Electromagnetic Induction – Notes

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Electromagnetic Induction

When an electric current flows through a conductor, a magnetic field is immediately brought into existence in the space surrounding the conductor. It can be said that when electrons are in motion, they produce a magnetic field. The converse of this is also true i.e. when a magnetic field embracing a conductor moves relative to the conductor, it produces a flow of electrons in the conductor.

This phenomenon whereby an e.m.f. and hence current (i.e. flow of electrons) is induced in any conductor which is cut across or is cut by a magnetic flux is known as electromagnetic induction.

Faraday’s Laws of Electromagnetic Induction

Faraday’s Laws of Electromagnetic Induction :

First Law. It states :

Whenever the magnetic flux linked with a circuit changes, an e.m.f. is always induced in it.
or
Whenever a conductor cuts magnetic flux, an e.m.f. is induced in that conductor.

Second Law. It states :

The magnitude of the induced e.m.f. is equal to the rate of change of flux-linkages.

Explanation. Suppose a coil has N turns and flux through it changes from an initial value of Φ­₁ webers to the final value of Φ­₂ webers in time t seconds. Then, remembering that by flux-linkages mean the product of number of turns and the flux linked with the coil, we have Initial flux linkages = NΦ­₁, add Final flux linkages = NΦ­₂

∴ induced e.m.f. e = NΦ­₂–NΦ­₁/t Wb/s or volt 

Putting the above expression in its differential form, we get

e = d(NΦ)/dt = N(dΦ/dt) volt

Usually, a minus sign is given to the right-hand side expression to signify the fact that the induced e.m.f. sets up current in such a direction that magnetic effect produced by it opposes the very cause producing it.

e = – N(dΦ/dt) volt

Direction of induced e.m.f. and currents

There exists a definite relation between the direction of the induced current, the direction of the flux and the direction of motion of the conductor. The direction of the induced current may be found easily by applying either Fleming’s Right-hand Rule or Flat-hand rule or Lenz’s Law. Fleming’s rule is used where induced e.m.f. is due to flux-cutting (i.e., dynamically induced e.m.f.) and Lenz’s when it is used to change by flux-linkages (i.e., statically induced e.m.f.).

Lenz’s Law

The direction of the induced current may also be found by this law which was formulated by
Lenz in 1835. This law states, in effect, that electromagnetically induced current always flows in such direction that the action of the magnetic field set up by it tends to oppose the very cause which produces it.

Induced e.m.f

Induced e.m.f. can be either (i) dynamically induced or (ii) statically induced. In the first case, usually the field is stationary and conductors cut across it (as in d.c. generators). But in the second case, usually the conductors or the coil remains stationary and flux linked with it is changed by simply increasing or decreasing the current producing this flux (as in
transformers).

Self-inductance

A coil of wire connected to a battery through a rheostat. It is found that whenever an effort is made to increase current (and hence flux) through it, it is always opposed by the instantaneous production of counter e.m.f. of self-induction. Energy required to overcome this opposition is supplied by the battery. As will be fully explained later on, this energy is stored in the additional flux produced.

If, now an effort is made to decrease the current (and hence the flux), then again it is delayed due to the production of self-induced e.m.f., this time in the opposite direction. This property of the coil due to which it opposes any increase or decrease or current of flux through it, is known as selfinductance.

Mutual Inductance

Mutual inductance may, therefore, be defined as the ability of one coil (or circuit) to produce an e.m.f. in a nearby coil by induction when the current in the first coil changes. This action being reciprocal, the second coil can also induce an e.m.f. in the first when current in the second coil changes. This ability of reciprocal induction is measured in terms of the coefficient of mutual induction M.

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