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Question

A system consists of two parallel planes carrying currents producing a uniform magnetic field of induction B between the planes. Outside this space there is no magnetic field. If the magnetic force acting per unit area of each plane is F1=B2xμ0. Find x

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Solution

By the circulation theorem B=μ0i,
where i= current per unit length flowing along the plane perpendicular to the paper. currents flow in the opposite sense in the two planes and produce the given field B by superposition.
The field due to one of the plates is just 12B. The force on the plate is,
12B×i×Length×Breadth=B22μ0 per unit area.
(Recall the formula F=BIl on a straight wire)

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