Stokes' theorem

Level AdvancedDifficulty ★★★★★Theorem⌖ Open in the map

What is it?

The circulation of a field around a closed curve equals the flux of its curl through any surface bounded by the curve. Green's theorem in 3D, and the integral form of Faraday's and Ampère's laws.

Statement

∮∂SF⋅dr=∬S(∇×F)⋅n dS.\oint_{\partial S}F\cdot\dd r = \iint_S(\nabla\times F)\cdot n\,\dd S.

Where it shows up in computing

Where is it used?

Computing topics reachable from here, through the chain of ideas that leads to them:

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