Question

The magnetic potential energy, when a magnetic bar of magnetic moment \( \vec{m} \) is placed perpendicular to the magnetic field \( \vec{B} \), is:

• A. \(-\frac{mB}{2}\)
• B. Zero
• C. \(-mB\)
• D. \(mB\)

Answer 1

The Correct Option is D

1. Magnetic Potential Energy: The magnetic potential energy (U) for a magnetic dipole (characterized by magnetic moment $\vec{m}$) within a magnetic field $\vec{B}$ is defined as: \[ U = -\vec{m} \cdot \vec{B} = -mB \cos\theta \] Here, $\theta$ represents the angle between the magnetic moment vector and the magnetic field vector. 2. Perpendicular Alignment ($\theta = 90^\circ$): If a magnetic bar is oriented perpendicular to the magnetic field, the angle $\theta$ equals $90^\circ$. Consequently, $\cos\theta = \cos(90^\circ) = 0$. \[ U = -mB(0) = 0 \] 3. Summary: The magnetic potential energy is null when the magnetic moment is perpendicular to the magnetic field.