A rectangular loop length I and breadth b is placed at distance of x from infinitely long wire carrying current I such that the direction fo current is parallel to breadth .If the loop moves away from the current wire in a direction prependicular to it with a velocity v, the magnitude of the emf in the loop is (`mu_(0)`= Permeability of free space)

Options

A. `(mu_(0)iv)/(2pix)((1+b)/b)`
B. `(mu_(0)i^(2)v)/(4pi^(2)x) log((b)/(1))`
C. `(mu_(0)ilbv)/(2pix(1+x)`
D. `(mu_(0)ilbv)/(2pi)log((x+1)/x)`

Answer

C

Explanation

Given that,
Rectangular lopp is moving away from the the current wire perpendicular to velocity direction.
The direction of current in the rectangular loop is indicated as shown in figure .
Net magentic filed induced on the loop is ,
`B=mu_(0)i((1)/x-1/(I+x))`
emf,e=`(vbmu_(0)il)/(2pix(1+x)`