A conducting square frame of side `'a'` and a long straight wire carrying current `I` are located in the same plane as shown in the figure. The frame moves to the right with a constant velocity `'V'`. The emf induced in the frame will be proportional to

Options

A. `1/((2x-a)^(2))`
B. `1/((2x+a)^(2))`
C. `1/((2x-a)(2x+a)`
D. `1//x^(2)`

Answer

C

Explanation

emf in PQ -
`e_(1)=B_(1)av=(mu_(0)I)/(2pi(chi-a/2))av`
emf in RS-
`e_(2)=B_(2)av=(mu_(0)I)/(2pi(chi+a/2))av`
`e_("net")=e_(1)-e_(2)=(mu_(0)Iav)/(2pi)[1/((chi-a/2))-1/((chi+a/2))]`
`e_("net")prop1/((2chi-a)(2chi+a))`.