The magnetic flux through a coil of resistance $R$ changes by an amount $\Delta \phi$ in time $\Delta t$.…
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
$\frac{\Delta \phi}{\Delta t}$
$-\frac{\Delta \phi}{\Delta t}+R$
$\frac{\Delta \phi}{R}$
$\frac{\Delta \phi}{\Delta t} \times R$
Solution
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 $\frac{\Delta \phi}{R}$
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