For a magnetic dipole of magnetic moment $\vec{m}$ placed in a uniform magnetic field $\vec{B}$:

• Torque magnitude is $\tau = mB\sin\theta$ where $\theta$ is the angle between $\vec{m}$ and $\vec{B}$.

• Potential energy is $U = -\vec{m}\cdot\vec{B} = -mB\cos\theta$

Condition for maximum torque:

Since $\tau = mB\sin\theta$ torque is maximum when $\sin\theta = 1 \Rightarrow \theta = 90^\circ$

Potential energy at maximum torque:

Put $\theta = 90^\circ$ in $U = -mB\cos\theta$ $U = -mB\cos 90^\circ = 0$

So, when torque is maximum, potential energy is zero.

Check the options:

• A: maximum potential energy when torque is maximum. False, because at maximum torque $U=0$, not maximum.
• B: zero potential energy when torque is minimum. False, minimum torque occurs at $\theta=0^\circ$ or $180^\circ$, where $U=-mB$ or $+mB$, not zero.
• C: zero potential energy when torque is maximum. True.
• D: minimum potential energy when torque is maximum. False, minimum potential energy is at $\theta=0^\circ$, not where torque is maximum.

Therefore, the correct answer is: $\boxed{\text{C}}$