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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 GSEB Board March 2020 (old course) · Current and charge flow

• (1) R²λω
• (2) Rλ²ω
• (3) Rλω
• (4) Rλω²

Step-by-step solution

Why the other options are wrong

• (1) Comes from writing the period as T = 2π/v with v = ω R, dropping the R of the path length: then I = λ(2π R)·(ω R)/(2π) = λω R². The period is T = (2π R)/v = (2π)/ω; the unit check fails too, since λω R² is in C m s⁻¹.
• (2) Fails a unit check. The current is proportional to the charge on the ring, so λ can appear only to the first power; λ² puts C² into the answer.
• (4) Fails a unit check: ω² leaves an extra s⁻¹, so this is not a current. The charge 2π Rλ passes a point once per period 2π/ω, which brings in ω only once.

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