Question

An electron is in a vacuum near the surface of the earth where should a second electron be placed so that the net force on the first electron due to the other electron and to gravity is zero?

Answer 1

you'll need to put the 2nd electron vertically between the first electron and the earth.

gravity will pull the 1st electron *down* according to Newton's gravitation law --> F1 = GMm/R^R, where R is the earth's radius (as we are looking to calculate "near" the surface), M is earth mass, m is electron's mass and G is the uni grav constant..

the electrostatic repulsive force will push the electron *up* according to Coulumbs law --->> F1 = ke^2/r^2 where r is the distance between the electrons, e is the charge in coulumbs of an electron, and k is Coulumb's constant.

set F1 = F2 and manipulate so you have an equation for r.