A non-conducting ring having a uniform linear charge density λ is rotating with an angular speed ω about an axis passing through its centre and perpendicular to its plane. The magnetic field at its centre is

Step-by-step solution

Let the radius of the ring is r . Charge on the ring, q = l λ = 2 π r λ ∵ l = 2 π r Current due to the rotation of the ring, i = q t = 2 π r λ 2 π ω ∵ t = 2 π ω = ω λ r i = ω λ r ...(i) ∴ Magnetic field at the centre of the ring due to the rotation of the charged ring. B = μ 0 2 . i r = μ 0 2 . ω λ r r = μ 0 2 . ω λ [Using Eq. (i)]