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 $F_1=\frac{B^2}{x{\mu }_0}$. Find $x$

Answer 1

By the circulation theorem $B={\mu }_{0}i$,
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 $\frac{1}{2}B$. The force on the plate is,
$\frac{1}{2}B\times i\times Length\times Breadth=\frac{B^2}{2{\mu }_0}$ per unit area.
(Recall the formula $F=BIl$ on a straight wire)