Question

Is it possible for a current loop to stay without rotating in a uniform magnetic field? If yes, what should be the orientation of the loop?

Answer 1

Yes, if the direction of the area vector coincides with the direction of the magnetic field, the torque acting on the loop due to the magnetic field will become zero. Hence, no rotation will be produced in the coil.
It follows from the fact that torque acting on the loop is directly proportional to sin$\theta$, where $\theta$ is the angle made by the area vector with the direction of the magnetic field. So, we can see from this correlation that torque is zero if
$\theta$ = 0 or $\theta$ = 180⁰.
$$\begin{gathered} \tau =\stackrel{\rightharpoonup }{m}\times \stackrel{\rightharpoonup }{B} \\ =mB\sin \left(\theta \right) \\ \Rightarrow \mathrm{For}\theta =0\mathrm{or}\mathrm{integral}\mathrm{multiple}\mathrm{of}\mathrm{\pi }, \\ \tau =0 \end{gathered}$$
Which implies that the coil will not rotate.