# Coulomb’s Law: Definition, Formula, & Constant

If two electrically charged bodies are placed nearby each other there will be an attraction or a repulsion force acting on them depending upon the nature of the charge of the bodies. The formula for the force acting between two electrically charged bodies was first developed by Charles-Augustin de Coulomb and the formula he established for determining the value of force acting to nearby charged objects is known as Coulomb’s law.

In his law, he stated that to similarly charged (either positive or negative) bodies will repeal each other and two dissimilarly charged bodies (one is positively charged and other is negatively charged) will attract each other. He had also stated that the force acting between the electrically charged bodies is proportional to the product of the charge of the charged bodies and inversely proportional to the square of the distance between the center of the charged bodies.

## Coulomb’s Law Formula

Let us imagine, Q1 and Q2 are the electrical charges of two objects.
d is the distance between the center of the objects.

The charged objects are placed in a medium of permittivity εoεr

Then we can write the force ‘F’ as:

## Statement of Coulomb’s Law

If you would prefer a video explanation, you can watch the video below:

### First Law

Like charged objects (bodies or particles) repel each other and unlike charged objects (bodies or particles) attract each other.

### Second Law

The force of attraction or repulsion between two electrically charged objects is directly proportional to the magnitude of their charge and inversely proportional to the square of the distance between them. Hence, according to the Coulomb’s second law,

Where,

1. ‘F’ is the repulsion or attraction force between two charged objects.
2. ‘Q1’ and ‘Q2’ are the electrical charged of the objects.
3. ‘d’ is distance between center of the two charged objects.
4. ‘k’ is a constant that depends on the medium in which charged objects are placed. In S.I. system, as well as in M.K.S. system k=1/4πεoεr. Hence, the above equation becomes.

The value of εo = 8.854 × 10-12 C2/Nm2.

Hence, Coulomb’s law can be written for mediumas,

Then, in air or vacuum εr = 1. Hence, Coulomb’s law can be written for air medium as,

The value of εr would change depends on the medium. The expression for relative permittivity εr is as follows;

## Principle of Coulomb’s Law

Suppose if we have two charged bodies one is positively charged and one is negatively charged, then they will attract each other if they are kept at a certain distance from each other. Now if we increase the charge of one body keeping other unchanged, the attraction force is obviously increased. Similarly, if we increase the charge of the second body keeping the first one unchanged, the attraction force between them is again increased. Hence, the force between the charge bodies is proportional to the charge of either bodies or both.

Now, by keeping their charge fixed at Q1 and Q2 if you bring them nearer to each other the force between them increases and if you take them away from each other the force acting between them decreases. If the distance between the two charge bodies is d, it can be proved that the force acting on them is inversely proportional to d2.

This development of force between two same charged bodies is not the same in all mediums. As we discussed in the above formulas, εr would change for various medium. So, depends on the medium, creation of force can be varied.

## Limitation of Coulomb’s Law

1. Coulomb’s law is valid, if the average number of solvent molecules between the two interesting charge particles should be large.
2. Coulomb’s law is valid, if the point charges are at rest.
3. It is difficult to apply the Coulomb’s law when the charges are in arbitrary shape. Hence, we cannot determine the value of distance ‘d’ between the charges when they are in arbitrary shape.

## Who Invented Coulomb’s Law?

Coulombs law was first observed in 600 BC by Greek philosopher Thales of Miletus. if two bodies are charged with static electricity, they will either repulse or attract each other depending upon the nature of their charge. This was just an observation but he did not establish any mathematical relation for measuring the attraction or repulsion force between charged bodies.

After many centuries, in 1785, Charles Augustin de Coulomb who is a French physicist published the actual mathematical relation between two electrically charged bodies and derived an equation for repulsion or attraction force between them. This fundamental relation is most popularly known as Coulomb’s law.