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

Answer 1

The correct option is B $\frac{AB}{R}$

EMF induced in ring $E=-\frac{d\varphi }{dt}$

Where, $\varphi$ is magnetic flux $=BA$

$iR=-\frac{d\varphi }{dt}$

$Ridt=-d\varphi$

$R\int idt=-\int d\varphi$

$Rq=|\varphi |$

$q=\frac{BA-0}{R}=\frac{BA}{R}$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(B\right)$ is the correct answer.