Question

A conducting current -carrying plane is placed in an external uniform magnetic field. As a result, the magnetic field. As a result, the magnetic induction becomes equal to $B_1$ on one side of the plane and $B_2$ on the other side. If the magnetic force acting per unit area of the plane is $\frac{F}{l_1{l}_2}=\frac{{B_1}^2-{B_2}^2}{x{\mu }_0}$. Find x.

Answer 1

Let external magnetic field is $B$ and $B_0$ is the magnetic field due to plane.
Then $B_1=B+B_0;B_2=B-B_0$
Where $B_0=\frac{{\mu }_{0}I}{2}$
Solving we get $B=\frac{B_1+B_2}{2},B_0=\frac{B_1-B_2}{2}$
Force on plane $F=B\left(J{l}_1\right)l_2$
Force per unit area:
$\frac{F}{l_1{l}_2}=BJ=\frac{B_1+B_2}{2}\left(\frac{2B_0}{{\mu }_0}\right)=\frac{{B_1}^2-{B_2}^2}{2{\mu }_0}$