Question

A bar magnet of moment $\overrightarrow{M}=\hat{i}+\hat{j}$ is placed in a magnetic field induction $\overrightarrow{B}=3\hat{i}+4\hat{j}+4\hat{k}$. The torque acting on the magnet is-

• A. $\hat{i}+\hat{j}+\hat{k}$
• B. $\hat{i}-\hat{j}$
• C. $\hat{i}+\hat{k}$
• D. $4\hat{i}-4\hat{j}+\hat{k}$

Answer 1

The correct option is D $4\hat{i}-4\hat{j}+\hat{k}$

$\overrightarrow{\tau }=\overrightarrow{M}\times \overrightarrow{B}$

$=(\hat{i}+\hat{j})$ $\times (3\hat{i}+4\hat{j}+4\hat{k}$)

$=4\hat{k}-4\hat{j}-3\hat{k}+4\hat{i}$

$\therefore \overrightarrow{\tau }=4\hat{i}-4\hat{j}+\hat{k}$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(D\right)$ is the correct answer.