Question

Charge \( q \) is uniformly spread on a thin ring of radius \( R \). The ring rotates about its axis with a uniform frequency \( f \). The magnitude of magnetic induction at the centre of the ring is

• A. \( \frac{\mu_0 q f}{2 R} \)
• B. \( \frac{\mu_0 q}{2 R} \)
• C. \( \frac{\mu_0 q f}{2 R^2} \)
• D. \( \frac{\mu_0 q f}{2 \pi R} \)

Hint:

For a rotating charged ring, the magnetic field at the center is proportional to the charge, frequency, and inversely proportional to the radius.

Answer 1

The Correct Option is A

The magnetic induction at the centre of the rotating ring is given by the formula \( B = \frac{\mu_0 q f}{2 R} \), where \( q \) is the charge, \( f \) is the frequency of rotation, and \( R \) is the radius of the ring.

Step 2: Conclusion.
The magnetic induction at the centre of the ring is \( \frac{\mu_0 q f}{2 R} \), corresponding to option (a).