Does a charged rod or a shell have a magnetic potential energy when it is kept in a uniform magnetic field?
Also, can anyone quantitatively explain why a wire loop carrying current would tend to be circular?
The magnetic moment of a dipole (in this case, the loop) is given by $$ \mu=I A $$ where $I$ is the current carried by the wire, and $A$ its area.
The potential energy of a dipole, when in presence of a magnetic field $B$ is $$ W=-\mu B \cos\theta $$ where $\theta$ is the angle between the direction normal to the wire and the direction of the magnetic field. In this case, we are taking $\theta=0$ (because the wire is perpendicular to the magnetic field), so $W=-IAB$.
With this, you can see that $W$ is minimised when $A$ is maximised.