Equations · equation
Stokes' Theorem
Calculus · 1854
- Equation
- ∮_C F · dl = ∫_S (∇ × F) · dA
- Field
- Calculus
- Named After
- George Gabriel Stokes
- Year
- 1854
Symbols
F a vector field · C a closed loop bounding the surface S · dl a step along the loop · ∇ × F the curl: how much the field circulates about a point
Significance
The circulation around a loop equals the curl through any surface it bounds. Faraday's law of induction is this theorem applied to a changing magnetic field; the Ampère–Maxwell law is it applied to current. Kelvin set it as an exam question in a letter to Stokes in 1850, and Stokes put it on the Smith's Prize paper in 1854 — Maxwell was among those who sat it.
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