Question

A square loop $A B C D$ carrying a current $i$, is placed near and coplanar with a long straight conductor $X Y$ carrying a current $I$, the net force on the loop will be

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

Answer 1

Answer: (D)

Consider the given figure,

$F_{B A}=\frac{\mu_{0} I i L}{2 \pi\left(\frac{L}{2}\right)} $
$\Rightarrow F_{C D}=\frac{\mu_{0} I i L}{2 \pi\left(\frac{3 L}{2}\right)}$
Therefore, net force on the loop $A B C D$ will be
$F_{\text {loop }} =F_{B A}-F_{C D}$
$=\frac{\mu_{0} I L}{2 \pi}\left[\frac{1}{(L / 2)}-\frac{1}{(3 L / 2)}\right] $
$F_{\text {loop }} =\frac{2 \mu_{0} i I}{3 \pi}$