Question

A coil carrying current i is wound around sphere as shown in figure. A vertical magnetic field is present.

• A. Friction force is must to keep sphere in rotational equilibria.
• B. Sphere can be in rotational equilibria without friction.
• C. Direction of magnetic field should be vertically up.
  for rotational equilibria.
• D. Translational equilibria is not necessary for rotational equilibria.

Answer 1

Answer: (A), (C), (D)

The correct options are
A Friction force is must to keep sphere in rotational equilibria.
C Direction of magnetic field should be vertically up.
for rotational equilibria.
D Translational equilibria is not necessary for rotational equilibria.


Limiting friction is $f_l=\mu mgcos\theta$
depending on $\mu$ & $\theta$ $f_l$ can be less than or equal or greater than mg sin $\theta$.
Torgue on loop due to $\overrightarrow{B}$ is T = $\mu$ B sin $\theta$ = i $\pi r^2$ B sin $\theta$
& Torque due to friction is T = fr
For rotational equilibria x fr = i $\pi r^2$ B sin $\theta$
or f = i $\pi r$ B sin $\theta$ and this can be less than mg sin $\theta$.