Integral from an electric field calculation

[klawlor419]

Hi all,

Any ideas how to solve this integral?

$$ \int_{0}^{\pi} \frac{(z-R\cos{\theta})\sin{\theta}d\theta}{R^2+z^2-2zr\cos{\theta}}$$

It crops up in a calculation of the electric field for a spherical charged shell. It has a uniform charge smear

Thanks ahead of time

 

[klawlor419]

The lower case r in the denominator should be a large R for the radius of the shell.

 

[klawlor419]

Well, I figured out that when z=R you recover the expected field of an infinite plane.

$$ E_z=\sigma/2\epsilon_0 $$