A circular coil having magnetic moment μ is placed in a uniform...

The magnetic potential energy of a magnetic dipole in a uniform magnetic field is given by $U = -\vec{\mu} \cdot \vec{B} = -\mu B \cos \theta$, where $\theta$ is the angle between the magnetic moment $\vec{\mu}$ and the magnetic field $\vec{B}$.

For the coil to be in equilibrium, the net torque acting on it must be zero. The torque is given by $\vec{\tau} = \vec{\mu} \times \vec{B}$, which implies $\tau = \mu B \sin \theta = 0$. This gives $\theta = 0^{\circ}$ or $\theta = 180^{\circ}$.

In a state of unstable equilibrium, the potential energy is maximum. This occurs when $\theta = 180^{\circ}$.

Substituting $\theta = 180^{\circ}$ in the expression for potential energy:

$U = -\mu B \cos(180^{\circ}) = -\mu B (-1) = +\mu B$

Answer: $+\mu B$