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I'm having difficulties understanding this thing. It would be lovable if someone could show me its derivations and prove it:

In a conducting loop, there is a relationship between the total displaced charge in a set amount of time and the change in magnetic flux which goes as: $$|\Delta \Phi| = R |\Delta q|$$ I'm having difficulties conceptualizing the reason behind the absolute value signs. Why isn't it written as $\Delta \Phi = R \Delta q$?

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  • $\begingroup$ I think you're going to have to give us much more context/background, like where did you see this relationship. $\endgroup$
    – Triatticus
    Commented Jul 8 at 20:46

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This comes from Faraday's law. I believe it is only valid in quasistatic (no radiation generated) situations. Faraday's law in differential form is $$-\frac{d\Phi_B}{dt} = \varepsilon.$$ If you have a restive ring with changing flux through it, this emf $\varepsilon$ will generate a current according to Ohm's law $\varepsilon=IR$. But current in the loop at any given point is the rate of charge transfer through that section of the loop $I=\frac{dQ}{dt}$ so $$=-\frac{d\Phi_B}{dt}=R\frac{dQ}{dt}.$$ Integrate both sides to get $$-\Delta \Phi_B=R\Delta Q.$$ Then apply absolute values.

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