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. Find the magnetic force acting per unit area of each plane.

Answer 1

By the circulation theorem B = μ₀ i, 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 1/2 B. The force on the plate is,

(Recall the formula F = BIl on a straight wire)