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

Answer: (D)

$mB$

Answer 2

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.