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Polar coordinate integration in different planes?

  1. Mar 10, 2013 #1
    I know that when you are integrated over dA in the xy plane, for your polar coordinates, x = rcosθ and y = rsinθ. However what about in the xz and yz plane?

    I noticed in one of the textbook problems, where the integration is over an area in the xz plane, x = rcosθ and z = rsinθ. How did the solution know to use that?
     
  2. jcsd
  3. Mar 10, 2013 #2
    What do you mean? Why would xy and xz-planes be any different? You can get xz-plane from xy-plane by just a simple rotation
     
  4. Mar 10, 2013 #3
    If you integrate over some polar area in the xy plane you find that x = rcosθ and y = rsinθ. but let's say instead of integrating over the xy plane, we integrate over the yz plane then what are y and z in terms of r and θ?
     
  5. Mar 10, 2013 #4
    Well, how do you define r and θ? I'm guessing r is the distance, so r=√(x2+z2) and θ is some angle, but what exactly is it?
     
  6. Mar 10, 2013 #5

    SteamKing

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    r, theta polar coordinates are for the plane only. If you have a three-dimensional problem to analyze, then spherical coordinates (r, theta, phi) would be called for.

    The conversion of polar coordinates (r, theta) to Cartesian (x, y), where x = r cos theta, y = r sin theta, is just simple trigonometry.
     
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