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) of a magnetic dipole (magnetic moment $\vec{m}$) in a magnetic field $\vec{B}$ is given by:
\[ U = -\vec{m} \cdot \vec{B} = -mB \cos\theta \]
where $\theta$ is the angle between the magnetic moment vector and the magnetic field vector.
2. Perpendicular Orientation ($\theta = 90^\circ$): When the magnetic bar is placed perpendicular to the magnetic field, the angle $\theta$ is $90^\circ$. Therefore, $\cos\theta = \cos(90^\circ) = 0$.
\[ U = -mB(0) = 0 \]
3. Conclusion: The magnetic potential energy is zero when the magnetic moment is perpendicular to the magnetic field.