Past exam of the physics course of the year 1 of the natural sciences course of the University of Cambridge / 2011 / Paper 1 / Section A / A1 / Solution

For the gravitational-electrostatic balance of equal charged spheres, the shell theorem and Coulomb's law give $F_g=G{M}^2/r^2$ and $F_e=q^2/(4\pi {ϵ}_0{r}^2)$ for well-separated spherical particles. Their separation cancels at balance. Since $M=4\pi \rho a^3/3$,The two charges have the same sign, so electrostatic repulsion opposes gravitational attraction. A zero charge gives no nontrivial force balance. Spherical symmetry of the external charge distribution, or the leading far-field monopole approximation, is understood.