Coulomb's law of electrostatic (in scallar form)

 Coulomb's law of electrostatic (Scalar form) 

We know the like charges reple each other and unlike charges attract each other. The force between two charges is given by coulomb's law. This is an electric analogue of newton's law of gravity. 

Statement:

It states that electrostatic force of attraction or repulsion between two charged bodies is directly proportional to the product of their charges and various inversely as the square of the distance between the two bodies. 

The force is also depends on the nature of the intervening medium and it act along the line joining two charges. 

Suppose two point charɡes q₁ and q₂ are situated at a distance r from each other in same medium. The maɡnitude of the electrostatic force F which one exerts on the other will be ɡiven by

    F ∝ q₁q₂  and  F ∝ 1/r² (inverse square law)

Combininɡ,

             F ∝ q₁q₂/r²    or    F ∝ β q₁q₂/r²

Where β is a constant of proportionality. In fact, the value of β depends on the nature of the medium in which the two charges are situated. It also depends on the units in which the quantities F, q₁, q₂ and r are measured. 

Coulomb's law is strictly true for point charges only. 

Units:

1) In C.G.S. (e.s.u.) system:

In C.G.S. (e.s.u.) system, β = 1/K

Where K = dielectric constant of the medium. 

Mathematical form of Coulomb's law in this system is -    

             1    q₁q₂      

     F=  —    ——             ( for any medium) 

           K        r²

In free space,       K = 1

         F = q₁q₂/r²             (for free space) 

2) In S.I. units:

In S.I. units,  β = 1/4πɛ = 1/4πɛ₀ɛr

Where ɛ₀ and ɛr are the absolute permittivity and relative permittivity, respectively. 

Mathematically, Coulomb's law can be written as :

     F = 1/4πɛ₀ɛr × q₁q₂ /r²   (for any medium) 

For free space, ɛr = 1

∴       F = 1/4πɛ₀ × q₁q₂ /r²    (for free space) 

 Some observations of coulomb's law:

1. Coulomb obtain this law to experiment so, it is basically and experiment law. 
2. The law is strictly applicable in case of a point charges. If a charged body possesses negligible dimensions the charge is said to be a point one. 
3. Each charges extract the some force on each other. 
4. Coulomb's force between two charges matually interaction. 
5. Coulomb's interaction is not affected by the present of other charges in the neibourhood. 
6. It is applicable only the charges at rest. While dealing with force between charges in motion, the expression has to be modified. 
7. Coulomb's law of electrostatic is not valid if r is less than 10^-15m.
8. Coulomb's force is attractive for dissimilar charges and while it is repulsive for similar charges. 
9. The magnitude of the force depend upon the magnitude of the charges separation between them and also depend upon the nature of the medium in between them. 
10. Coulomb's force is a central force that is the force acting alone the link joining the two charges. 
11. Coulomb's force is conservative nature i.e the work done by the electrostatic force over a closed path is zero and it independ of the path follow.