When the metals touch together, half the charge of the charged metal flows to the other because the electrons all repel each other. Therefore this also means that each metal ball contains the same amount of electrons. Each ball has 5^10 electrons, this is equivalent to a total charge of:
Q1 = Q2 = (1.602 * 10^-19 coulombs / electron) 5^10 electrons = Q
Q = 1.564 * 10^-12 C
Now using the Coulombs law to find for the electric force:
F = k q1 q2 / r^2 = k (Q)^2 / r^2
where k is a contant = 9 * 10^9 N m^2 / C^2
r = the distance of the two metals = 0.2 m
So,
F = (9 * 10^9 N m^2 / C^2) (1.564 * 10^-12 C)^2 / (0.2 m)^2
F = 5.51 * 10^-13 N
Since the two metals repel therefore they are the one which exerts the force hence the magnitude must be negative:
F = - 5.51 * 10^-13 N
