# COULOMB’S LAW: Understand With Examples

## What are Electrostatics? and Electric Force?

The study of electric charges at rest under the action of electric forces is known as electrostatics. An electric force is a force that holds the positive and negative charges that make up atoms and molecules. The human body is composed entirely of atoms and molecules, thus we owe our existence to the electric force

## COULOMB’S LAW

We know that there are two kinds of charges, namely, positive and negative charges. The charge on an electron is assumed to be negative and the charge on a proton is positive Moreover, we also learned that like charges repel each other and unlike charges attract each other. Now we investigate the quantitative nature of these forces. The first measurement of the force between electric charges was made in 1874 AD by Charles Coulomb, a French military engineer. On the basis of these measurements, he deduced a law known as Coulomb’s law. It states that

### What is k in coulomb’s law?

The force between two point charges is directly proportional to the product of the magnitudes of charges and inversely proportional to the square of the distance between them. It is mathematically expressed as (f=kq1q2/r^2)

where F is the magnitude of the mutual force that acts on each of the two-point charges q. q and r is the distance between them/The force Falways acts along the line joining the two-point charges (Fig. 12.1), k is the constant of proportionality. Its value depends upon the nature of the medium between the two charges and the system of units in which F, q, and rare are measured. If the medium between the two-point charges is free space and the system of units is SI, then k is represented as

where (3) is an electrical constant known as permittivity of free space In SI units its value is 8.85 × 10 Substituting the value of E, the constant

As stated earlier, Coulombs’ force is mutual force, it means that if q, exerts a force on q. then q, also exerts an equal and opposite force on q. If we denote the force exerted on q, by q. as F and that on charge q, due to q as F. then

F₁₂ = -Far

(12.4)

The magnitude of both these two forces is the same and is given by Eq. 12.3. To represent the direction of these forces we introduce unit vectors. If, is the unit vector directed from qto q, and r is the unit vector directed from q, to q.. then

1 9192 21 1 9,92 12 F₁ = F₁ =

12.5 (a)

and

12.5 (b)

The forces F₂, and F, are shown in Fig. 12.2 (a & b). It can be seen that =-F2, so Eqs. 12.5 (a & b) show that

F₁₁ = – F₁₂

The sign of the charges in Eqs. 12.5 (a & b) determine whether the forces are attractive or repulsive.

## What is coulomb’s constant?

We shall now consider the effect of medium between the two charges upon the Coulomb’s force. If the medium is an insulator, it is usually referred to as the dielectric. It has been found that the presence of a dielectric always reduces the electrostatic force as compared with that in free space by a certain factor which is a constant for the given dielectric. This constant is known as relative permittivity and is represented by & The values of relative permittivity of different dielectrics are given in Table 12.1.

Thus Coulomb’s force in a medium of relative permittivity

E is given by

F=

1 9.9

(12.6)

It can be seen in the table that e. for air is 1.0006. This value is so close to one that with negligible error, Eq. 12.3 gives the electric force in the air.