Question

A long, cylindrical tube of inner and outer radii a and b carries a current i distributed uniformly over its cross section. Find the magnitude of the magnetic field at a point (a) just inside the tube (b) just 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 = $\frac{{\mu }_{0}i}{2\pi \frac{3r}{2}}=\frac{{\mu }_{0}i}{3\pi r}$