Relation between induced charge and change in magnetic flux

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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

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 / 5

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

${\mathcal {E}}=2\frac{d\phi}{d t}$

${\mathcal {E}}=\frac{d \phi}{d t}$

${\mathcal {E}}=\frac{d \phi}{dt^2}$

None

2 / 5

2. Induced charge depends on the

change in magnetic force

change in electric field

change in magnetic field

change in magnetic flux

3 / 5

3. Charge induced in the loop increases, iff

change in flux increases

resistance increases

change in flux decreases

resistance decreases

4 / 5

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

$\frac{\Delta \phi}{R}$

$2\frac{\Delta \phi}{R}$

$\frac{\Delta \phi}{2R}$

None

5 / 5

5. Charge induced in the loop is inversely proportional to

Resistance

magnetic flux

induced EMF

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