## Explanation of Coulomb’s Law

It 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.### Statement of Coulomb’s Law

#### First Law

Like charge particles repel each other and unlike charge particles attract each other.

#### Second Law

The force of attraction or repulsion between two electrically charged particles is directly proportional to the magnitude of their charges and inversely proportional to the square of the distance between them.

### Formulas of Coulomb’s Law

According to the Coulomb’s second law,

Where,

- ‘F’ is the repulsion or attraction force between two charged bodies.
- ‘Q
_{1}’ and ‘Q_{2}’ are the electrical charged of the bodies. - ‘d’ is distance between the two charged particles.
- ‘k’ is a constant that depends on the medium in which charged bodies are presented. In S.I. system, as well as M.K.S.A. system k=1/4πε. Hence, the above equation becomes.
- Coulomb’s law is valid, if the average number of solvent molecules between the two interesting charge particles should be large.
- Coulomb’s law is valid, if the point charges are at rest.
- 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.

The value of ε_{0} = 8.854 X 10^{-12} C^{2}/Nm^{2}.

Hence, Coulomb’s law can be written for medium as,

Then, in air or vacuum ε_{r} = 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 ε_{r} 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 second body keeping first one unchanged, the attraction force between them is again increased. Hence, force between the charge bodies is proportional to the charge of either bodies or both.

Now, by keeping their charge fixed at Q_{1} and Q_{2} 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 d^{2}.

This development of force is not same for 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.