Solution to the March, 2022 Challenge The pot and the kettle.*

doi:10.1119/10.0014317

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: $F = \frac{Q q}{8 π ε_{0} R^{2}}$

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 = \frac{k Q}{2 R^{2}}

where

k = \frac{1}{4 π ε_{0}} .

The...

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Solution to the March, 2022 Challenge The pot and the kettle.*

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