Coulomb's Law

Coulomb's Law describes the force acting between static electrically charged particles. It helped in the development in the theory of electromagnetism.

Like charges repel and unlike charges attract. In this charged particles exert electric forces. Coulomb's law tells us about the electric force between two point

charges. Point charges are charges whose dimensions are very small, i.e., they can be considered single dimensioned.


Consider two charges q1 and q2 separated by a distance r. We are not going to talk about the magnitude or nature of the charges here.

Coulomb's Law states that the force between two point charges is:

1. Inversely proportional to the square of the distance between the charges

∴The force between two point charges increases as the force between them decreases and decreases as the distance between them increases.
 

    2. Directly proportional to the product of magnitude of the charges.
 

 

 ∴The force between two point charges increases as the magnitude of the charges increases. It doesn't talk about the nature of charges and only tells us about the magnitude of force.
 
   3. It acts along the line which joins the two charges.

Combining 1. and 2. :

When we remove the proportionality sign, a constant k is added.

This is the scalar form of the law, i.e, it only talks about the magnitude of force and not the direction. The direction is always along the line joining the two point charges and hence we add a unit vector. (I've not shown it here)

This is Coulomb's Law.

 

Constant k

k = 9.0 x 10⁹ N. m² / C²

The value of k was later experimentally determined and defined as :

                                                

Where ε₀ (epsilon knot) is the permittivity of free space = 8.85 × 10⁻¹²  C²⋅N⁻¹⋅m⁻²

 

 

Bibliography:

https://en.wikipedia.org/wiki/Coulomb%27s_law

https://en.wikipedia.org/wiki/Vacuum_permittivity