Fig. $(a)$ shows a square loop, $20 cm$ on each side in the $x - y$ plane with its Centre at the origin. The loop carries a current of $78 A$ . above it at $y = 0, z = 12 cm$ is an infinitely long wire parallel to the $x$ $-$ axis carrying a current of 10 A. Find the net force on the loop.

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$3 \times 10^{- 2} N$

$6 \times 10^{- 2} N$

$6 \times 10^{- 4} N$

$3 \times 10^{- 4} N$

answer is C.

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Detailed Solution

Resultant force on wires $A B$ and $C D$ is zero. The components $F_{1} \sin θ$ and $F_{2} \sin θ$ on wires $B C$ and $D A$ add, whereas components $F_{1} \cos θ$ and $F_{2} \cos θ$ cancel.

Thus the resultant force acting on the coil

$= 2 Fcos θ = \frac{μ_{0} I_{1} I_{2}}{2 π r} \sin θ = \frac{4 \times 10^{- 7} \times 65 \times 78 \times 0.1 \times (5 \times 10^{- 2})}{13^{2} \times 10^{- 4}} = 6 \times 10^{- 4} N$