Question

A paramagnetic sample shows a net magnetization of \(8\) A/m when placed in an external magnetic field of \(0.6\) T at a temperature of \(4\) K. When the same sample is placed in an external magnetic field of \(0.2\) T at a temperature of \(16\) K, the magnetization (in \(\frac{A}{m}\)) will be

• A. \(\frac{2}{3}\)
• B. \(\frac{32}{3}\)
• C. \(6\)
• D. \(2.4\)

Hint:

By Curie's law, magnetisation is proportional to B divided by T.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept
For a paramagnetic sample, Curie's law gives \(M\propto\dfrac{B}{T}\).

Step 2: Ratio
\(\dfrac{M_2}{M_1}=\dfrac{B_2}{B_1}\times\dfrac{T_1}{T_2}=\dfrac{0.2}{0.6}\times\dfrac{4}{16}=\dfrac{1}{12}\).

Step 3: Calculation
\(M_2=8\times\dfrac{1}{12}=\dfrac{2}{3}\) A/m.

Final Answer:
The magnetisation becomes 2/3 A/m. \[ \boxed{\text{(A) }\dfrac{2}{3}} \]