Question

A paramagnetic substance, in the form of a cube with sides $1cm$ , 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 $=1cm=10^{-2}$ $m$
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
$I=\frac{M}{V}=\frac{20\times 10^{-6}}{10^{-6}}=20A{m}^{-1}$
Now, magnetic susceptibility $\chi$ is
$\chi =\frac{\text{ Intensity of magnetisation }}{\text{ Applied magnetic intensity }}=\frac{I}{H}$
$\chi =\frac{20}{60\times 10^3}$
$\Rightarrow \chi =\frac{1}{3}\times 10^{-3}$
$\Rightarrow \chi =3.3\times 10^{-4}$