Question

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

• A. \( (3)3 \times 10^{-2} \)
• B. \( (2)3 \times 10^{-4} \)
• C. \( (2)3 \times 10^{-2} \)
• D. \( (3)3 \times 10^{-4} \)

Hint:

Magnetic Susceptibility. Magnetization \(M = m/V\) (magnetic moment per unit volume). Susceptibility \(\chi = M/H\). Ensure volume is in m\(^3\).

Answer 1

The Correct Option is D

Given: Total magnetic dipole moment \(m = 20 \times 10^{-6}\) J/T (equivalent to A·m\(^2\)).
Volume of the cube \(V = (1 \, \text{cm})^3 = (10^{-2} \, \text{m})^3 = 10^{-6} \, \text{m}^3\).
Applied magnetic intensity (field strength) \(H = 60 \times 10^3\) A/m.
First, calculate the Magnetization (\(M\)), which is the magnetic dipole moment per unit volume: $$ M = \frac{m}{V} = \frac{20 \times 10^{-6} \, \text{A}\cdot\text{m}^2}{10^{-6} \, \text{m}^3} = 20 \, \text{A/m} $$ Magnetic susceptibility (\(\chi\)) is defined as the ratio of magnetization (\(M\)) to the applied magnetic intensity (\(H\)): $$ \chi = \frac{M}{H} $$ $$ \chi = \frac{20 \, \text{A/m}}{60 \times 10^3 \, \text{A/m}} = \frac{20}{60000} = \frac{1}{3000} $$ $$ \chi = \frac{1}{3} \times 10^{-3} \approx 0.
33(3).
.
\times 10^{-3} = (3)3(3).
.
\times 10^{-4} $$ The magnetic susceptibility is approximately \((3)3 \times 10^{-4}\).
Susceptibility is dimensionless.