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A ring of radius R and linear charge density λ on its surface is performing rotational motion about an axis perpendicular to its plane. If the angular velocity of the ring is ω, how much current is constituted by the ring?

Asked in RS Academy GUJCET booklet · Current and charge flow

• (1) Rωλ
• (2) 2π Rωλ
• (3) (Rωλ)/(2π)
• (4) 2Rωλ

Step-by-step solution

Why the other options are wrong

• (2) 2π Rωλ multiplies the charge by ω as if ω were the number of revolutions per second. Revolutions per second is ω/(2π), and that 2π cancels the one in the charge.
• (3) (Rωλ)/(2π) takes the charge as λ R, using the radius instead of the circumference 2π R. The whole ring carries 2π Rλ.
• (4) 2Rωλ uses the diameter in place of the radius, as if the ring moved at 2Rω. A point on the ring moves at v = ω R, so I = λω R.

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