Electric potential generated by an hemispherical charge distribution

AI Thread Summary
The discussion focuses on calculating the electric potential generated by a hemispherical charge distribution along an axis normal to its flat surface. To solve the integral ∫1/|x-x'| d^3x' over the volume, it is suggested to divide the hemisphere into circular slices. Each slice's contribution to the electric field can be computed, and using polar coordinates is recommended for simplification. This method allows for a clearer understanding of the electric potential generated by the charge distribution. The approach emphasizes the importance of breaking down complex geometries into manageable components for analysis.
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I need the electric potential generate by an hemuspherical constant charge density along the axis normal to the plane surface of the distribution an passing for the center of the hemisphere.

In practice i have to solve the integral:

∫1/|x-x'| d^3x' over the volume occupied by the distribution.

how to do?
 
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Cut the hemisphere into circular slices - work out the field due to each slice. Helps to use polar coordinates.
 

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