I'm not sure if this post should go here or in the Calc setion, but I figure more knowledgable people browse this form. This question is relating to 'directionality' of doing closed loop integrals.(adsbygoogle = window.adsbygoogle || []).push({});

If you have some 2D wire structure, lets image it looks like a square wave, or a square well. Ok, square well, so we have a U shape, lets say with 4 points, ABCD where BC is the bottom of the well. Now if I were to sum the segments in the Y direction I would have AB + CD, and we can see that AB = DC = -CD

So we have AB - AB = 0.

Now rather then summing in the Y direction, were summing along a path. We define this path by the normals or tangentials (curl or div theorem respectively) of the segments. Since the N(ormal)ab = Ndc = -Ncd we have shown this works with the previous addition.

Now increase the rank so its summing surfaces to get a volume. Does the stoke's theorem incorporate a direction such that opposite sides of this cube-well now, when added together in say the Z direction are 0, but are , for the stokes, not added in directions but added with their normals taken into account? So like 2 opposite ends of the well would add rather than cancel?

I hope Im being clear. Its a difficult problem to visualize.

**Physics Forums - The Fusion of Science and Community**

Dismiss Notice

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!

# Directionality in Stokes Theorem for Volumes

Loading...

Similar Threads - Directionality Stokes Theorem | Date |
---|---|

A Stokes' theorem on a torus? | Apr 27, 2017 |

I Do derivative operators act on the manifold or in R^n? | Jul 26, 2016 |

I Directional Derivatives and Derivations - Tangent Spaces | Feb 23, 2016 |

Tangent vectors as directional derivatives | Mar 4, 2015 |

A question on defining vectors as equivalence classes | Feb 5, 2015 |

**Physics Forums - The Fusion of Science and Community**