An electron is released above the earth's surface. a second electron directly below it exerts just enough of an electric force on the first electron to cancel the gravitational force on it. find the distance between the two electrons.

The gravitational force on the first electron is equal to its weight:

where  is the electron mass and  is the gravitational acceleration. Substituting, we find that the gravitational force is


Instead, the electric force exerted by the second electron on the first one is

where 
is the Coulomb's constant
is the charge of each electron
r is the distance between them.

The problem says that the distance r is such that the electric force cancels the gravitational force, so the electric force must be equal to the gravitational force:  . So, if we use this value in the formula of the electric force, we can calculate the distance r between the two electrons: