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 magnitude filed at a point (a) just inside the tube (b) just outside the tube.

Answer 1

Explanation:

The magnitude of the magnetic field at a point (a) just inside the tube:

In any conducting tube, the magnetic field is always zero.

There is zero magnetic field inside the tube.

The magnitude of the magnetic field at a point (b) just outside the tube.

Let the point with distance b outside the tube be P.

Considering an American loop , as the figure shows.

loop Length, $l=2 \pi \times b=2 \pi b$

Enclosed current in the loop = I

If we apply the law of Ampere, we obtain

$\int B \cdot d l=\mu_{0} i$

$B \times 2 \pi b=\mu_{0} i$

$B=\frac{\mu_{0} i}{2 \pi b}$