Step $1:$

Given a hollow cylinder that has infinite length and carrying current per unit length $\lambda$ along the circumference.

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

$I =\lambda 2 \pi r \text { (1) }$

The magnetic field inside the cylinder is given by

$B =\frac{\mu_0}{4 \pi} \times \frac{2 I }{ r } \text { (2) }$

Step $2:$

Substitute the value of I from eq: $(1)$ in $(2)$ we get

$B =\frac{2 \mu_0}{4 \pi} \times \frac{\lambda 2 \pi r }{ r }$

$\Rightarrow B =\mu_0 \lambda$