What is electromagnetic induction ? State its Faraday's laws. Find an expression for the e.m.f. induced due to change in the area of a coil lying in a uniform magnetic field.

Explanation

Induced emf due to change in area of a coil lyirig in a uniform magnetic fleld:
Suppose magnetic field is confined to the region OLMN acting in vertically downward direction. ABCD is a coil which is placed in the magnetic field.
Let `I=BC=` Length of the coil
`x=BA.=CD.=` Part of coil inside the magnetic field.
Then, Area of coil inaid the magnetic field at any time tis given by
`A=BC xx CD`
`A = lx`
Magnetic flux linked with coil at time `t=phi = BA = Blx`

Suppose that the coil is pulled out of the magnetic field with velocity v. As the coil is out, the area of the coil pulled inside the magnetic field and hence magnetic flux linked with the coil changes. The time rate of change of magnetic flux linked with the coil is given by
`(d phi)/(dt) =(d)/(dt) (B lx) =Bl (dx)/(dt)=Blu`
If e is induced emf produced, then
`e =-(d phi)/(dt)`
`e=-B l u`
which gives the expression for the motional emf