depends upon the type of current which passes through the body. Shocks are generally more severe with alternating currents than with direct currents because the intensity of alternating currents is continuously changing and so it provides strong sensory stimulation.
Types of Electric Shock
According to the severity of the shock, it could be of following types:
- Minor electric shock
- Major or severe electric shock
Effects of Electric Shock
- Minor electric shock: In minor electric shock the victim gets frightened and distressed. In this type of shock there is no loss of consciousness.
- Major or severe electric shock: In major or severe electric shock there is a fall of blood pressure and patient may become unconscious. There could be cessation of respiration, followed by ventricular fibrillations and cardiac arrest. These could be diagnosed by seeing absence of pulse in the carotid artery and with fully dilated pupils.
Treatment of Electric Shock
- The current should be switched off immediately.
- The victim to be disconnected from the source of supply.
- If there is no switch in the circuit, the victim must be removed from contact with the conductor, but rescuer must take care not to receive a shock himself from touching the affected person, contact with whom should be made only through a thick layer of insulating material.
- Following a minor shock the patient is to be re-assured that everything is alright and allowed to rest.
- Water may be given to drink, but hot drinks should be avoided as they may cause vasodilatation.
- Tight clothing should be loosened and plenty of air allowed.
- If respiration has ceased, the airway must be cleared and artificial respiration is to be commenced immediately by the mouth to mouth or mouth to nose method
- Cardiopulmonary resuscitation may also be given.
- Oxygen therapy may also be administered if required.
- Patient must be shifted to the hospital after the primary care.
Precautions to avoid electric shock:
- All apparatus should be tested before use.
- Connections to be checked before application.
- Controls should be checked to ensure that they are at zero before switching on.
- Adequate warming up time should be allowed.
- The current intensity should be increased with care.
- Patients should never be allowed to touch electrical equipment.
- All apparatus should be serviced regularly by a competent person.
- Machine should be properly insulated.
- Mishandling of apparatus by unqualified person should be avoided.
- All safety measures should be taken before application to the patient.
Earth shock: When a shock is due to a connection between the live wire of the main and the earth it is called an earth shock.
Earth circuit: Electric power is transmitted by one live cable and one neutral cable which is connected to earth. The earth forms part of the conducting pathway and any connection between the live wire of the main and earth completes a circuit through which current passes. If some person forms part of this circuit he receives an earth shock. Thus an earth shock is liable to occur if any person makes contact with the live wire of the main while connected to earth.
Causes of Earth Shock
Earth shock may be caused by the following two reasons:
- Connection to the live wire.
- Connection to the earth.
Connection to the live wire:
- When wire is not properly insulated.
- When, the switch is put in the neutral wire, the neutral wire is disconnected and live wire is not disconnected.
- Live wire is touched to metal casing.
- Live wire is touched to any wet thing.
Connection to the earth
- If the floor is made up of stone.
- If the conductor is touching any conductor which is connected to the earth, such as gas pipe or water pipes.
- If the conductor is touched to any radiated metal casing or metal wire.
- Proper arrangement of the physiotherapy department.
- Proper flooring should be done with rexin.
- Insulation should be proper.
- While treatment patient should not touch any of the machine part.
- The metal casing of all apparatus must be connected to the earth.
- The floor should be kept dry.
- While using water containers, containing water, should be kept on an insulating material, e.g. a wooden table.
- Leaky bathtub should not be used.
- The bathtub should not have fixed taps or water pipes.
Simultaneous connection to the live wire and earth can occur in a variety of ways,
- A patient who is receiving treatment with a current that is not earth-free may rest her hand on a water pipe.
- A physiotherapist holding an electrode that is connected to the live wire may touch the earthed apparatus-casing.
- If someone standing on a damp stone floor touches the casing of apparatus which is not connected to earth and with which the live wire is in contact, he too will receive an earth shock.