Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Divergence of curl in spherical coordinates

  1. Apr 27, 2014 #1


    User Avatar
    Gold Member

    Hey pf!!

    I was thinking about how div(curl(f)) = 0 for any vector field f. However, is this true for div and curl in spherical coordinates? It doesn't seem to be.

    If not, what needs to happen for this to be true in spherical coordinates??

    Thanks all!!
  2. jcsd
  3. Apr 27, 2014 #2


    User Avatar
    Homework Helper

    div and curl do not depend on coordinates so the result holds for all coordinates including spherical

    Keep in mind you omitted some conditions, f must be well behaved for that to be true
  4. Apr 28, 2014 #3


    User Avatar
    Homework Helper

    If you don't get [itex]\nabla \cdot (\nabla \times F) = 0[/itex] for well-behaved [itex]F[/itex] in spherical coordinates then you are making an error in your calculations, such as forgetting that the basis vectors are functions of position and not constant as in the Cartesian case.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook