A square (each side of length L) wire loop is kept with a long straight wire carrying current I. The emf induced in the square loop is _____

Options

A. `(mu_(0)Ii)/(2pi)`
B. `(2mu_(0)IiL)/(3pi)`
C. `(mu_(0)IiL)/(2pi)`
D. `(2mu_(0)Ii)/(3pi)`

Answer

D

Explanation

Resultant force acting on loop,
`F=F_(BA)-F_(CD)`
= `(mu_(0)IiL)/(2piy_(1))-(mu_(0)IiL)/(2piy_(2))`
= `(mu_(0)IiL)/(2pixxL/2)-(mu_(0)IiL)/(2pixx(3L)/2)`
= `(mu_(0)IiL)/(piL)-(mu_(0)IiL)/(3piL)=(mu_(0)iL)/pi-(mu_(0)Ii)/(3pi)`
`thereforeF=(2mu_(0)Ii)/(3pi)`