Coulomb's Law to find the electrostatic force between the charges.

# 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 q1 and q2 placed at a distance r apart then the force between these charges is

1. Along the line joining q1 and q2
2. Proportional to the product of charges i.e. q1q2
3. Inversely proportional to the square of the distance between them i.e. r2

#### Mathematical statement of Coulomb’s Law

Mathematically, it is represented as follows:

$F=k\frac{q_1q_2}{r^2}$

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

Mathematically k is given as,

$k=\frac1{4\pi\varepsilon}$

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

$\varepsilon=\varepsilon_0K$

Here, K is the dielectric constant and ε0 is the permittivity of the free space which is equal to 8.854 × 10-12 F/m.

So, the law becomes,

$\boxed{F=\frac1{4\pi\varepsilon_0K}\frac{q_1q_2}{r^2}}$

#### 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 q1 because of q2; and this will be exactly equal and opposite of the force experienced by q2 because of q1.

The vector form for the force on q2 because of q1 is,

${\overrightarrow F}_{21}=\frac1{4\pi\varepsilon}\frac{q_1q_2}{r^2}{\overset\frown r}_{12}$

Here, F21 is the force on q2 because of q1. r12 is the unit vector along the line joining the charges directing from 1 to 2.

The vector form for the force on q1 because of q2 is,

${\overrightarrow F}_{12}=\frac1{4\pi\varepsilon}\frac{q_1q_2}{r^2}{\overset\frown r}_{21}$

Here, F12 is the force on q1 because of q2. r21 is the unit vector along the line joining the charges directing from 2 to 1.

So it is easily concluded that F12 = – F21.

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