Q.How will you induce an emf by changing the area enclosed by the coil ?

Sliding a conducting rod along two parallel rails in a magnetic field steadily changes the area enclosed by the circuit, and by Faraday's law this changing flux induces an emf -- the motional emf $\varepsilon=Bvl$.

1. Arrangement. Consider two straight, parallel conducting rails a distance $l$ apart, lying in a plane, placed in a region of uniform magnetic field $B$ perpendicular to that plane. A conducting rod $PQ$ of length $l$ rests across the rails and is free to slide, completing the circuit with the rails and any external resistor/load.

2. Change in flux. The magnetic flux linked with the circuit is $\Phi = B\cdot A$, where $A$ is the area enclosed between the rod and the closed end of the rails. If the rod is pulled with velocity $v$, the enclosed area increases (or decreases) at the rate

$\dfrac{dA}{dt} = l\,v$

so the flux changes at the rate

$\dfrac{d\Phi}{dt} = B\,l\,v$

3. Induced emf (Faraday's Law). By Faraday's law of electromagnetic induction,

$\varepsilon = -\dfrac{d\Phi}{dt} = -B\,l\,v$

The magnitude of the induced emf is therefore

$\varepsilon = Bvl$ …