Question

A thin circular ring of the 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 suddenly squeezed to zero areas, the charge flowing through the galvanometer is:
A) $\dfrac{{BR}}{A}$
B) $\dfrac{{\left( {AB} \right)}}{R}$
C) $ABR$
D) $\dfrac{{E^2}A}{R^2}$
E) $None$

Answer 1

The voltage will be produced when the magnetic flux through a coil is changed. The measure of the number of magnetic fields passing through an area is called magnetic flux. First, determine its magnetic flux, then by using the induced emf we can determine the charge flowing through the galvanometer.

Formula used:
$\varphi = BA$
Where $B$ is the magnetic field, $A$ is the area.
$i = \dfrac{E}{R}$
Where $E$ is the induced emf, $R$ is the total resistance.

Complete step by step solution:
The voltage will be produced when the magnetic flux through a coil is changed. The measure of the number of magnetic fields passing through an area is called magnetic flux. The magnetic flux provides the measurement of the total magnetic field that passes through a surface area. The SI unit of magnetic flux is weber.
The magnetic flux is given by the formula
$\varphi = BA$
The induced emf is given by
$E = \dfrac{{\vartriangle \varphi }}{{\vartriangle t}}$
Induced emf is produced when the magnetic flux changes.
The current is given by
$i = \dfrac{E}{R}$
Now substitute the value of current and induced emf in the above equation
$\dfrac{Q}{{\vartriangle t}} = \dfrac{{BA}}{{R\vartriangle t}}$
Then
$Q = \dfrac{{BA}}{R}$

Hence option $\left( A \right)$ is the right answer.

Note: A galvanometer is a device used to detect and indicate the electric current. The voltage will be produced when the magnetic flux through a coil is changed. The measure of the number of magnetic fields passing through an area is called magnetic flux. The SI unit of magnetic flux is weber. Induced emf is produced when the magnetic flux changes