**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.