A paramagnetic cube (side 1 cm) has a magnetic dipole moment of 20 times 10^ -6 text J/T when subjected to a magnetic intensity H = 60 times 10^3 text A/m . Its magnetic susceptibility chi is:

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EEJ MAIN Physics QUESTION #7010

Question 1

A paramagnetic cube (side 1 cm) has a magnetic dipole moment of $20 \times 10^{-6}\ \text{J/T}$ when subjected to a magnetic intensity $H = 60 \times 10^3\ \text{A/m}$. Its magnetic susceptibility $\chi$ is:

$3.3 \times 10^{-2}$
$4.3 \times 10^{-2}$
$2.3 \times 10^{-2}$
$3.3 \times 10^{-4}$✔️

Correct Answer Explanation

Magnetic susceptibility: $\chi = \frac{M}{H}$, where $M$ is magnetisation (magnetic moment per unit volume).

Volume of cube: $V = (1\times10^{-2})^3 = 10^{-6}\ \text{m}^3$

Magnetisation: $M = \frac{\text{dipole moment}}{V} = \frac{20\times10^{-6}}{10^{-6}} = 20\ \text{A/m}$

$\chi = \frac{M}{H} = \frac{20}{60\times10^3} = 3.33\times10^{-4}$

$\chi \approx 3.3 \times 10^{-4}$

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