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Magnetic properties of matter

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Question

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

Moderate

Solution

Given
Side of cube $= 1 {cm=10}^{- 2} m$
Magnetic dipole moment $M = 20 \times 10^{- 3} J / T$
Magnetic intensity $H = 6 \times 10^{3} J / T$
Magnetic susceptibility $χ = \frac{Intensity of magnetization}{Magnetic field intensity}$
$\Rightarrow χ = \frac{I}{H} = \frac{M}{V \times H} = \frac{20 \times 10^{- 3}}{10^{- 6} \times 6 \times 10^{3}} = \frac{20}{6} = 3.33$

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