The total charge induced in a conducting loop | vedclass

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(C) According to Faraday's law of electromagnetic induction, the induced electromotive force $(e)$ is given by $e = -\frac{d\phi}{dt}$.From Ohm's law,

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The total change in magnetic flux

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(C) According to Faraday's law of electromagnetic induction, the induced electromotive force $(e)$ is given by $e = -\frac{d\phi}{dt}$.From Ohm's law, the induced current is $i = \frac{e}{R} = -\frac{1}{R} \frac{d\phi}{dt}$, where $R$ is the resistance of the loop.Since current is the rate of flow of charge, $i = \frac{dq}{dt}$.Equating the two expressions for current: $\frac{dq}{dt} = -\frac{1}{R} \frac{d\phi}{dt}$.Integrating both sides, we get $q = -\frac{1}{R} \Delta \phi$.Therefore, the total charge induced $(q)$ depends on the total change in magnetic flux $(\Delta \phi)$ and the resistance of the loop $(R)$, and is independent of the time taken or the rate of change of flux.Thus, the correct option is $(C)$.

The total charge induced in a conducting loop when it is moved in a magnetic field depends on

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