Question

A magnetic dipole in a constant magnetic field has

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

Answer 1

The correct option is B

zero potential energy when the torque is maximum

Formula used

$U=-\overrightarrow{\mu }.\overrightarrow{B}=\mu B\cos \left(\theta \right)\dots \left(i\right)$, where $U$ is the potential energy, $\mu$ is the magnetic moment and $B$ the magnetic field.

$\tau =\mu B\sin \left(\theta \right)\dots \left(ii\right)$, where $\tau$ is the torque.

Definitions

1. Magnetic dipole: A magnetic dipole is the limit of a closed system of electric current or a pair of poles when the size of the source is decreased to zero while the magnetic moment remains constant in electromagnetism.
2. Torque in the magnetic field: The normal vector of a current loop strives to align with the magnetic field when it is subjected to a magnetic field. This is called torque.
3. Potential Energy in the magnetic field: The amount of work required to rotate a magnetic dipole from zero potential energy to any desired location is defined as the potential energy of the dipole in a magnetic field. In a magnetic field, a current loop does not feel a net force. It, on the other hand, is subjected to torque.

Solution

1. From equations (i) and (ii) we can observe that potential energy will be zero when $\cos \left(\theta \right)$ will be zero which will be at a value of $90°$.
2. And, at $90°$ $\sin \left(\theta \right)$ is maximum that is one.
3. This means in turn the torque will be maximum.

Hence, the correct answer is option (B).