# Inverse Function of Curl

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

1. ### Michael Lin Thread Starter Member

Sep 20, 2005
13
0
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?

Thanks.
Michael

2. ### cookevillain New Member

Dec 1, 2005
4
0
Michael,

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.

C-villain