# Converting a Vector Field from Cartesian to Cylindrical Coordinates

1. Jan 13, 2010

### jayz

1. The problem statement, all variables and given/known data
I have a rather complicated vector field given in cartesian coordinates that I need to evaluate the line integral of over a unit square. I know to use Stoke's Theorem to do this, and I suspect that the integral would be greatly simplified if it were in cylindrical coordinates, but I am having trouble with the conversion.

V(x,y) = Vx*ex+Vy*ey

Vx = sqrt(x/(x^2+y^2)
Vy = y/(sqrt(x^2+y^2))

2. Relevant equations

x = rcos(theta)
y = rsin(theta)
r = sqrt(x^2+y^2)

3. The attempt at a solution

I converted Vx to sqrt(rcos(theta)/r^2
and Vy to rsin(theta)/r

But I'm not sure how to relate Vx and Vy to Vr and Vtheta so that I can take the curl.
Any help would be appreciated! Thanks!