Inverse Function of Curl

Discussion in 'Physics' started by Michael Lin, Nov 6, 2005.

  1. Michael Lin

    Thread Starter Member

    Sep 20, 2005
    Mathematically, I know that to recover a vector from the gradient of a vector, I need to integrate and the solution is not unique.
    If i want to recover the vector from the curl of a vector, is there a standard way to do it? How? I'm pretty sure this vector is not unique too, correct?

  2. cookevillain

    New Member

    Dec 1, 2005

    One thing to keep in mind is that there is no such thing as the curl of a vector: you can only find the curl of a vector field. This out of the way, you are right: there is no unique way to get the original vector field back: the curl is a differential operator so shifting everything by a constant vector would preserve it. Moreover, there are plenty of fields with zero curl. Another complication arises from the question: what is the domain of the field? If your field is defined on the whole R^3 (euclidean space), techniques based on Stokes' theorem can help, otherwise one has to get a bit more sophisticated. Hope this helps.