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The magnetic field existing in the region is given by
$B = B_{0} [1 + \frac{x}{l}] \hat{k}$
A square loop of edge $l$ and carrying current $I$ is placed with its edges parallel to the xy-axis. The magnitude of the net magnetic force experienced by the loop is

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zero

$B_{0} I L$

$2 B_{0} I L$

$4 B_{0} I L$

answer is C.

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Detailed Solution

$F_{b c} + F_{d a} = 0 F_{a b} = I L B_{0} (1 + \frac{x}{l}) = I B_{0} l + I B_{0} x$

which will be towards right

$F_{c d} = I L B_{0} (1 + \frac{x + l}{l}) = 2 I B_{0} l + I B_{0} x$

which will be towards left

$∴ F_{n e t} = F_{c d} - F_{a b} = I B_{0} l$ (which will be towards left)

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