Two uniformly charged hollow hemispheres have charges Q and q, and radii R and r, respectively. The hemispheres are concentric and share their equatorial plane as shown in the figure. Calculate the electrostatic force F between the hemispheres.

answer: F=Qq8πε0R2

Assume that the charge distribution on the hemispheres is uniform. Now imagine the hemisphere Q is covering a sphere of charge q′ = 2q as shown in figure below

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Due to the symmetry, the sphere can be replaced by a point charge q′ at its centre. It is well-known (and can be shown by integration) that the electric field at the center of a hemisphere with charge Q is

E=kQ2R2

where k=14πε0. The...

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