Question

A paramagnetic substance in the form of a cube of side 3 cm has a magnetic moment of \(243 \times 10^{-6}\) Am\(^2\), when a magnetic field of intensity \(150 \times 10^{3}\) Am\(^{-1}\) is applied. The susceptibility of the substance is:

• A. \(8 \times 10^{-5}\)
• B. \(12 \times 10^{-5}\)
• C. \(6 \times 10^{-5}\)
• D. \(3 \times 10^{-5}\)

Hint:

For calculating susceptibility, always remember the relationship between magnetic moment, volume, and magnetic field intensity. Rearranging the formula appropriately helps find the required value.

Answer 1

The Correct Option is C

The formula for magnetic moment \(M\) of a paramagnetic substance is given by: \[ M = \chi \times V \times H \] Where: - \(M\) is the magnetic moment,
- \(\chi\) is the susceptibility,
- \(V\) is the volume of the substance,
- \(H\) is the magnetic field intensity.
Given:
- \(M = 243 \times 10^{-6}\) Am\(^2\),
- \(H = 150 \times 10^{3}\) Am\(^{-1}\),
- The side length of the cube is 3 cm, so the volume \(V = (3 \, \text{cm})^3 = 27 \, \text{cm}^3 = 27 \times 10^{-6} \, \text{m}^3\).
Rearranging the formula to find \(\chi\): \[ \chi = \frac{M}{V \times H} \] Substituting the given values: \[ \chi = \frac{243 \times 10^{-6}}{(27 \times 10^{-6}) \times (150 \times 10^{3})} \] \[ \chi = \frac{243}{27 \times 150} \] \[ \chi = \frac{243}{4050} = 6 \times 10^{-5} \] Thus, the correct answer is \(6 \times 10^{-5}\).