Question

Two large metal sheets carry surface current as shown in figure. The current through a strip of width dl is kdl where k is a constant. Find the magnetic field at the point P, Q & R

Answer 1

From symmetry, B at P and R should be same. Using Ampere's law,
${\int }_0^L\overrightarrow{B}\cdot \overrightarrow{dl}={\mu }_{0}i={\mu }_0(kL-kL)$
$\overrightarrow{B}.\overrightarrow{L}=0\Rightarrow B=0$ hence at P and R, B $=$ 0
Now, let us apply Ampere's law between Q and R.
Here, ${\int }_0^L\overrightarrow{B}.\overrightarrow{dl}={\mu }_{0}kL$
$\Rightarrow BL+0\times L={\mu }_{0}kL$ ($\because$ B is zero at R)
$\Rightarrow B={\mu }_{0}k$ towards right