A coil having effective area A, is held with its plane normal to a magnetic field of induction B. The magnetic induction is quickly reduced to `25%` of its initial value in `2s`. Then e.m.f. induced across the coil will be

Options

A. `(3AB)/(8)`
B. `(3AB)/(4)`
C. `(AB)/(4)`
D. `(AB)/(2)`

Answer

A

Explanation

`B_(2)=(25)/(100)B_(1)=(B_(1))/(4)`
`e=(phi_(1)-phi_(2))/(dt)=(AB_(1)-AB_(2))/(dt)`
`=(A)/(dt)(B_(1)-B_(2))`
`=(A)/(dt)(B_(1)-(B_(1))/(4))`
`e=(3AB_(1))/(4dt)=(3AB)/(4xx2)=(3AB)/(8)`