Consider an electron and a proton separated by a distance of 1.0 nm. a.) calculate the magnitude of the gravitational force between them. b.) calculate the magnitude of the electric force between them. c.) explain how the ratio of these gravitational and electric forces would change if the distance were increased to 1.0 m

1) The gravitational force between the proton and the electron is given by:

where
G is the gravitational constant
is the mass of the proton
is the mass of the electron
is their separation

Substituting the numbers, we have


2) The electric force between the proton and the electron is given by:

where
k is the Coulomb's constant
is the charge of the proton and of the electron (it is the same)
is their separation

Substituting the numbers into the equation, we get


C) The ratio between the two forces is therefore

This ratio would not change if we change the distance between the two particles: in fact, both forces have the same dependance on the distance (as ), therefore they change by the same proportion, so their ratio remains the same.