# How Strong is the Coulomb Force Relative to the Gravitational Force?

How Strong is the Electrostatic or Coulomb Force Relative to the Gravitational Force? To find this we will calculate the electrostatic force and the gravitational force between an electron and proton separated by 0.530×10-10 m. (This distance is their average separation in a hydrogen atom)

This will give us an estimate of the relative strength of the electrostatic force and the gravitational force.
[ Note: Electrostatic force is also known as Coulomb’s force]

## Calculate the electrostatic force between an electron and a proton

To find this we will use the equation of Coulomb’s law: F = k | q1q2 | / r2 ….. (1)
k = 8.99×109 N m2 / C2

q1= q2 = 1.60×10-19 Coulomb

r = 0.530×10-10 meter

The electrostatic force between an electron and a proton = F = k | q1q2 | / r2

F = (8.99×109 ) (1.60×10-19 ) (1.60×10-19 ) /(0.530×10-10 )2
=> F = 8.19×10-8 N.

The charges are opposite in sign, so this is an attractive force. This is a very large force for an electron.

## Calculate the gravitational force between an electron and a proton

The gravitational force is given by Newton’s law of gravitation as:
FG = GmM/r2 ……………(2)

Here, G = universal gravitational constant = 6.67 x 10-11 N m2 kg-2

Here m and M represent the electron and proton masses, m = 9.11×10-31 kg and M = 1.67×10-27 kg

Now, putting these values in equation (2) above, we get the value of the gravitational force FG = 3.61×10-47 N

This is also an attractive force (gravitational force is always attractive)

## Comparison of electrostatic force and gravitational force between an electron and proton

The ratio of the magnitude of the electrostatic force to the gravitational force between an electron and proton, is, thus,
F /FG = 8.19×10-8 N / 3.61×10-47 N = 2.27×1039

Conclusion: Electrostatic force(or Coulomb force) is remarkably larger than the gravitational force.

Note that this will be the ratio of electrostatic force to gravitational force for an electron and a proton at any distance (taking the ratio before entering numerical values shows that the distance cancels).

This ratio gives some indication of just how much larger the Coulomb force is than the gravitational force between two of the most common particles in nature.

How Strong is the Coulomb Force Relative to the Gravitational Force?
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