Question

a ring of radius r is uniformly charged with charge q. if the ring is rotated about its axis with angular frequency omega (w), the magnetic induction at its centre will be?

Answer 1

The total magnetic induction at the center of the ring will be μ₀qω/4πr

Explanation:

since the total charge is q and we know that current = charge/time

=> I = q/t

The angular velocity is equal to ω = 2π/t

Time period, t = 2π/ω

=> I = qω/2π

we know that magnetic field at the center of a current carrying conductor,

B = μ₀I/2r

putting the value of I from the above equation, we get

B = (μ₀/2r) x qω/2π

=> B = μ₀qω/4πr

Hence the total magnetic induction at the center of the ring will be μ₀qω/4πr