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

Answer

D

Explanation

At `x=0, B=B_(0)`, so `e_(1)=B_(0)v_(0)d`
At, `x=d, B=B_(0)(1+(d)/(a))`, so `e_(2)=B_(0)(1+(d)/(a))v_(0)d`
Now `e_("net")=e_(2)-e_(1)=(B_(0)v_(0)d^(2))/(a)`