Question

A current $I$ flows along a lengthy thin-walled tube of radius $R$ with longitudinal slit of width $h$. Find the induction of the magnetic field inside the tube under the condition $h<<R$.

Answer 1

The thin walled tube with a longitudinal slit can be considered equivalent to a full tube and a strip carrying the same current density in the opposite direction. Inside the tube, the former does not contribute so the total magnetic field is simply that due to the strip. It is

$B=\frac{{\mu }_0}{2\pi }\frac{\left(I/2\pi R\right)h}{r}=\frac{{\mu }_{0}Ih}{4{\pi }^{2}Rr}$

where $r$ is the distance of the field point from the strip.