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Converting a Vector Field from Cartesian to Cylindrical Coordinates
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Jan13-10, 10:27 PM
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!
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