The magnetic flux through a coil of resistance \(R\) changes by an amount \(\Delta \phi\) in time \(\Delta t\). The total quantity of induced electric charge \(Q\) is

From Faraday's law of EMI, emf induced in the circuit is given by,
\(e=-\frac{\Delta \phi}{\Delta t}\)
And if \(R\) is the resistance in the circuit then it becomes,
\(\begin{aligned} & I=\frac{e}{R} \\ & \quad \Rightarrow I=-\frac{\Delta \phi}{\Delta t \cdot R}\end{aligned}\)
So, the total amount of charge passing through the circuit will become,
\(\begin{aligned} & \because \Delta Q=I \times \Delta t \\ & \Rightarrow \Delta Q=-\frac{\Delta \phi}{\Delta t \cdot R} \cdot \Delta t \\ & \Rightarrow \Delta Q=-\frac{\Delta \phi}{R}\end{aligned}\)
So, the total amount of charge passing through the circuit is given by \(\frac{\Delta \phi}{R}\)