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Gauss's theorem & electric flux

  1. Feb 21, 2009 #1
    1. The problem statement, all variables and given/known data

    I am reading through my textbook about an application of the divergence theorem involving a point charge enclosed by some arbitrary Gaussian surface. When the author evaluates the ∫sE dot dA, they rewrite the expression as a double integral in spherical coordinates I am fine with this except I can't quite grasp the limits of integration that are given; they are 0 to pi and 0 to 2pi. I am having trouble picturing how these rotations integrate over the whole sphere, as I keep visualizing that both the limits should be 0 2pi. Any suggestions would be greatly appreciated. Thanks.

    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Feb 21, 2009 #2

    lanedance

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    that would cover the surface twice

    2 pi is one full revolution

    imagine half a circle, swept by a line rotated at its base from 0 to pi

    then rotate this about the axis defining by the half circle by full 2 pi to generate a sphere

    http://mathworld.wolfram.com/SphericalCoordinates.html
     
  4. Feb 21, 2009 #3

    lanedance

    User Avatar
    Homework Helper

    that would cover the surface twice

    2 pi is one full revolution

    imagine half a circle, swept by a line rotated at its base from 0 to pi

    then rotate this about the axis defining by the half circle by full 2 pi to generate a sphere

    http://mathworld.wolfram.com/SphericalCoordinates.html
     
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