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

Question

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:

TestHub · Accepted Answer

Force on segment 1-2 and 3-4 will get cancel out.
Force on segment 4-1,
$F_{1} = \frac{μ_{0} I_{1} I_{2}}{2 π a} \times a$ toward Right
Force on segment 2-3:
$F_{2} = \frac{μ_{0} I_{1} I_{2}}{2 π (2 a)} \times a$ toward left
Net force on loop:
$F_{n e t} = F_{1} - F_{2}$ toward Right
$= \frac{μ_{0} I_{1} I_{2}}{2 π} - \frac{μ_{0} I_{1} I_{2}}{4 π}$
$= \frac{μ_{0} I_{1} I_{2}}{4 π}$ toward Right or repulsive

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