(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The surface of a sphere of radius a is charged with a constant surface density [tex]\sigma[/tex]. What is the total charge Q' on the sphere? Find the force produced by this charge distribution on a point charge q located on the z axis for z > a and for z < a.

2. Relevant equations

3. The attempt at a solution

For z>a, I found [tex]\vec{F}[/tex] = [tex]\frac{\normalsizeq\sigma\hat{z}}{\epsilon_{0}z^{2}}[/tex]

Now, during my calculations, there was one point where I evaluated the integral for [tex]\normalsize\vartheta[/tex] to be [tex]\normalsize\frac{1}{z}\left(\frac{z-r^{'}}{\left(z^{2}-r^{'}^{2}-2zr^{'}\right)^{1/2}+\frac{z+r^{'}}{\left(z^{2}+r^{'}^{2}+2zr^{'}\right)}[/tex]

My thinking is that when I simplify the fractions, I obtain |z-r| and |z+r| in the denominator if I want the positive square root, which is the z > a case. So would the z<a case simply mean the square roots would have negative signs out, ie -|z-r| and |z+r| (z+r is stil positive).

Edit: My latex syntax is messed up. But basically I got (z-r') / (z^2+r'^2-2zr')^(1/2) + (z+r')/(z^2+r'^2+2zr')^(1/2)

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# Force on a point charge due to constant sphere surface charge density.

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