Question

A hollow cylindrical conductor of inner radius a and outer radius b carries a current I uniformly spread over its cross-section. Find the magnetic field induction at a point inside the body of the conductor at a distance r [where a lt r lt b] from the axis of the cylinder.

Answer 1

Here is your answer:

Explanation:

Current passing through the cylindrical shell of:

inner radius a and outer radius r is :

I′= I/π(b2−a2)× π(r2−a2) = I(r2−a2) / (b2−a2)

Let B→ be the magnetic field induction at P.

So Using Ampere's circuital law:

∮B→⋅dl→ = μ0I′

or B2πr = μ0 /I (r2−a2)/(b2−a2)

or B=μ0I (r2−a2) / 2π(b2−a2)r