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The magnetic field existing in a region ...

The magnetic field existing in a region is gicen by `vecB =B_0(1+(x)/(l))vec k.` A square loop of edge l 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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The magnetic field in the region
`B=B_0(1+x/l)hatk`
Force on AB,
`F_1=iB_0(1+0/l)l=iB_0l`
Force on CD,
`F_2=iB_0(1+l/l)l=iB_02l`
The forces due to wires BC and AD will be equal and opposite. Hence, the force on BC and AD will cancel. Net force, `F_2-F_1=iB_0l`
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