# 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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