Question

A long, cylindrical wire of radius b carries a current i distributed uniformly over its cross section. Find the magnitude of the magnetic field at a point inside the wire at a distance a from the axis.

Answer 1

Given:

Magnitude of current = i

Radius of the wire = b

For a point at a distance a from the axis,

Current enclosed, i'=iπb2×πa2

By Ampere's circuital law,

∮B.dl = μ0i'

For the given conditions,

B×2πa= μ0iπb2×πa2⇒B=μ0ia2πb2