# Coulomb’s Laws of Electrostatics

**Charles-Augustin de Coulomb** discovered the **Laws of Electrostatics** in 1785 known as **Coulomb’s Law**. Until 1784, no one knew about the unit of the electric charge, then Coulomb introduced these laws after multiple experiments on the force between two masses based on the **Inverse Square Law**. Coulomb’s laws of electrostatic can be stated as follow:

**First Law**

Coulomb’s first law states that like charges of electricity repel each other, whereas unlike charges attract each other.

**Second Law**

The second law of electrostatic states that the force exerted between two small charged bodies (point charges) is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

In other words, the electric force of attraction or repulsion between two charged points varies directly as the product of the charged points and inversely as the square of the distance between those charge points.

Coulomb’s Laws of electrostatic can be mathematically represented as follows.

Where:

- F = Force
- Q1, Q2 = Two charged bodies or points
- d = Distance between the two charged bodies
- K = Constant which values depends on the measurement units of F, Q1, and Q2, and characteristics of the dielectric insulating medium between two charged bodies. The constant K is also represented by the symbol of λ (Lambda). The
**value of constant K = 1 / 4πε**in both_{o}ε_{r}**SI**and**MKS systems**.

#### Coulomb’s Laws of Electrostatics in Vacuum & Free Space

If the medium between two charged points is vacuum or free space and the units of measurements are in MKS system (Force (F) in Newtons, Distance (d) in meters and charged body (Q) in Coulombs), then the Coulomb’s force in free space due to absolute permittivity (ε_{o}) of space would be as follows:

Where:

ε_{o} = Absolute permittivity in space

#### Coulomb’s Laws of Electrostatics in a Medium

If the medium between two charged bodies is insulation or dielectric material, then the electrostatic force of repulsion or attraction between them is less than the electrostatic force in free space due to the relative permittivity (ε_{r}) of dielectric material. In that case, the coulomb’s force for such a medium is as follow:

Where:

ε_{r} = Relative permittivity of dielectric material

While the value of ε_{o} is 8.854×10^{-12} F/m and the value of ε_{r} in the air is 1.006. If the values of Q_{1} and Q_{2} are in Coulombs, distance in meters, and ε in farads per meter (F/m), then the value of force (F) is in Newtons. This way, Coulomb’s law can be written as follow:

In short, we have added the value of K which is 1 / 4πε_{o}ε** _{r}**in the first and second laws.

In case of air:

ε_{r} = 1

ε_{o} = 8.854×10^{-12} F/m

Q_{1} = Q_{2} = 1 Coulomb

d = 1 meter

F = 8.997 x 10^{9} N

F = 9 x 10^{9} N (approx.)

Hence, Coulomb’s laws of electrostatic can be written for air, vacuum, and medium as follows.

Coulomb’s Law in Air Vacuum

**F = 9 x 10 ^{9} (Q_{1}Q_{2}/d^{2})**

Coulomb’s Law in a medium

**F = 9 x 10 ^{9} (Q_{1}Q_{2}/ε_{r} d^{2})**

According to the above explanation, a One-coulomb charge can be defined as follow:

When a charge (amount of electricity) is placed in air to another uniform or non-uniform charge separated by the distance of one meter, then the force of repulsion or attraction is 9 x 10^{9} Newton between them.

**Example of Coulomb’s Laws of Electrostatic**

**Example:**

Calculate the electrostatic force of repulsion between two alpha “α” – particles when at a distance of 10^{-13} meters from each other. The charge of an alpha “α” particle is 3.2 x 10^{-19} C. If the mass of each particle is 6.68 x 10^{-27} kg, compare this force with the gravitational force between them. Take the gravitational constant as equal to the 6.67 x 10^{-11} N-m^{2} / kg^{2}.

Solution:

Here, Q1 = Q2 = 3.2 x 10^{-19}

d = 10^{-13} m

Putting the values

= 2.976 ×10^{-37} N

As seen, this force is negligible as compared to the electrostatic force between these two bodies.

Good to know:

**Permittivity (ε):**The capacity of concentrating the electric flux in a dielectric or insulator is called permittivity. It is also known as dielectric constant and represented by the symbol of Epsilon “**ε**“.

** ε = ε _{o} ε_{r}**

For example, the permittivity for mica is 8.854 x10^{-12} x 5 = **44.27 x10-12 F/m** (where ε_{o} for mica is 8.854 x10^{-12 }and ε_{r} is 5.)

**Absolute Permittivity (ε**The ratio of D/E for an electric field in a vacuum in farad per meter (F/m) is called the permittivity of free space or the electric space constant . Where “E” is Electric Field Strength and “D” is the Resulting Flux Density._{o}):

** ε _{o} = D/E = εo ε_{r}**

**Relative Permittivity (ε**It is the ratio of the absolute permittivity “ε” of a material to the absolute permittivity “ε_{r}):_{o}“.

** ε _{r} = ε / ε_{o}**

The value of ε_{r} in space and air is unity (1) i.e. ε_{r} = 1. There is no unit for relative permittivity as it is a ratio between permittivity and absolute permittivity.

- Coulomb’s Law or laws of electrostatic is related to the static electricity and capacitors (static charge) while Faraday’s Law of electromagnetic induction is related to static and dynamic induced EMF, magnetism, and generation of electricity in the alternator.