An infinitely long hollow conducting cylinder with radius R carries a uniform current along its surface.
Choose the correct representation of magnetic field (B) as a function of radial distance (r) from the axis of cylinder.

Solution

Physics sir · 4 steps

Draw an Amperian circle inside the hollow cylinder: it encloses no current, so B is zero there.

1. Inside, r < R. Take a circle of radius r < R centred on the axis. All the current flows on the surface at radius R, so this loop encloses no current. Ampere's law gives B · 2π r = 0, so B = 0 everywhere inside.
2. Outside, r ≥ R. A circle of radius r ≥ R encloses the full current I. By symmetry B is the same all around the loop.

   B · 2π r = μ₀ I ⇒ B = (μ₀ I)/(2π r)

3. Shape of graph. So B is zero up to r = R, jumps to (μ₀ I)/(2π R) at the surface, and then falls off as 1/r.
4. So. Only graph (d) shows zero field inside and a 1/r fall outside. The answer is (d).

The idea to keep. In Ampere's law, B depends only on the current your loop encloses. A hollow conductor carries all its current on the surface, so the field inside is zero.

Answer from the NTA final answer key. Solution by PrepWiser.