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Surface integral

  1. Mar 6, 2006 #1
    I am really struggling with this one:

    Calculate [tex] \Int F.ndS [/tex], where

    [tex] F = a * x^3 * i + b*y^3*j + c*z^3*k [/tex]

    where a,b and c are constants,

    over the surface of a sphere of radius a, centred at the origin.

    note that F and n are vectors (sorry, tried to type them in bold...but it doesn't work)


    So, this is my attempt:

    convert everything in polar coordinates and integrate it


    dS = r^2*sinx*cosz (

    for only a hemisphere though...I would multiply it by 2 afterwards to make it a sphere)

    the final integral is then:

    [tex] dS = \Int {a*dS} = \Int {r^3 (a*sin^3x*sin^3z + b*sin^3x*sin^3z + c*cos^3x) * r^2*sinx*cosz} [/tex]

    And this is just a mess. What is wrong here?
    Last edited: Mar 6, 2006
  2. jcsd
  3. Mar 6, 2006 #2


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    Science Advisor
    Homework Helper

    Try doing the dot product in Euclidean coordinates, but then still write the integral in polar coordiantes. The result of a dot product is a scalar, and the scalar will therefore be simpler to convert into polar coordinates than those nasty vectors.

    Last edited: Mar 6, 2006
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