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. $\frac{2{\mu }_{0}IiL}{3\pi }$
• C. $\frac{{\mu }_{0}IiL}{2\pi }$
• D. $\frac{2{\mu }_{0}Ii}{3\pi }$

Answer 1

Answer: (D)

$F_{AB}=i\ell B(Attractive)$
$F_{AB}=i(L).\frac{{\mu }_{0}I}{2\pi (\frac{L}{2})}(\leftarrow )=\frac{{\mu }_{0}iI}{\pi }(\leftarrow )$
$F_{BC}(\uparrow )$ and $F_{AD}(v)\Rightarrow$ cancels each other
$F_{CD}=i(L)\frac{{\mu }_{0}I}{2\pi (\frac{3L}{2})}(\to )=\frac{{\mu }_{0}iI}{3\pi }(\to )$
$\Rightarrow F_{net}=\frac{{\mu }_{0}iI}{\pi }-\frac{{\mu }_{0}iI}{3\pi }=\frac{2{\mu }_{0}iI}{3\pi }$