The magnetic field in a region is given by `vec(B)=B_(0)(1+(x)/(a))hat(k)`. A square loop of edge length 'd' is placed with its edge along X-axis and Y-axis. The loop is moved with a constant velocity `vec(V)=V_(0)hat(i)`. The emf induced in the loop is

Options

A. `(v_(0)B_(0)d^(2))/(a)`
B. `(v_(0)B_(0)d^(3))/(a)`
C. `(v_(0)B_(0)d^(2))/(2a)`
D. `0`

Answer

A

Explanation

`epsilon =|(dphi)/(dt)|implies epsilon =A(dB)/(dt)`
`epsilon =d^(2)(d)/(dt)B_(0)(1+(x)/(a))`
`epsilon=d^(2)B_(0)((1)/(a))(dx)/(dt)`
`=(B_(0)d^(2).v_(0))/(a)`