Skip to main content

Illustration Curl Integral Theorem

Curl Integral Theorem
Curl Integral Theorem
Download

Share โ€” copy and redistribute the material in any medium or format

Adapt โ€” remix, transform, and build upon the material for any purpose, even commercially.

Sharing and adapting of the illustration is allowed with indication of the link to the illustration.

The Curl Integral Theorem combines the rotation \( \nabla \times \boldsymbol{F} \) of a vector field \(\boldsymbol{F}\) within a surface \(A\) with the line integral of the vector field along the edge \(L\) of the considered surface \(A\): \[ \int_{A} (\nabla \times \boldsymbol{F}) \cdot \text{d}\boldsymbol{a} ~=~ \oint_{L} \boldsymbol{F} \cdot \text{d}\boldsymbol{l} \]