Question

If a copper rod (free to move and rotate) is brought in a region of a non – uniform magnetic field, then it will align itself

• A. Along the direction of the magnetic field, at a location where the magnetic field is strongest
• B. Along the direction of the magnetic field, at a location where the magnetic field is weakest
• C. Perpendicular to the direction of the magnetic field, at a location where the magnetic field is strongest
• D. Perpendicular to the direction of the magnetic field, at a location where the magnetic field is weakest

Answer 1

Answer: (D)

Perpendicular to the direction of the magnetic field, at a location where the magnetic field is weakest

Answer 2

Key concepts

• Copper is diamagnetic, so it develops an induced magnetic moment opposite to the applied field.
• The magnetic potential energy for a magnetic moment $\vec m$ in field $\vec B$ is
  $$ U = -\vec m \cdot \vec B. $$
• For a diamagnet, $\vec m$ is antiparallel to $\vec B$, so to minimize energy the rod seeks regions of weaker field.
• Torque $\tau = \vec m \times \vec B$ aligns the rod so that $\vec m\perp\vec B$, making $m\cdot B=0$.

Therefore, the copper rod aligns perpendicular to the field in the weakest region.