Stokes' Theorem
A fundamental vector calculus theorem relating the surface integral of the curl of a vector field over an open surface S to the line integral of the field around its boundary curve ∂S.
Governing formula
∮_(∂S) F · dr = ∬_S (∇ × F) · dA
SI unit
Vector Line/Surface Integral Equality
In depth
Equates total boundary circulation to interior field rotation. Converts integral forms of Faraday's law and Ampere's law into differential vector forms.
Examples in the real world
Converting integral Ampere's law ∮ B · dl = μ₀ I into differential form ∇ × B = μ₀ J.