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Physics LibreTexts

5.8.5: Hollow Hemisphere

Any element of mass, \(δM\) on the surface of a hemisphere of radius \(a\) is at a distance \(a\) from the centre of the hemisphere, and therefore the potential due to this element is merely  \(−G δM/a\). Since potential is a scalar quantity, the potential of the entire hemisphere is just \(−GM/a\).