890
Coulomb's law is
F = k * q1 * q2 / r^2
where
F = force
k = Coulomb's constant 8.99x10^9 N m^2/C^2
q1,q2 = signed charges
r = distance between charges
Since the charges are the same, let's simplify the equation, solve for q, then substitute the known values and calculate.
F = k * q1 * q2 / r^2
F = k * q^2 / r^2
F*r^2 = k * q^2
F*r^2/k = q^2
sqrt(F*r^2/k) = q
sqrt(4.57x10^-21 N * (0.2m)^2 / (8.99x10^9 N m^2/C^2)) = q
sqrt((4.57x10^-21 N * 0.04m^2) / (8.99x10^9 N m^2/C^2)) = q
sqrt((1.828x10^-22 N*m^2) / (8.99x10^9 N m^2/C^2)) = q
sqrt(2.03337x10^-32 C^2) = q
1.42596x10^-16 C = q
So each sphere has to have an excess of 1.42596x10^-16 Coulombs of electrons. A coulomb is 6.24150934x10^18 electrons, so let's do the multiplication:
1.42596x10^-16 * 6.24150934x10^18 = 8.9001426584664x10^2 = 890
So each sphere has an extra 890 electrons.
