Electric Charge
Before you go through this article, make sure that you have gone through the previous article on Electric Charge. It explains the basic concepts related to electric charge.
We have learnt
 Two like point charges repel each other.
 Two unlike point charges attract each other.
In this article, we will discuss about Coulomb’s Law.
Coulomb’s law helps us to calculate the magnitude of Electric Force between two stationary point charges.
Coulomb’s Law
The French physicist Charles Augustine de Coulomb experimentally measured the electric forces between small charged spheres by using a torsion balance.
He formulated his observations in the form of Coulomb’s law.
Coulomb’s law states that The magnitude of force of attraction or repulsion between two stationary point charges is

Let two point charges q_{1} and q_{2} are at rest and separated by a distance r, then they exert a force on each other called electrostatic force.
According to Coulomb’s law, the force F between the two charges is such that
On combining, we get
Or
(Equation01)
Here, k is a constant of proportionality called as electrostatic force constant or Coulomb’s constant.
Coulomb’s Constant
The value of Coulomb’s constant depends upon the following two factors
 the system of unit chosen to measure F, q_{1}, q_{2} and r
 the nature of medium between the two charges
In SI unit,
(Equation02)
Here,
 ε = absolute electrical permittivity of the medium present between the two charges
 ε_{0} = absolute electrical permittivity of the free space
 ε_{r} = relative electrical permittivity of the medium present between the two charges also called as dielectric constant.
What is permittivity?Permittivity is a property of the medium which determines the electric force between two charges present in that medium. 
Using equation02 in equation01, we get
(Equation03)
Dielectric Constant
 The dielectric constant of a material medium can be defined as the ratio of the absolute electrical permittivity of the medium to the absolute electrical permittivity of the free space.
 It is denoted by K.
 It expresses the extent to which a material can hold electric flux in it.
Mathematically,
As it is the ratio of two like entities, it is a unit less and dimensionless quantity. It is a pure number.
The following table lists the value of dielectric constant for different materials
Medium 
Value of Dielectric Constant 
Air / Vacuum  1 
Metals  Infinite 
Water  80 
For free space i.e. air or vacuum, ε_{r} = 1. Hence, equation03 becomes
(Equation04)
Absolute Electrical Permittivity of Free Space (ε_{0})
The value of absolute electrical permittivity of free space (ε_{0}) is given as
Deriving SI unit of ε_{0}–
From equation04, we have
We know, in SI,
 The unit of q_{1} and q_{2} (charges) is coulomb (C)
 The unit of F (force) is newton (N)
 The unit of r (distance) is meter (m)
So, the SI unit of ε_{0} may be calculated as
Deriving Dimensional Formula of ε_{0}–
From equation04, we have
We know,
 The dimensional formula of q_{1} or q_{2} is [AT]
 The dimensional formula of F is [MLT^{2}]
 The dimensional formula of r is [L]
Now, the dimensional formula of ε_{0} can be given as
[ε_{0}] = { [AT] x [AT] } / { [MLT^{2}] x [L]^{2} }
[ε_{0}] = [A^{2}T^{2}] / [ML^{3}T^{2}]
[ε_{0}] = [M^{1}L^{3}T^{4}A^{2}]
Thus,
The dimensional formula of ε_{0} is [M^{1}L^{3}T^{4}A^{2}]. 
Limitations of Coulomb’s Law
The Coulomb’s law suffers from the following limitations
 Coulomb’s law is valid only for stationary point charges.
 It is not a universal law.
 It loses its validity for distances less than 10^{15} m.
 It is difficult to implement Coulomb’s law where charges are in arbitrary shape.
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