# Coulomb's Law in Electrostatics

Coulomb's law in electrostatics is the electrical analog of Newton's law of gravitation. In 1785, Coulomb measured the force of attraction or repulsion between two electrical charges by using a torsion balance. His observations are known as Coulomb's law in electrostatics.

It states that two-point charges attract or repel each other with a force that is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them.

The force is repulsive if the charges are alike and attractive in case of unlike charges. Further, the electrostatic force between two charges is central in nature. It may be pointed out that Columb's law in electrostatics holds for stationary charges. Further, the two charges should be points in size. Consider that two charges q, and q2 are present at points A and B at a the distance r apart as shown in Fig. 1.03. Then, the force between the two charges, Combining the equations (1.01) and (1.02), we have

F  q1q2..............................(1.01)

1/r^2.............................(1.02)
Combining the equations (1.01) and (1.02), we have
F ∝ q1q2/r2
Or
F=k(q1q2/r2)

where k is the constant of proportionality. Its value depends upon the nature of the medium in which the two charges are located and also the system of units adopted to measure F, q1,q2 and r. In SI, when the two charges are located in a vacuum or air,

k=1/4π€

where E, is called the absolute permittivity of free space. Therefore, from equation (1.03), the force between two charges located in air or vacuum  given by

Fvac= 1/4π€. q1q2/r2

The absolute permittivity of free space is measured to be
€=8.854 x 10-12 C² N-1 m-²

= 1/4π8.854 x 10-12 C² N-1 m-² .

=9x10⁹ Nm² C-2

Hence, the equation (1.04) may be written as

Fvac = 9 x 10^9 x q1q2/r^2 (in newton)........(1.05)

## SI Unit of charge

In SI, the force between two charges ₁ and 2 held at a distance r apart in a vacuum is given by

F= 9 × 10⁹ × 2^9 x q₁ q₂/r^2

Suppose that q₁ q₂ = q (say); r = 1 m and Fie = 9 × 10⁹ N

Then,

9 × 10⁹=9 × 10⁹ q₁ q₂/r^2
or

q² =1
q= + or  - 1 coulomb (C)

Therefore, one coulomb is a charge which repels an equal and similar charge with a force of 9×10° N, when placed in a vacuum (or air) at a distance of one meter from it.

Note. 1. In an electrostatic cgs system, the unit of charge is known as the electrostatic unit of charge (e.s.u. of charge). It is also called statcoulomb (stat C)

1 C=3 x 10⁹ stat C

2. In an electromagnetic cgs system, the unit of charge is known as the electromagnetic unit of charge (e.m.u. of charge).

1 1C=  1/10 e.m.u. of charge