Relation between induced charge and change in magnetic flux

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Relation between induced charge and change in magnetic flux

Relation between induced charge and change in magnetic flux

According to the faraday’s law, the induced EMF is given as $$ {\mathcal {E}}=\frac{\Delta \phi}{\Delta t}$$ If $R$ is the total resistance of the closed-loop, the induced current will be $$I=\frac{\mathcal {E}}{R} \quad or \quad \frac{\Delta q}{\Delta t} =\frac{\Delta \phi}{\Delta t}\cdot\frac{1}{R}$$ Hence, the charge induced in the loop in time $\Delta t$ is

$$\Delta q =\frac{\Delta \phi}{R}= \frac{\text{Net change in magnetic flux}}{\text{Resistance}}$$

Clearly, we can see the induced current depends on the net change in magnetic flux and does not depend on the time interval $\Delta t$ of the flux change. Thus, the induced charge does not depend on the rate of change of magnetic flux.

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1. According to Faraday's law of electromagnetic induction, induced EMF is given as

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2. Induced charge depends on the

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3. Charge induced in the loop increases, iff

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4. charge induced in the loop in time $\Delta t$ is

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5. Charge induced in the loop is inversely proportional to

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