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Griffiths 4.12

  1. Apr 5, 2008 #1
    1. The problem statement, all variables and given/known data
    This question refers to Griffiths E and M book.

    Of course I am stuck with the integral.

    I chose z to be in the same direction as the polarization.

    The integral is then
    [tex]P \int d\Omega r'^2 dr'\frac{\left(\mathbf{r} -\mathbf{r'}\right)\cdot \hat{\mathbf{z}}}{\left(\mathbf{r} -\mathbf{r'}\right)^2}[/tex]

    BTW, how do you get the script r that Griffiths uses in latex?


    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Apr 6, 2008 #2

    pam

    User Avatar

    Your denominator should be [tex]({\bf r-r')}^3[/tex].
     
  4. Apr 6, 2008 #3
    Yes, the integral is a pain in the neck, but you should notice that it is the same integral as a uniformly charged sphere. I would probably just use mathematica, but if you don't have that luxury then I believe you can use trig substitutions and partial fractions to get it done.
     
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