Question

A circular current carrying loop of radius $r$ is bent about its diameter by ${90}^o$ and placed in a magnetic field $\overrightarrow{B}=B_0(\hat{i}+\hat{j})$ as shown in figure.

• A. The torque acting on the loop is zero
• B. The magnetic moment of the loop is $\frac{I\pi R^2}{2}(-\hat{i}-\hat{j})$
• C. The torque acting on the loop is non zero
• D. Both (a) & (b)

Answer 1

The correct option is D Both (a) & (b)

For the loop lying in $y-z$ plane and consdering given direction of current

$\overrightarrow{A}=\frac{\pi R^2}{2}(-\hat{i})$

Similarly, for the loop lying in $x-z$ plane

$\overrightarrow{A}=\frac{\pi R^2}{2}(-j)$

Thus the area vector for loop shown is

$\overrightarrow{A}=\frac{\lambda R^2}{2}(-i-\hat{j})$

$\overrightarrow{M}=I\overrightarrow{A}$

$\overrightarrow{M}=I\frac{\pi R^2}{2}(-\hat{i}-\hat{j}$)

Now $\overrightarrow{B}=B_0(\hat{i}+\hat{j})$

Thus torque acting on loop is,

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

or, $\overrightarrow{\tau }=\frac{I\pi R^2}{2}(-\hat{i}-\hat{j})\times B_o(\hat{i}+\hat{j})$

$\overrightarrow{\tau }=0$

Hence, option $\left(D\right)$ is the correct answer.