Question

A thin but long, hollow, cylindrical tube of radius r carries a current i along its length. Find the magnitude of the magnetic field at a distance $r/2$ from the surface (a) inside the tube (b) outside the tube.

Answer 1

(a) Magnetic field inside the tube = 0

[Since magnetic field inside in any conducting fube is zero.]

(b) The point outside the tube with distance $\frac{r}{2}$

Then net distance from centre = $r+\frac{r}{2}=\frac{3r}{2}$

So, net magnetic field = $\frac{{\mu }_{0}i}{2\pi \frac{3r}{2}}=\frac{{\mu }_{0}i}{3\pi r}$