Question

A square loop ABCD, carrying a current I₂, is placed near and coplanar with a long straight conductor XY carrying a current I₁, as shown in figure. The net force on the loop will be

• A. $\frac{\mu_{0}I_{1}I_{2}}{2\pi}$
• B. $\frac{\mu_{0}I_{1}I_{2}L}{2\pi}$
• C. $\frac{2\mu_{0}I_{1}I_{2}L}{3\pi}$
• D. $\frac{2\mu_{0}I_{1}I_{2}}{3\pi}$

Answer 1

Answer: (C)

$F =1 LB \sin \theta$
$B =\frac{\mu_{0} I }{2 \pi r }$
$F _{ AB }=\frac{- I _{2} \mu_{0} I _{1} L }{2 \pi x }$
$F _{ CD }=\frac{ I _{2} \mu_{0} 1 L }{2 \pi( L + x )}$
$F =\frac{\mu_{0} I _{1} L _{2} l ^{2}}{2 \pi\left( x ^{2}+1 x \right)}$ taking $x =\frac{1}{2} 1$
$F =\frac{2 \mu_{0} I _{1} I _{2}}{3 \pi}$