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Question

Figure 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 7 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. The net force on the loop is ———×105 N.


Solution

When viewed along x axis, force on BC & DA of loop can be considered as



Force due to infinite long wire on AB & CD cancel eachother
Net force F=(F1+F2)sinθ
We know that F1=F2=[μ0i1i22πr][a]
F=[μ0i1i22a2πr][a2r]
F=[μ0i1i2a22πr2]
F=2×107×7×10×400×104244×104
F=0.23×104
F=2.3×105 N

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