[[Maxwell's equations]]
# Faraday's law of induction

**Faraday's law of induction** describes how a changing magnetic field results in an electromotive force and thus current flow,
and vice versa,
$$
\begin{align*}
\mathcal{E}= \oint_{\partial\Sigma}\vab E \cdot d\vab\ell = - \frac{ \partial }{ \partial t } \iint_{\Sigma}\vab B \cdot d\vab a = -\frac{d\Phi_{B}}{dt}
\end{align*}
$$
^Integral

or equivalently by [[Stokes's theorem]]
$$
\begin{align*}
\vab\nabla\times\vab E = -\frac{ \partial\vab B }{ \partial t } 
\end{align*}
$$
^Differential

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#state/tidy | #lang/en | #SemBr