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Converting a Vector Field from Cartesian to Cylindrical Coordinates

  1. Jan 13, 2010 #1
    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!
  2. jcsd
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