A thin circular ring of area A is held perpendicular to a uniform magnetic field of induction B. A small cut is made in the ring and a galvanometer is connected across the ends such that the total resistance of the circuit is R. When the ring is suddenly squeezed to zero area, the charge flowing th…

Question

A thin circular ring of area A is held perpendicular to a uniform magnetic field of induction B. A small cut is made in the ring and a galvanometer is connected across the ends such that the total resistance of the circuit is R. When the ring is suddenly squeezed to zero area, the charge flowing through the galvanometer is .......

Accepted Answer

(2) (AB)/R. Given: ring of area A perpendicular to B, so the initial flux is Φ₁ = BA; after squeezing, Φ₂ = 0; total resistance R. Idea: at every instant I = (|ε|)/R = 1/R|(dΦ)/(dt)|, so the total charge is Q = ∫ I dt = (|ΔΦ|)/R — it does not depend on how quickly the ring is squeezed. |ΔΦ| = BA - 0 = BA. Q = (BA)/R = (AB)/R.

Step-by-step solution

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