A thin ring of radius R meter has charge q coulomb uniformly spread on it. The ring rotates about its axis with a constant frequency of f revolutions/s. The value of magnetic induction in Wb/m² at the centre of the ring is

Options

(a) µ₀q f / 2π R
(b) µ₀q / 2π f R
(c) µ₀q / 2 f R
(d) µ₀q f / 2 R

Correct Answer:

µ₀q f / 2 R

Explanation:

Current in the ring due to the rotation,
I = q/T = q? / 2π = q.2π f / 2π
Therefore, magnetic field at the centre of the ring is
B = µ₀I / 2R = µ₀/2R . q2π f / 2π
= µ₀q f / 2 R