Coulombs Law – A force of attraction Cr repulsion acts between two charged bodies. How is this force affected when the quantity of the charge on the two bodies or the distance between them is changed? In order to find the answer of this question, a “French scientist Charles coulomb” performed a number of experiments and found that:
The force of attraction or repulsion between two charged bodies is directly proportional to the product of the quantity of charges on them and inversely proportional to the square of the distance between them.
This law is known as coulombs law after the name of its discoverer.
If the distance between two charged bodies is much greater as compared to their size, the bodies are considered as point charges. Fig. 15.6 shows the force acting on two point charges q1 and q2. F12 is that force which the charge q1 experiences due to q2 and F21 is the force on q2 due to q1. Both these forces F12 and F21 are known as coulumb’s force. They always act along the line joining the two point charges. Fig. 15.6 (a,b) show the two forces when the charges are of the same kind and fig. 15.6 © shows the forces when they are of opposite kinds. The coulumb’s forces F12 and F21 have equal magnitude but always act in opposite directions.
Interesting information
A metallic chain can be seen hanging from the rear side of a petrol supply tanker. This chain rolls on the road as the tanker moves. Due to friction with air, the body of the tanker gets charged and tiny spark can cause havoc. This charge is continuously being transferred to the ground through the metallic chain. Thus the danger of spark is eliminated.
Usually the coulombs force is represented by f.
If the distance between two point charges q1 and q2 is r, coulomb’s law can be, mathematically, written as
Where k is a constant whose value depends upon the medium between the two charges and the system of units in which F, q and r are measured.
For your information
The SI unit of charge is known as coulomb. It is equal to the charge of 6.25 
electrons. This is a very big unit. Usually the charge is measured in micro coulomb (µC). It is given by 
In SI system, if the medium between the two charges is space or air then in this case the value of k will be 9 
.
In order to show the dependence of k upon the medium, usually it is oxpressed in terms of a property of medium known as permittivity. In case of free space it is represented by 
. The relation between k and is given by
By using Eq. 15.2, we can find the force between two points’ charges placed in free space or air.
Example 15. 1: two bodies are oppositely charged with 500 µC and 100 µC. find the force between the two charges if the distance between them in air is 0.5 m.
Solution:
Distance between the charges = r = 0.5 m
Substituting the values in equation of coulomb’s law
= 1800 N
Fig 15.6: coulomb’s force between two point charges q1
Do you know?
During flight, body of an aeroplane gets charged. Its tyres are of some conducting material. As the aeroplane lands, this charge is easily transferred to ground and the danger of sparking is eliminated while petrol is filled in it.