Question

A magnetic dipole in a constant magnetic field has

• A. zero potential energy when the torque is maximum
• B. minimum potential energy when the torque is maximum
• C. maximum potential energy when the torque is maximum
• D. zero potential energy when the torque is minimum

Hint:

For a magnetic dipole: Maximum torque $\Rightarrow \theta=90^\circ$ and potential energy $U=0$.

Answer 1

The Correct Option is A

Step 1: Torque on a magnetic dipole $\vec{m}$ in a magnetic field $\vec{B}$ is \[ \tau = mB\sin\theta \] where $\theta$ is the angle between $\vec{m}$ and $\vec{B}$.
Step 2: Torque is maximum when \[ \sin\theta = 1 \Rightarrow \theta = 90^\circ \]
Step 3: Potential energy of a magnetic dipole in a magnetic field is \[ U = -mB\cos\theta \]
Step 4: At $\theta = 90^\circ$, \[ \cos 90^\circ = 0 \Rightarrow U = 0 \]
Step 5: Hence, when the torque is maximum, the potential energy is zero.