Combining charged caps

Two spherical caps with constant volume charge densities ρ1\rho_{1} and ρ2\rho_{2} are in contact and form a ball or radius R as shown in the figure. Find the force of interaction FF between the caps in Newtons if ρ1=1×103 C/m3\rho_{1}=1\times 10^{-3}~\text{C}/\text{m}^{3}, ρ2=2×103 C/m3\rho_{2}=2\times 10^{-3}~\text{C}/\text{m}^{3}, R=10 cmR=10~\text{cm} and h=5 cmh=5~\text{cm}.

Details and assumptions

The vacuum permittivity is ε0=8.85×1012 F/m\varepsilon_{0}=8.85\times 10^{-12}~\text{F}/\text{m}.

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