Question

A system consists of two parallel planes carrying currents producing a uniform magnetic field in induction $B$ between the planes. Outside this space there is no magnetic field. The magnetic force acting per unit area of each plane is found to be $B^2/N{\mu }_0$. Find $N$.

Answer 1

Let $J$ is the current per unit length
$B=2\left[\frac{{\mu }_{0}J}{2}\right]={\mu }_{0}J$
Magnetic field due to one plane$=B/2$
Force on other plane $F=\frac{B}{2}\left(J{l}_1\right)l_2$
This force per unit area:
$\frac{F}{l_1{l}_2}=\frac{B}{2}J=\frac{B}{2}\frac{B}{{\mu }_0}=\frac{B^2}{2{\mu }_0}$
Hence $N=2$