Help! Question on the electric force?

Question

An electron is released a short distance above the surface of the Earth. A second electron directly below it exerts an electrostatic force on the first electron just great enough to cancel the gravitational force on it. How far below the first electron is the second?

Answer 1

To solve this problem one needs to set the gravitational force experienced by the electron due to the Earth (9.81 m/s^ towards the ground) equal to the electrostatic force experienced by the electron due to the other electron.

If we call the direction towards the found negative and the upward direction positive then,
Gravitational force due to the Earth = m_e * g
Electrostatic force due to the other electron = (k_e * q^2) / (r^2)
Where q is the charge on the electron, m_e is the mass of an electron, and r is the distance between the electrons.

The sum of these two should be zero so,
-m_e * g = (k_e * q^2) / (r^2)
And now we want to solve for the distance between the electrons, r.

r^2 = (k_e * q^2) / (m_e * -g)

k_e = 8.99 E9 N (m/C)^2
q = 1.60 E-19 C
m_e = 9.11 E-31 kg
-g = 9.81 m/s^2

r^2 = 25.75 meters^2
r = sqrt (25.75 m^2)
r = 5.07 meters

So the electrons are a little more than 5 meters apart.