A hollow cylinder having infinite length and carrying uniform current per unit length $\mathrm{\lambda }$ along the circumference as shown. Magnetic field inside the cylinder is

Given a hollow cylinder that has infinite length and carrying current per unit length λ along the circumference

here, $\mathrm{\lambda }=\frac{\mathrm{I}}{2\mathrm{\pi r}}$current flowing per unit length.

$\mathrm{I}=\mathrm{\lambda }2\mathrm{\pi r}$

The magnetic field inside the cylinder is given by

$\mathrm{B}=\frac{{\mathrm{\mu }}_0}{4\mathrm{\pi }}\times \frac{2\mathrm{I}}{\mathrm{r}}$

$\mathrm{B}=\frac{2{\mathrm{\mu }}_0}{4\mathrm{\pi }}\times \frac{\mathrm{\lambda }2\mathrm{\pi r}}{\mathrm{r}}$

$\Rightarrow \mathrm{B}={\mathrm{\mu }}_0\mathrm{\lambda }$