Question

The magnetic flux through a circuit of resistance R changes by an amount $\Delta \varphi$ in a time $\Delta t$. Then the total quantity of electric charge Q that passes any point in the circuit during the time $\Delta t$ is represented by :

• A. $Q=\frac{\Delta \varphi }{\Delta t}$
• B. $Q=\frac{\Delta \varphi }{R}$
• C. $Q=R\cdot \frac{\Delta \varphi }{\Delta t}$
• D. $Q=\frac{1}{R}\frac{\Delta \varphi }{\Delta t}$

Answer 1

The correct option is B $Q=\frac{\Delta \varphi }{R}$

We have, $e=\left|\frac{\Delta \Phi }{\Delta t}\right|$
$\therefore$ Current, $I=\frac{e}{R}=\frac{\Delta \Phi }{R\Delta t}$
So, charge $Q=I\cdot \Delta t=\frac{\Delta \Phi }{R\Delta t}\cdot \Delta t=\frac{\Delta \Phi }{R}$.