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 ?

Electric force is times stronger than gravitational force

Explanation:

The gravitational force between two objects is given by:

where

G is the gravitational constant

m1, m2 are the masses of the two objects

r is the separation between the objects

Here we have:

(mass of the proton)

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

So,

The electric force between two charged object is given by

where

k is the  Coulomb constant

q1, q2 are the two charges

r is the separation

Here we have

(charge of the proton)

(charge of the helium nucleus is twice that of the proton)

So,

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

well clustered together.

points close on a scatter diagram