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

Given Curl V, can you find V?

  1. Apr 24, 2010 #1
    Say V is a vector field.
    Is there a way (or rather a reasonable algorithm) to find V, given Curl V?

  2. jcsd
  3. Apr 24, 2010 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    If I told you curlV=0, can you give me a bunch of different functions that satisfy this requirement?
  4. Apr 24, 2010 #3
    Okay, let's impose V satisfies boundary conditions on a (hyper)surface or something. (Though I don't remember the conditions for uniqueness and regularity and so on of PDE solutions)

    I guess I asked the wrong question.
    Is there a way to find V within a transformation in what we might call the Kernel of the curl operator?

    (Like when someone asks what differentiates to f, it's understood that we can add a constant...)
  5. Apr 25, 2010 #4
    Yes, if the domain is good enough. The conventional way to phrase the problem is: given a vector field T with div T = 0, find V so that curl V = T. This should be in all multivariable calculus textbooks. But perhaps only after the discussion of vector integration.
  6. Apr 25, 2010 #5


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    You can determine V out of its curl, up to an arbitrary gradient field.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook