Combining charged caps

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

Details and assumptions

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

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