Editing Circulation (physics) (section)

=== Fundamental equations of electromagnetism ===
In electrodynamics, the [[Faraday's law of induction#Maxwell–Faraday equation|Maxwell-Faraday law of induction]] can be stated in two equivalent forms:<ref>{{Cite web | title=The Feynman Lectures on Physics Vol. II Ch. 17: The Laws of Induction | url=https://feynmanlectures.caltech.edu/II_17.html | access-date=2020-11-02 | website=feynmanlectures.caltech.edu}}</ref> that the curl of the electric field is equal to the negative rate of change of the magnetic field,
<math display="block">\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}} {\partial t}</math>

or that the circulation of the electric field around a loop is equal to the negative rate of change of the magnetic field flux through any surface spanned by the loop, by Stokes' theorem
<math display="block">\oint_{\partial S} \mathbf{E} \cdot \mathrm{d}\mathbf{l} = \iint_S \nabla\times\mathbf{E} \cdot \mathrm{d}\mathbf{S} =
 - \frac{\mathrm{d}}{\mathrm{d}t} \int_{S} \mathbf{B} \cdot \mathrm{d}\mathbf{S}.</math>

Circulation of a [[static magnetic field]] is, by [[Ampère's law]], proportional to the total current enclosed by the loop
<math display="block">\oint_{\partial S} \mathbf{B} \cdot \mathrm{d}\mathbf{l} = \mu_0 \iint_S \mathbf{J} \cdot \mathrm{d}\mathbf{S} = \mu_0 I_\text{enc}.</math>

For systems with electric fields that change over time, the law must be modified to include a term known as Maxwell's correction.