# Coulomb’s Law

We know that charged bodies exerts force on each other and force between these two charges is known as the electric interaction. An experimentation and studies of these charges have shown that

1. There are only two types of charges, positive and negative
2. Unlike charges attract each other
3. Like charges repel each other

Coulomb studied about these charges and his conclusion is that if the charged bodies were small as compared to distance between them, then the force between them depends on the magnitude of charge and distance between them. After experimentation, he formulated a law determining the force between charges called coulomb’s law. According to this law the force between two charges is

1. directly proportional to the product of the quantity of charges
2. inversely proportional to the square of the distance between them
3. the direction of force lies along the line joining the centers of charged body

Let $Q_1$ and $Q_2$ be magnitude of charges which are separated by the distance $r$ then we have

$F \propto Q_1 Q_2$

$F \propto \dfrac{1}{r^2}$

combining above two equations we get

$F \propto \dfrac{Q_1Q_2}{r^2}$

$F = k\dfrac{Q_1Q_2}{r^2}$

where k is proportionality constant called permittivity.

Permittivity

The permittivity k depends on the system of unit used and medium between charges. In SI unit the charge is measured in coulomb, force in Newton and distance in meter. So, permittivity (k) is given by

$k = \dfrac{1}{4\pi\epsilon_0}$

where $\epsilon_0$ is a constant called permittivity of free space. Using this value of k in force equation we got above, we have

$F = \dfrac{1}{4\pi\epsilon_0} \dfrac{Q_1Q_2}{r^2}$

From this we can see that the SI unit of $\epsilon_0$ is $(coulomb)^2(Newton)^{-1}(meter)^{-2}$. The value of $\epsilon_0$ is $8.85 \times 10^{-12}Fm^{-1}$. So,

$\dfrac{1}{4\pi\epsilon_0} = 9 \times 10^9$

It should be noted that permittivity of the medium differs. If charges are for example placed in water or oil, the force between charges is reduced. So, for a medium k is written as

$k = \dfrac{1}{4\pi\epsilon}$

Here $\epsilon$ is called permittivity of the medium. Its value is different for different medium.