A paramagnetic sample shows a net magnetisation of 6 A/m when it is placed in an external magnetic field of 0.4 T at a temperature of 4 K. When the sample is placed in an external magnetic field of 0.3 T at a temperature of 24 K, then the magnetisation will be:

Solution

Physics sir · 3 steps

Curie's law says magnetisation goes as B over T, so just scale 6 A/m by both ratios.

1. Curie's law. In a paramagnet the applied field tries to line up the atomic dipoles, and heat tries to scramble them. So the magnetisation grows with the field B and falls with the temperature T: M ∝ B/T.

   M₂/M₁ = B₂/B₁ × T₁/T₂

2. Put in numbers. The field ratio is 0.3/0.4 = 0.75 and the temperature ratio is 4/24 = 1/6. So M₂ = 6 × 0.75 × 1/6 A/m.
3. So. M₂ = 0.75 A/m, which is option (c).

The idea to keep. For a paramagnet, remember M ∝ B/T (Curie's law). When the field and the temperature both change, multiply by both ratios: field up means more M, temperature up means less.

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