A uniform current density $j$ flows inside an infinite plate of thickness $2d$ parallel to its surface. The magnetic field induction is   

The linear current density along the plane of sheet at a distance r from the central plane of thickness dr is given  by $\lambda =\frac{\mathrm{I}}{\mathrm{I}}=\frac{\mathrm{Jldr}}{\mathrm{I}}=\mathrm{Jdr}$ where l = width of the sheet .

The magnetic field at point$P$ due to this elemental sheet at a distance of $\mathrm{x}(<\mathrm{d})$ from median plane is,

$\begin{array}{l}\mathrm{dB}=\frac{{\mu }_0\lambda }{2}=\frac{{\mu }_0\mathrm{Jdr}}{2}\\ \mathrm{B}={\int }_{-x}^d \frac{{\mu }_0\mathrm{Jdr}}{2}-{\int }_{-x}^{-d} \frac{{\mu }_0\mathrm{Jdr}}{2}\\ =\frac{{\mu }_0\mathrm{J}}{2}\left(2\mathrm{x}\right)={\mu }_0\mathrm{Jx}\end{array}$

for point $P$ outside the plane  $(x>d)$.

$B={\int }_{-d}^d \frac{{\mu }_{0}Jdr}{2}={\mu }_0\text{ Jd when }x>d$.