Converting a Vector Field from Cartesian to Cylindrical Coordinates

[jayz]

Homework Statement

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))

Homework Equations

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

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!

 

[mighty2000]

Hello! It seems like you are on the right track with converting the vector field to cylindrical coordinates. In order to relate Vx and Vy to Vr and Vtheta, you can use the following equations:

Vr = Vx*cos(theta) + Vy*sin(theta)
Vtheta = -Vx*sin(theta) + Vy*cos(theta)

Using these equations, you can then take the curl of the vector field in cylindrical coordinates to evaluate the line integral using Stoke's Theorem. I hope this helps! Let me know if you have any further questions.