How do you interpret the divergence or curl of the unit normal defined on a surface? This sometimes comes up when applying Stokes' theorem. A simple example would be(adsbygoogle = window.adsbygoogle || []).push({});

Surface area =

[tex]\int_{S} \hat{n} \cdot \hat{n} dA = \int_{V} \nabla \cdot \hat{n} dV[/tex]

where S is the closed surface that bounds a volume V. Since the normal n is defined on S, how do you interpret div n in the interior region? Do you just extend the field n on S to a field N on V in such a way that it is continuously differentiable and satisfies N = n on S?

I am assuming that there's nothing wrong with applying Stokes'/Divergence theorem when the vector field being integrated depends on the region of integration.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Divergence, curl of normal vector

Loading...

Similar Threads for Divergence curl normal |
---|

I Divergent series question |

I What does normalizing a straight line mean? |

A Angular Moment Operator Vector Identity Question |

I Finding a unit normal to a surface |

I Unit normal vector of a surface |

**Physics Forums | Science Articles, Homework Help, Discussion**