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Level 3
Level 3 requires the basics of vector calculus, differential and integral calculus. Suitable for undergraduates and high school students.

Illustration Surface integral with orthogonal surface vector + vector field

Surface integral with orthogonal surface vector + vector field

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Visualizing the surface integral of a vector field \(\boldsymbol{F}\) within a surface \(A\):\[ \int_A \boldsymbol{F} \cdot \text{d}\boldsymbol{a} \]where \(\text{d}\boldsymbol{a}\) is an infinitesimal surface element of the surface \(A\).

The vector field \(\boldsymbol{F}\) can be divided into component \(\text{d}\boldsymbol{F}_{||}\) parallel to \(\text{d}\boldsymbol{a}\) and into component \(\boldsymbol{F}_{\perp}\) perpendicular to \(\text{d}\boldsymbol{a}\). The scalar product \(\boldsymbol{F}_{\perp} \cdot \text{d}\boldsymbol{a} = 0 \) with the vertical component does not contribute to the surface integral.

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  • License: CC BY 4.0This illustration may be used with indication of the copyright!
  • Copyright: © 2020
  • This illustration was uploaded by FufaeV on .
  • This illustration was updated by FufaeV on .