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

Options

A. `(BR)/(A)`
B. `(AB)/(R)`
C. `ABR`
D. `(B^(2)A)/(R^2)`

Answer

B

Explanation

Initial flux in the ring `phi_(1)=BA`
Since the ring is suddenly squeezed to zero area, final flux `phi_(f)=0`.
Change of flux `dphi = phi_(i)-phi_(f)=phi_(i) = BA`
Induced e.m.f. = `-(d phi)/(dt)` and induced current `i=(|e|)/(R)`
`:. I = (dq)/(dt) = 1/R (d phi)/(dt)`
`:. dq = 1/R d phi :. int dq = 1/R int d phi`
`:. q = (phi)/(R) = (BA)/(R)`.