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

Given that the hemisphere has a charge +Q distributed through its surface with radiusa. Find the electric potential on any point on z axis (the plane of the hemisphere is oriented in positive z direction).

2. Relevant equations

[itex]\phi[/itex] = [itex]\int[/itex][itex]\frac{kQ}{|R-R'|}[/itex]*ds

(surface integral)

3. The attempt at a solution

So i decided to break this problem into little pieces of the surface using some trig.

I made a angle θ from the plane of the hemisphere around the cross section (so there is semi circles) and then an angle [itex]\varphi[/itex] on the xy-plane.

I found ds to be a[itex]^{2}[/itex]d[itex]\varphi[/itex]d[itex]\theta[/itex] (using the arc lengths of my angles and radii).

Now my problem is finding an equation for the vector R-R'. I tried making it a function of [itex]\theta[/itex] (i.e. i got (sqrt(z[itex]^{2}[/itex] + a[itex]^{2}[/itex]sin[itex]^{2}[/itex]([itex]\theta[/itex])

but the integral was not a nice one and it lead me to believe that it wasn't correct. if someone can help me along that would be great!

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# Potential energy of an hemispheric shell

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