Question

A thin ring of radius 'R' metre has charge 'q' coulomb uniformly spread on it. The ring rotates about its axis with a constant frequency of 'f' revolution/s. The value of magnetic induction at the centre of the ring in \(\text{Wb/m}^2\) is

( \(μ_0\) = permeability of free space )

• A. \(\frac{μ_0q}{2fR}\)
• B. \(\frac{μ_0q}{2πR}\)
• C. \(\frac{μ_0qf}{2R}\)
• D. \(\frac{μ_0qπ}{2fR}\)

Hint:

A rotating charge forms a current I = q f.

Answer 1

The Correct Option is C

Step 1: Current
$I = q/T = qf$.

Step 2: Loop field
$B = \mu_0 I/(2R)$ at the centre.

Step 3: Result
$\mu_0 qf/(2R)$. Option (C).

Final Answer:
Option (C). \[ \boxed{\frac{\mu_0 q f}{2R}} \]