Question

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

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

Answer 1

The correct option is D $2.3\times {10}^{-4}$

Intensity of magnetisation

Volume of cube $=1cm\times 1cm\times 1cm=1c{m}^3$

$={10}^{-6}{m}^3$

intensity of magnetisation

$I=\frac{\text{magnetic moment}}{\text{volume}}$

$=\frac{20\times {10}^{-6}J/T}{{10}^{-6}{m}^3}$

$=20N/m^2$

magnetic susceptibility

susceptibility, $\chi =\frac{I}{H}$ ($H=$ magnetic intensity )

$=\frac{20N/m^2}{60\times \times {10}^{3}A/m}$

$=3.3\times {10}^{-4}$

Hence, correct option is $\left(c\right)$