A proton is placed 100 micrometers from a helium nucleus. Gravity pulls the proton and nucleus together, while the electric force pushes them apart. Which is stronger, and by how much?

The electric force is times stronger than the gravitational force

Explanation:

The magnitude of the electrostatic force between two charges is given by:

where:

is the Coulomb's constant

are the two charges

r is the separation between the two charges

In this problem:

(charge of the proton)

(charge of a nucleus of helium, twice the charge of a proton)

So the electric force is

Instead, the magnitude of the gravitational force between two objects is given by :

where

is the gravitational constant

m1, m2 are the masses of the two objects

r is the separation between them

Here we have:

is the mass of the proton

is the mass of a nucleus of helium (4 times the mass of the proton)

is the separation

So the gravitational force is

So, we see that the electric force is much stronger than the gravitational factor, by a factor of: