Question

A paramagnetic sample shows a net magnetization of $0.8A{m}^{-1}$, when placed in an external magnetic field of strength $0.8T$ at a temperature $5K$. When the same sample is placed in an external magnetic field of $0.4T$ at a temperature of $20K$, the magnetization is:

• A. $0.8A{m}^{-1}$
• B. $0.8A{m}^{-2}$
• C. $0.1Am$
• D. $0.1A{m}^{-1}$

Answer 1

The correct option is D $0.1A{m}^{-1}$

Given : $T_1=5K$ $T_2=20K$ $M_1=0.8A{m}^{-1}$ $B_1=0.8T$ $B_2=0.4T$

Using $\chi =\frac{M}{H}=\frac{C}{T}$ where $B={\mu }_{o}H$

$\therefore$ $\frac{M{\mu }_o}{B}=\frac{C}{T}$

OR $\frac{MT}{B}=\frac{C}{{\mu }_o}=constant$

$⟹$ $\frac{M_1{T}_1}{B_1}=\frac{M_2{T}_2}{B_2}$

$\therefore$ $\frac{0.8\times 5}{0.8}=\frac{M_2\times 20}{0.4}$ $⟹M_2=0.1$ $A{m}^{-1}$