- #1
ELB27
- 117
- 15
Homework Statement
While trying to find the electric field at a distance z from the center of a spherical surface that carries a uniform surface charge ##\sigma## I got stuck with the following integral (which I'm quite sure is correct):
[tex]\int_0^\pi \frac{(z-Rcos\theta)sin\theta d\theta}{(R^{2}+z^{2}-2Rzcos\theta)^{3/2}}[/tex]
Homework Equations
The Attempt at a Solution
The only idea I had is to let ##u=cos\theta ; du=-sin\theta d\theta##,then the integral becomes:
[tex]\int_0^\pi \frac{(Ru-z)du}{(R^{2}+z^{2}-2Rzu)^{3/2}}[/tex]
and now I'm stuck. This looks very similar to a partial fractions problem except there is a square root in the denominator and if I understand correctly I'm not allowed to use partial fractions in this case.
Any help will be appreciated!