A sqaure loop `ABCD`, carrying a current `I_(2)` is placed near and coplanar with a long straight conductor `XY`, carrying a current `I_(1)` as shwon in Figure. The net force on the loop will be

Options

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

Answer

A

Explanation

`F_(AB)=ilB`(Attractive)
`F_(AB)=i(L).(mu_(0)I)/(2pi((L)/(2)))(larr)=(mu_(0)il)/(pi)(larr)`
`F_(BC)(uarr)` and `F_(AD(darr)`implies These cancel each other
`F_(CD)=ilB` (Repulsive)
`F_(CD)=i(L)(mu_(0)I)/(2pi((3L)/(2)))(rarr)=(mu_(0)il)/(3pi)(rarr)`
`impliesF_(net)=(mu_(0)il)/(pi)-(mu_(0)il)/(3pi)=(2mu_(0)il)/(3pi)`