Question

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

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

Answer 1

Answer: (A)

Given, side of the cube $=1 cm =10^{-2}$ $m$
Then, the Volume of the cube, $V=10^{-6}$ $m ^{3}$
Dipole moment, $M=20 \times 10^{-6} J T ^{-1}$
Applied magnetic intensity, $H=60 \times 10^{3}$ A $m ^{-1}$
Intensity of magnetisation
$I=\frac{M}{V}=\frac{20 \times 10^{-6}}{10^{-6}}=20 A m ^{-1}$
Now, magnetic susceptibility $\chi$ is
$\chi=\frac{\text { Intensity of magnetisation }}{\text { Applied magnetic intensity }}=\frac{I}{H}$
$\chi=\frac{20}{60 \times 10^{3}}$
$\Rightarrow \chi=\frac{1}{3} \times 10^{-3}$
$\Rightarrow \chi=3.3 \times 10^{-4}$