Question

A paramagnetic sample shows a net magnetization of $6A/m$ when it is placed in an external magnetic field of $0.4T$ at a temperature of $4K$. When the sample is placed in an external magnetic field of $0.3T$ at a temperature of $24K$, then the magnetization will be:

• A. $4A/m$
• B. $1A/m$
• C. $0.75A/m$
• D. $2.25A/m$

Answer 1

The correct option is C

$0.75A/m$

Step 1: Given Data

Net magnetization, $M=6A/m$

External magnetic field, $B_{ext}=0.4T$

Step 2: Find net magnetization when the External magnetic field, $B_{ext}=0.3T$ and temperature $T=24K$

Net magnetization is given by,

$\begin{array}{rcl}M& =& \frac{C{B}_{ext}}{T}\\ 6& =& \frac{C\times 0.4}{4}\\ C& =& 60\end{array}$

Thus, net magnetization when the External magnetic field, $B_{ext}=0.3T$ and temperature $T=24K$ is

$\begin{array}{rcl}M& =& \frac{C{B}_{ext}}{T}\\ M& =& \frac{60\times 0.3}{24}\\ M& =& 0.75A/m\end{array}$

Hence, option C is correct.