Prove that induced charge depends on the net change in the magnetic flux and not on the time interval of the flux change.

\begin{tabular}[t]{|l|l|} Proof of induced charge

$\displaystyle 3$

Using Faraday's law of electromagnetic induction \[\begin{aligned} & |\varepsilon|=\frac{\Delta \phi}{\Delta t} \\ & I=\frac{|\varepsilon|}{R} \\ & I=\frac{1}{R}\left(\frac{\Delta \phi}{\Delta t}\right) \\ & \frac{\Delta Q}{\Delta t}=\frac{1}{R}\left(\frac{\Delta \phi}{\Delta t}\right) \\ & \Delta Q=\frac{\Delta \phi}{R} \end{aligned} \] Hence induced charge depends on change in magnetic flux, not on the time interval of flux change. \end{tabular}