The magnetic flux through a circuit of resistance R changes by an amount Δφ in a time Δ t. Then the total quantity of electric charge Q that passes any point in the circuit during the time Δ t is represented by

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(2) Q=(Δφ)/R. The induced current is i=ε/R=1/R(dφ)/(dt). Integrating over the interval, Q=∫ i dt=1/R∫ dφ=(Δφ)/R. The Δ t cancels: the charge depends only on how much the flux changed, not on how quickly. A slow change gives a small current for a long time and a fast change a large current briefly, and both move the same charge.

The magnetic flux through a circuit of resistance R changes by an amount Δφ in a time Δ t. Then the total quantity of electric charge Q that passes any point in the circuit during the time Δ t is represented by

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