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Griffiths 4.12

  • Thread starter ehrenfest
  • Start date
1,996
1
1. Homework Statement
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. Homework Equations



3. The Attempt at a Solution
 

Answers and Replies

pam
455
1
Your denominator should be [tex]({\bf r-r')}^3[/tex].
 
1,860
0
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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