Question 225 of 276

A rigid square loop of side $‘a’$ and carrying current ${I}_{2}$ is lying on a horizontal surface near a long current ${I}_{1}$ carrying wire in the same plane as shown in figure. The net force on the loop due to the wire will be:

AAttractive and equal to $\dfrac{{\mu }_{0}{I}_{1}{I}_{2}}{3\pi }$BRepulsive and equal to $\dfrac{{\mu }_{0}{I}_{1}{I}_{2}}{4\pi }$CRepulsive and equal to $\dfrac{{\mu }_{0}{I}_{1}{I}_{2}}{2\pi }$DZero

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Answer: (B) Repulsive and equal to $\dfrac{{\mu }_{0}{I}_{1}{I}_{2}}{4\pi }$

Force on segment 1-2 and 3-4 will get cancel out.
Force on segment 4-1,
${F}_{1}=\dfrac{{\mu }_{0}{I}_{1}{I}_{2}}{2\pi a}\times a$ toward Right
Force on segment 2-3:
${F}_{2}=\dfrac{{\mu }_{0}{I}_{1}{I}_{2}}{2\pi (2a)}\times a$ toward left
Net force on loop:
${F}_{net}={F}_{1}-{F}_{2}$ toward Right
$=\dfrac{{\mu }_{0}{I}_{1}{I}_{2}}{2\pi }-\dfrac{{\mu }_{0}{I}_{1}{I}_{2}}{4\pi }$
$=\dfrac{{\mu }_{0}{I}_{1}{I}_{2}}{4\pi }$ toward Right or repulsive