Faraday’s Law

The average induced emf in conducting coil of the N loop is equal to the negative of N time the rate of change of magnetic flux through the coil.

ε = -N (∆∅)/∆t

Explanation

The motional induced emf in a rod moving perpendicular to the magnetic field is given by

ε = -VBL → eq 1

Consider a conducting rod L moves

 

from position 1 to position 2 through the distance ∆x=x2-x1 in the time ∆t. The velocity of the rod is given by,

V = ∆x/∆t → eq 2

Putting this value in equ.1

ε= -VBL = – ∆x/∆t BL → eq 3

As the rod moves through the distance, the increase in the area of the loop is given by ∆A= ∆XL, T his increases the flux through the loop by ∆∅,

∆∅=∆AB=∆XLB → eq 4

Eq 3 becomes,

ε = – (∆∅)/∆t → eq 5

 

If three is a coil of N loop instead of a single loop, Then

ε= -N (∆∅)/∆t → eq 6

This shows induced emf will become N tims and vesting shows the direction of the induced emf is such that it opposes the change of flux.