A square loop ABCD carrying a current i , is placed near and coplanar with a long straight conductor XY…

A square loop $\mathrm{ABCD}$ carrying a current $\mathrm{i}$, is placed near and coplanar with a long straight conductor $\mathrm{XY}$ carrying a current $\mathrm{I}$, the net force on the loop will be:

1. $\frac{2{\mathrm{\mu }}_0\mathrm{I}\mathrm{i}}{3\mathrm{\pi }}$
2. $\frac{{\mathrm{\mu }}_0\mathrm{I}\mathrm{i}}{2\mathrm{\pi }}$
3. $\frac{2{\mathrm{\mu }}_0\mathrm{I}\mathrm{i}\mathrm{L}}{3\mathrm{\pi }}$
4. $\frac{{\mathrm{\mu }}_0\mathrm{I}\mathrm{i}\mathrm{L}}{2\mathrm{\pi }}$

Solution

${\mathrm{F}}_1=\frac{{\mathrm{\mu }}_0\mathrm{I}\mathrm{i}\mathrm{L}}{2\mathrm{\pi }\frac{\mathrm{L}}{2}\mathrm{ }}=\frac{{\mathrm{\mu }}_0\mathrm{I}\mathrm{i}}{\mathrm{\pi }}\mathrm{ }$
${\text{F}}_{\text{2}}=\frac{{\mathrm{\mu }}_0\mathrm{I}\mathrm{i}\mathrm{L}}{2\mathrm{\pi }\frac{3\mathrm{L}}{2}}=\frac{{\mathrm{\mu }}_0\mathrm{I}\mathrm{i}}{3\mathrm{\pi }}$

$\therefore {\mathrm{F}}_{\mathrm{n}\mathrm{e}\mathrm{t}}={\mathrm{F}}_1-{\mathrm{F}}_2$
${\mathrm{F}}_{\mathrm{n}\mathrm{e}\mathrm{t}}=\frac{2}{3}\frac{{\mathrm{\mu }}_0\mathrm{I}\mathrm{i}}{\mathrm{\pi }}$

Asked in: MHT CET Full Test 8

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