**Coulomb’s law** is a quantitative statement about the force between two point charges.

When the linear size of charged bodies are much smaller than the distance separating them, the size may be ignored and the charged bodies are treated as **point charges**.

Coulomb measured the force between two point charges and found that it varies inversely as the square of the distance between the charges and was directly proportional to the product of the magnitude of the two charges and acted along the line joining the two charges.

Thus, if two point charges q1, q2 are separated by a distance r in vacuum, the magnitude of the force (F) between them is given by

_{}

where k is a constant of proportionality, called **electrostatic force constant. **The value of k depends on the nature of the medium between the two charges and the system of units chosen to measure F, q_{1 },q_{2} and r.

where ε_{0} is called permittivity of free space.

### Units of charges:

- The SI unit of charge is coulomb. In the above equation, if q
_{1 }= q_{2 }= 1C and r = 1m, then

- In electrostatic cgs system, the unit of charge is known as electrostatic unit of charge (e.s.u. of charge) or statcoulomb (stat C)

- In electromagnetic cgs system, the unit of charge is abcoulomb or electromagnetic unit of charge (e.m.u of charge).

## Coulomb’s Law in vector form

- Let the position vectors of charges q
_{1}and q_{2}be r_{1}and r_{2}respectively [see Fig 1].

*Fig. 1 (a) Geometry and (b) Forces between charges*

- We denote force on q
_{1}due to q_{2}by F_{12}and force on q_{2}due to q_{1}by F_{21}. - The two-point charges q
_{1}and q_{2}have been numbered 1 and 2 for convenience and the vector leading from 1 to 2 is denoted by r_{21}:

In the same way, the vector leading from 2 to 1 is denoted by r_{12}:

Coulomb’s force law between two point charges q_{1} and q_{2} located at r_{1} and r_{2} is then expressed as

The force **F**_{12} on charge *q*_{1} due to charge *q*_{2},

Thus, Coulomb’s law agrees with Newton’s third law.