A current I flows through a lengthy thin walled tube of radius R having a longitudinal slit of width W. The magnetic field inside the tube at the axis under the condition $\text{W}<<\text{r}$ is (r = distance of a point in the tube from slit)

r = distance of inside point from slit

$\Rightarrow$ In the absence of the slit, B = 0 at any inside point.

When the slit is made the remaining part of the pipe will produce some non zero field. This will be equal and opposite to the field produced by slit.

Field $\text{B}=\frac{{\mu }_0}{2\pi \text{r}}.\text{d}I$

$\text{d}I=\frac{I}{2\pi \text{R}}\left(\text{W}\right)\Rightarrow \text{B}=\frac{{\mu }_0\text{WI}}{4{\pi }^2\text{Rr}}$