# Applications of Green's theorem to physics

1. May 10, 2012

### cesaruelas

I am reading Etgen's Calculus: One and Several Variables section on Green's theorem. I was wondering if there is any direct application of this concept to physics or is it only used to calculate areas?

2. May 10, 2012

### Amok

Well, since Green's theorem may facilitate the calculation of path (line) integrals, the answer is that there are tons of direct applications to physics. Line or surface integrals appear whenever you have a vector function (vector fields) in the integrand. Potential energies are obtained wen you integrate a force over a path. If that path is closed, then you can find the potential energy by integrating over the region bound by that path (do away with parametrizations). Moreover, Green's theorem is a special case of Stokes theorem, which appears everywhere in electromagnetism (think about how you get from the differential form to integral form of the last two Maxwell equations). I'm sure a lot people here will come up with tons of specific examples (which can also come from fluid mechanics, for example).