Question

A paramagnetic substance in the form of a cube with sides \(1\) cm has a magnetic dipole moment \(20\times 10^{-6}\) J/T when a magnetic intensity \(60\times 10^{3}\) A/m is applied. Its magnetic susceptibility is

• A. \(3.3\times 10^{-4}\)
• B. \(3.3\times 10^{-2}\)
• C. \(4.3\times 10^{-2}\)
• D. \(2.3\times 10^{-2}\)

Hint:

Find magnetisation as dipole moment per unit volume, then susceptibility is magnetisation divided by magnetic intensity.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept
Susceptibility \(\chi=\dfrac{I}{H}\), where \(I\) is the magnetisation, equal to dipole moment per unit volume.

Step 2: Volume and Magnetisation
Volume \(=(10^{-2})^{3}=10^{-6}\) m\(^{3}\).
\(I=\dfrac{20\times10^{-6}}{10^{-6}}=20\) A/m.

Step 3: Calculation
\(\chi=\dfrac{20}{60\times10^{3}}=3.3\times10^{-4}\).

Final Answer:
The magnetic susceptibility is 3.3 x 10-^4. \[ \boxed{\text{(A) }3.3\times10^{-4}} \]