Question

A square loop $ABCD$ carrying a current $I_2$ is placed near and coplanar with a long straight conductor $XY$ carrying a current $I_1$, the net force on the loop will be :

• A. $\frac{\mu_0 Ii}{2 \pi}$
• B. $\frac{2 \mu_0 Ii L}{3 \pi}$
• C. $\frac{\mu_0 Ii L }{2 \pi}$
• D. $\frac{2 \mu_0 Ii}{3 \pi}$

Answer 1

Answer: (D)

$F_{AB} = i \ell B (Attractive)$
$F_{AB} = i(L). \frac{\mu_0I}{2 \pi (\frac{L}{2})} (\leftarrow) = \frac{\mu_0iI}{\pi} (\leftarrow)$
$F_{BC}(\uparrow)$ and $F_{AD}(v) \, \Rightarrow $ cancels each other
$F_{CD} = i(L) \frac{\mu_0I}{2 \pi ( \frac{3L}{2} )} (\rightarrow) = \frac{\mu_0iI}{3\pi} (\rightarrow)$
$\Rightarrow \, F_{net} = \frac{\mu_0iI}{\pi} - \frac{\mu_0iI}{3 \pi} = \frac{2 \mu_0 iI}{3\pi}$