A magnetic dipole in a uniform magnetic field has: (Take zero potential energy when magnetic dipole is perpendicular to magnetic field)

Let us denote the magnetic dipole moment vector by $$\vec p$$ and the uniform magnetic field by $$\vec B$$. The angle between the two vectors is called $$\theta$$.

First, we recall two standard relations for a magnetic dipole kept in a uniform magnetic field:

1. Magnitude of torque

We have the vector formula $$\vec \tau = \vec p \times \vec B$$. Taking magnitudes, the cross-product gives

$$\tau = pB\sin\theta.$$

2. Potential energy

The scalar product of two vectors tells us

$$U = -\,\vec p \cdot \vec B.$$

This dot product becomes

$$U = -pB\cos\theta.$$

The question clearly states that the reference level of potential energy is chosen to be zero when the dipole is perpendicular to the field. Mathematically, when $$\theta = 90^{\circ}$$ we obtain

$$\cos 90^{\circ} = 0 \;\;\Longrightarrow\;\; U = -pB \times 0 = 0,$$

so the usual formula $$U = -pB\cos\theta$$ is already consistent with the given convention; no extra constant has to be added.

Now we compare the conditions for maximum torque and for the potential energy values:

Maximum torque

From $$\tau = pB\sin\theta$$ the sine term reaches its greatest value of 1 when

$$\sin\theta = 1 \;\;\Longrightarrow\;\; \theta = 90^{\circ}.$$

Hence the torque is maximum when the dipole is perpendicular to the field.

Potential energy at that same orientation

Substituting $$\theta = 90^{\circ}$$ in the energy expression, we get

$$U = -pB\cos 90^{\circ} = -pB \times 0 = 0.$$

So, exactly at the orientation where the torque attains its maximum value, the potential energy is zero (with the chosen reference point).

Among the given statements we therefore select the one that says “zero potential energy when the torque is maximum.”

Hence, the correct answer is Option B.