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

• A. $\frac{BR}{A}$
• B. $\frac{BA}{R}$
• C. ABR
• D. $\frac{B^{2}A}{R^2}$

Answer 1

Answer: (B)

$\frac{BA}{R}$

The individual emf produced in the coil $e=\frac{-d\varphi }{dt}$

$\therefore$ The current induced will be $i=\frac{|e|}{R}$

$\Rightarrow i=\frac{1}{R}\frac{d\varphi }{dt}$

But $i=\frac{dq}{dt}\Rightarrow \frac{dq}{dt}=\frac{1}{R}\frac{d\varphi }{dt}$

$\Rightarrow \int dq=\frac{1}{R}\int d\varphi$

$\Rightarrow q=\frac{BA}{R}$