## ELECTROMAGNETIC INDUCTION

 Electromagnetic induction Experiments of Faraday and Henry Magnetic flux Faraday’s law Statement and explanation Induced EMF Lenz’s law Statement explanation and its significance as conservation of energy Motional emf Eddy currents Inductance Mutual induction Self inductance Energy stored in the coil. Ac generator Working Derivation of instantaneous emf in an ac generator Hydro – electric generators Numericals Concept based problems

## Magnetic flux:

The magnetic flux through a surface of area A placed in a uniform magnetic field B is defined as,
ΦB = B.A = BA cos θ
where θ is the angle between B and A

Faraday’s laws of induction imply that the emf induced in a coil of N turns is directly related to the rate of change of flux through it,

Here ΦΒ is the flux linked with one turn of the coil. If the circuit is closed, a current I = ε/R is set up in it, where R is the resistance of the circuit.

## Lenz’s law:

Lenz’s law states that the polarity of the induced emf is such that it tends to produce a current which opposes the change in magnetic flux that produces it. The negative sign in the expression for Faraday’s law indicates this fact.

## Induced emf:

When a metal rod of length l is placed normal to a uniform magnetic field B and moved with a velocity v perpendicular to the field, the induced emf (called motional emf) across its ends is,
ε = Blv

## Inductance:

Inductance is the ratio of the flux-linkage to current. It is equal to NΦ/I.

## Mutual inductance:

A changing current in a coil (coil 2) can induce an emf in a nearby coil (coil 1).
This relation is given by,

The quantity M12 is called mutual inductance of coil 1 with respect to coil 2. One can similarly define M21. There exists a general equality,
M12 = M21

## Self-induced emf:

When a current in a coil changes, it induces a back emf in the same coil. The self-induced emf is given by,

L is the self-inductance of the coil. It is a measure of the inertia of the coil against the change of current through it.
The self-inductance of a long solenoid, the core of which consists of a magnetic material of relative permeability µr , is given by
L = µr µ0 n2 Al
where A is the area of cross-section of the solenoid, l its length n is the number of turns per unit length.