**Statement**

It states that

“The magnitude of force between any two point charges either attractive or repulsive, is directly proportional to the product of charges and inversely proportional to the square of the distance between their centres”.

**Derivation**

Consider two point spherical charges of magnitude** q _{1}** and

**q**with distance of separation between them being

_{2}**r**. Force

**F**is exerted between these two charges where

**r̂**is a unit vector indicating the direction of force.

According to Coulomb’s Electrostatics Law, force **F** experienced is:

► Directly proportional to the product of two point charges**F ∝ q _{1}q_{2}**

► Inversely proportional to the square of the separation between the charges

**F ∝ 1 / r**

^{2}► Combining these two relations, we get :

**F ∝ q**

_{1}q_{2}/ r^{2}**F = kq**

_{1}q_{2}r̂ / r^{2}**r̂ **is a unit vector which indicates the direction of force **F** acting between the two charges **q _{1}** and

**q**

_{2}**k**is a proportionality constant equal to

**1 / 4πεo**

*(= 9 x 10*^{9}Nm^{2}C^{-2}).**ε**is known as permittivity of free space or vacuum equal to

_{o}

**8.85 x 10**^{-12}C^{2}Nm^{-2}**Vector Form Of Coulomb’s Law**

In the given figure above, **r̂ _{21} **is a unit vector pointing towards

**q**which shows the direction of force

_{1}**F**on charge

_{2}**q**due to charge

_{1}**q**.

_{2}Similarly, **r̂ _{12 }**is a unit vector pointing towards

**q**which shows the direction of force

_{2}**F**

_{1}_{ }on charge

**q**due to charge

_{2}**q**.

_{1}Thus, the force experienced by charge **q _{1}** due to charge

**q**is

_{2}**F**. According to Coulomb’s Law, we have:

_{2}**F _{2} = kq_{1}q_{2} r̂_{12} / r^{2}**

**—> (1)**

**F _{1} = – kq_{1}q_{2} r̂_{21} / r^{2}**

**—> (2)**

From the figure, it is clearly depicted that both the unit vectors ** r̂_{12}** and

**are oppositely directed. Hence, their forces**

**r̂**_{21}**and**

**F**_{2}**will be also oppositely directed**

**F**_{1}*i.e negative in sign*.

Comparing equations (1) and (2), we get:

**F _{1} = – F_{2}**

This shows us that Coulomb’s Law of Electrostatics conforms with Newton’s third law of motion.

**Coulomb’s Law in Material Media (Dielectric)**

When the medium between the two charges is other than air or vacuum then the force decreases by an amount ** ε_{r}** .

ε is known as the permittivity of material media. For convenience, we replace ε by product of ε_{0}(Permittivity of free space) and ε_{r}(Relative permittivity or Dielectric constant)

Permittivity is the measurement of resistance to the expansion of electric field lines in a medium.

According to electrostatic force of attraction between two charged bodies relatively at rest, its mathematical equation can be deduced as follows:

The medium between any two charges is vacuum or air then electrostatic force of attraction is given by:

**F _{vac} = q_{1}q_{2} / 4πε_{o} r^{2}**

**—> (3)**

And if the medium between any two charges is replaced by other medium ** i.e. Dielectric** then electrostatic force of attraction is given by:

**F _{med} = q_{1}q_{2} / 4πε_{o}ε_{r} r^{2}**

**—> (4)**

From the above equation (4), it is clear that **F **decreases by an amount **ε _{r}**

*(Dielectric constant of the medium)*when dielectric is placed between the two charges other than vacuum or air.

**F _{med} = (1/ε_{r}) q_{1}q_{2} / 4πε_{o} r^{2} —> (5)**

The above equation can also be written as:

**F _{med} = (1/ε_{r}) Fvac —> (6)**

**Limitations of Coulomb’s Law**

**Coulomb’s Law is only applicable to point charges.****Coulomb’s Law is only applicable to spherical charges.****Coulomb’s Law is only applicable for charges at relative rest.**