Question

Find the magnitude and direction of the magnetic induction vector $\overrightarrow{B}$ of two parallel infinite planes carrying currents of linear densities $\overrightarrow{i}$ and $\overrightarrow{-i}$; the vectors $\overrightarrow{i}$ and $\overrightarrow{-i}$ are constant at all points of the corresponding planes.

Answer 1

Magnetic field due to each plane can be calculate by applying Ampere's law in the loop shown,

$\oint B.dl={\mu }_{0}i\left(l\right)$

$⟹B\left(2l\right)={\mu }_{0}il$

$⟹B=\frac{{\mu }_{0}i}{2}$

The magnetic field is horizontal and parallel to the plane.

This magnetic field for each plane adds in between the planes, making the net magnetic moment=${\mu }_{0}i$

Outside the planes, the magnetic field cancels, giving no magnetic field.