Question

A current carrying loop placed in a uniform magnetic field as shown in the figure. The magnitude of torque on the loop is $\frac{\alpha \pi I r^{2} B}{8}$. Find $\alpha$.

Answer 1

$\vec{\tau}=\vec{M} \times \vec{B}$, where $\vec{M}=\left(\pi r^{2} I\right) \hat{i}$ and $\vec{B}=B(\hat{k})$
$\Rightarrow \vec{\tau}=\left(\pi I r^{2} B\right)(\hat{i} \times \hat{k})=\left(\pi I r^{2} B\right)(-\hat{j})$