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Faraday's Law.md

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The [[EMF]] around a closed path is equal to the negative of the time rate of change of the magnetic [[Flux]] enclosed by the path. $$\mathcal{E} = -\frac{d \Phi_B}{dt}$$ Accordingly, a [[Solenoid]] with $N$ total turns will have an EMF $N$ times as large as that induced by just one of its loops: $$\mathcal{E} = -N\frac{d \Phi_B}{dt}$$ Of a rotating loop with $N$ total turns and angular velocity $\omega$: $$\mathcal{E} = -N\frac{d \Phi_{B}}{dt} = NBA \omega sin(\omega t)$$

Stationary Faraday's Law

If the path is stationary: $$\oint \vec{E} \cdot d \vec{l} = -\frac{d \Phi_B}{dt}$$ Inside a [[Solenoid]]: $$\oint \vec{E} \cdot d \vec{l} = -\frac{dB}{dt}A = -\mu_{0}n \frac{dI}{dt} A$$