A rectangular loop of length `'l'` and breadth `'b'` is placed at a distance of `x` from an infinitely long wire carrying current `'i'` such that the direction of current is parallel to breadth. If the loop moves away from the current wire in a direction perpendicular to it with a velocity `'v'`, the magnitude of the e.m.f. in the loop is: (`mu_(0)=` permeability of free space)

Options

A. `(mu_(0)iv)/(2pix)((l+b)/(b))`
B. `(mu_(0)i^(2)v)/(4pi^(2)x)log((b)/(l))`
C. `(mu_(0)ilbv)/(2pix(l+x))`
D. `(mu_(0)ilbv)/(2pi)log((x+l)/(x))`

Answer

C

Explanation

We can show the situation as

Since, loop is moving away from the wire, so the direction of current in the loop will be as shown in the figure.
Net magnetic field on the loop due to wire,
`B=(mu_(0)i)/(2pi)((1)/(x)-(1)/(1+x))=(mu_(0)il)/(2pix(l+x))`
So, the magnitude of the emf in the loop,
`e=vBb=(mu_(0)ilvb)/(2pix(l+x))`