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Physicist137 took a crack at showing why this follows from the structure of the electric field in the absence of time-dependent magnetic fields. That doesn't hold once you have induction in the system, however. So let's look at a simpler approach. Anything that you want to treat as a potential (whether it is a real potential or not) has to have a simple ...


The rotational of the electric field: $$ \nabla\times\mathbf E = -\frac{\partial\mathbf B}{\partial t} $$ Using Stokes' Theorem on this equation, we get the integral form of this equation: $$ \varepsilon = \oint_{\gamma}\mathbf E\cdot\mathbf{dl} = -\frac{d}{dt}\iint_S\mathbf B\cdot\mathbf{dS} = -\frac{d\Phi}{dt} $$ Which means, the electric field in a ...

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