Question

A circular current carrying loop of radius $r$ is placed in $xy$ plane in a uniform magnetic field $\overrightarrow{B}=(\hat{i}-\hat{k})T$ as shown in figure, then $\hat{i}$

• A. Potential energy of the system is negative
• B. Magnetic dipole moment is in the direction of positive $z-\text{axis}$
• C. Torque acting on the loop along negative $y-\text{axis}$
• D. Force experienced by the current carrying loop is zero

Answer 1

Answer: (A), (B), (C)

Torque acting on the loop along negative $y-\text{axis}$

As we know
The torque is given as,
$\overrightarrow{\tau }=\overrightarrow{M}\times \overrightarrow{B}=i\pi r^2(-\hat{k})\times (\hat{i}-\hat{k})=-\hat{j}\left(i\pi r^2\right)$
The potential energy given as
$U=-\overrightarrow{M}.\overrightarrow{B}=-\left(i{r}^2\pi \right)(-\hat{k}).(\hat{i}-\hat{k})=-\left(i\pi r^2\right)<0$
The direction of magnetic dipole moment is perpendicular to the plane of the current loop.
Hence, the correct options are $\text{(}a,bandd)$