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

A Impossible Curl of a Vector Field

  1. Mar 21, 2017 #1
    Let's assume the vector field is NOT a gradient field.

    Are there any restrictions on what the curl of this vector field can be?

    If so, how can I determine a given curl of a vector field can NEVER be a particular vector function?
  2. jcsd
  3. Mar 21, 2017 #2


    Staff: Mentor

    Can give us a context here or some example that you're looking at?
  4. Mar 21, 2017 #3
    No example in particular... but I guess I can come up with one.


    Curl of vector field F = <2x, 3yz, -xz^2>

    Is this possible??
  5. Mar 21, 2017 #4
    sure. if a vector field v is a curl of some another vector field then ##\mathrm{div}\,v=0## Locally the inverse is also true
  6. Mar 21, 2017 #5
    Well, is the above post #3 a possibility?
  7. Mar 21, 2017 #6
  8. Mar 30, 2017 #7
    Nvm. I got it.
  9. Mar 31, 2017 #8
    You can obtain some results concerning that question by examining the Fourier transforms. This approach suffers from the obvious shortcoming that not all functions have Fourier transforms, but anyway, it could be that Fourier transforms still give something.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted