A perfectly diamagnetic sphere has a small spherical cavity at its centre, which is filled with a paramagnetic substance. The whole system is placed in a uniform magnetic field B⃗ . Then the field inside the paramagnetic substance is :

Solution

Physics sir · 4 steps

A perfect diamagnet lets no field through, so the paramagnet in the cavity has nothing to strengthen.

1. Perfect diamagnet. A perfectly diamagnetic material has susceptibility χ = -1, so its permeability is μ = μ₀(1 + χ) = 0. Its magnetisation exactly cancels the applied field, and the field inside the material is zero. A superconductor behaves this way (the Meissner effect).

   B_(inside) = μ₀ (1 + χ) H = μ₀ (1 - 1) H = 0

2. Shielded cavity. The field lines bend around the outside of the sphere and never pass through it. So no field reaches the cavity at the centre, just as no field gets inside a hollow superconducting shell.
3. Paramagnet inside. A paramagnet only strengthens a field that is already acting on it, since M = χ H. With no field reaching the cavity, its dipoles stay randomly oriented and it adds nothing.
4. So. The field inside the paramagnetic substance is zero, which is option (b).

The idea to keep. A perfect diamagnet (χ = -1) is a complete magnetic shield. Whatever sits inside it, paramagnetic or not, sees zero field, because a material can only respond to a field that reaches it.

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