Coulomb Force Strength versus Gravitational Force strength

Last updated on April 20th, 2023 at 05:30 am

Coulomb Force Strength versus Gravitational Force Strength – 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]

Coulomb Force Strength versus Gravitational Force strength – comparison of strengths

As written above, we will first calculate the electrostatic force and the gravitational force between an electron and proton separated by 0.530×10^-10 m. Then we will compare these strength values.

Electrostatic force between an electron and a proton – calculation

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.

Gravitational force between an electron and a proton – calculation

The gravitational force is given by Newton’s law of gravitation as:
F_G = 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 F_G = 3.61×10^-47 N

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

Coulomb Force Strength versus Gravitational Force strength – comparison of strengths

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

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

Also, know about other similarities and differences between electric force (electrostatic force or Coulomb force) and gravitational force.