Inside Story

# COULOMB’S LAW

Coulomb’s Law and are also called inverse square law is experimental law of physics, which quantify the electrical force between the two static electrical charges, which is seperated by the some distance r.

The force between the two static electrical charges are called electrostatic force or coulomb’s force. This law was first published in 1785 by the French physicist Charles Augustin de coulomb. Coulomb’s Law is the first step in the development of theory of electromagnetism.

Watch the practical video of coulomb’s Law

In this section we will discuss the coulomb’s Law in details so tuned with us till end.

## DEFINITION

Coulomb performed various experiment to find the force between the two stationary electrical charges.

After a successful experiment C.A de coulomb established the following law known as coulomb’s Law.

*The magnitude of electrostatic force between the two stationary electrical point charges which is seperated by the distance r is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.*

Mathematically it is given as –

F ∝ q1q2

F ∝ 1/r²

F ∝ q1q2/r²

F = Kq1q2/r²

## POINTS TO BE REMEMBERED

1). This law is applicable only for points charges.

2). K is called the proportionality constant and in vaccum it is expressed as 1/4πε0. Where ε0 is called the permittivity of the free space. And it’s numerical value is 8.85×10-¹² C²N-¹m-². In any medium other than vaccum is expressed as

1/4πε , where ε is called the absolute permittivity of the medium.

3). The ratio of ε/ε0 is εr called relative permittivity of the medium or dielectric constant of the medium and also denoted as K. It is a dimensionless quantity.

ε/ε0 = εr = K

4). The value of relative permittivity εr varies from 1 to ∞ , for vaccum it is 1 and for air it is nearly equal to 1 and we take 1 for simipicity in calculations, and for metals it is ∞.

5). If any charge is placed in the medium having relative permittivity εr then the electrostatic force between them is (1/4πεr).q1q2/r²

6). The value of 1/4πε0 is 9×10⁹Nm²C-²

7). The force between the two points charges is always acts along the line joining these two points charges. This force is equal in magnitude but opposite in directions, irrespective of the medium in which they are placed.

8). Electrostatic force is conservative in nature i.e the work done by the electrostatic force to move a charge in close loop of any shape is zero.

9). This electrostatic force is a central force, in the absence of other external force, the angular momentum of one particles with respect to the other particle ( in two partices system) is conserved.

11). Coulomb’s Law is analogous to the gravitational Law because both are inverse square law.

F(g) = Gm1m2/r²

F(e) = Kq1q2/r²

Where G = 6.67×10-¹¹Nm²kg-² and K = 1/4πε0 is 9×10⁹Nm²C-²

After comparing both forces we get –

F(e) = 10³⁹ F(g)

12). This electrostatic force can be attractive or repulsive on the basis of nature of the charge.

If both charges are positive/negative then force is repulsive if they are unlike then the force is attractive.

## COULOMB’S LAW IN VECTOR FORM

Lets take two points charges q1 and q2 which is placed at point A and point B as shown in following figure.

According to coulomb’s Law the magnitude of force on q1 due to q2 and the magnitude of force on q2 due to q1 is given by –

|F12| = |F21| = q1q2/4πε0.r². …….. (1)

Now if

**r**12 is unit vector pointing from q1 to q2 and**r**21 is the unit vector pointing from q2 to q1 then the forces is – F12 = (q1q2/4πε0.r²)

**r**21 ……. (2)[ F12, is the force applied from q2 to q1 along unit vector

**r**21 ] F21 = (q1q2/4πε0.r²)

**r**12 ……. (3)[ F21, is the force applied from q1 to q2 along unit vector

**r**12.From this we can conclude that the unit vector

**r**21 is opposite to the unit vector**r**12.**r**21 = –

**r**12

Then equation (2) becomes –

F12 = -(q1q2/4πε0.r²)

**r**12 ….. (4)(q1q2/4πε0.r²)

**r**12 this force is equal to F21, now the equation (4) becomes – F12 = – F21

This force is equal in magnitude but opposite in directions and this is same as Newton’s third law.

Watch this video for more reference.