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_0I^'I)/(3pi)`
B. `(mu_0I^'I)/(2pi)`
C. `(2mu_0I^'IL)/(3pi)`
D. `(mu_0I^'IL)/(2pi)`

Explanation

Total force on loop is
`vecF_(lo op)=vecF_(AB)+vecF_(BC)+vecF_(CD)+vecF_(DA)`
(As `vecF_(BC)=-vecF_(DA)`)
`vecF_(AB)+vecF_(CD)`
`vecF_(AB)=(mu_02I^'IL)/(4pi(L//2))` along `_|_r` to Ab towards the linear conductor XY.
`vecF_(CD)=(mu_0)/(4pi)(2I^'IL)/((3L//2))` acting `_|_r` to CD away the linear conductor XY
`:.` Net force on loop is
`F_(lo op)=F_(AB)-F_(CD)`
`=(mu_0)/(4pi)2I^'I[(L)/(L//2)-(L)/(3L//2)]=(2mu_0I^'I)/(3pi)`