Two iron spheres each have a volume of 10 cm^3 and a mass of 78g. How many electrons must be placed on each sphere so that the electrostatic force of repulsion between them just balances the force of gravitational attraction? Assume the distance between the spheres is more than 2 meters.

Answer 1

You can treat the spheres as point charges at R >2m separation. If e is the charge on each sphere, for the electrical repulsion to equal the gravitational attraction,

G M^2 /R^2 = k Q^2/R^2

GM^2 = k Q^2

G is the Newton gravity constant and k is the Coulomb law constant

Solve for Q. The number of electrons is Q/e.
e is the elctron charge.