# What is Coulomb’s Law?

French physicist, Charles-Augustin de Coulomb, has observed that there is an interaction or a force between two charged particles. He formulated this force as an electrostatic force and known as Coulomb’s Law.

## The statement of Coulomb’s Law

Coulomb’s Law states that, if there are two charges q_{1} and q_{2} placed at a distance r apart then the force between these charges is

- Along the line joining q
_{1}and q_{2} - Proportional to the product of charges i.e. q
_{1}q_{2} - Inversely proportional to the square of the distance between them i.e. r
^{2}

#### Mathematical statement of Coulomb’s Law

Mathematically, it is represented as follows:

Here, k is the proportionality constant which depends on the surrounding medium within which the charges are placed.

Mathematically k is given as,

Here, ε is the permittivity of the medium which is given as,

Here, K is the dielectric constant and ε_{0} is the permittivity of the free space which is equal to 8.854 × 10^{-12} F/m.

So, the law becomes,

#### Coulomb’s Law in Vector form

According to Coulomb’s Law, there is a force between two point charges. But force is a vector quantity and one must state the direction of that force too.

This force which is also called as a Coulombic force is experienced by one charge because of the remaining one. In other words, the force is experienced by q_{1} because of q_{2}; and this will be exactly equal and opposite of the force experienced by q_{2} because of q_{1}.

The vector form for the force on q_{2} because of q_{1} is,

Here, F_{21} is the force on q_{2} because of q_{1}. r_{12} is the unit vector along the line joining the charges directing from 1 to 2.

The vector form for the force on q_{1} because of q_{2} is,

Here, F_{12} is the force on q_{1} because of q_{2}. r_{21} is the unit vector along the line joining the charges directing from 2 to 1.

So it is easily concluded that F_{12} = – F_{21.}

From the above vector forms, it is also evident that the like charges repel each other while unlike charges attract each other.

*Suggested Read: What is Electromagnetics?*

*Suggested Community: Electromagnetics for GATE & ESE*

Tag:Electromagnetism