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in Physics by (60.8k points)

The magnetic field existing in a region is given by vector B = B0(1 + x/l)vector k.

A square loop of edge I and carrying a current i, is placed with its edges parallel to the X-Y axes. Find the magnitude of the net magnetic force experienced by the loop.

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f1 = force on AB = iB0[1 + 0]l = iB0l

f2 = force on CD = iB0[1 + 0]l = iB0l

f3 = force on AD = iB0[1 + 0/1]l = iB0l

f4 = force on AB = iB0[1 + 1/1]l = 2iB0l

Net horizontal force = F1 – F2 = 0

Net vertical force = F4 – F3 = iB0l

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