Coulomb’s Law of Electrical Force

Coulomb’s Law Statement

According to Coulomb’s law of electrical force,  the electrostatic force between two point charges is directly proportional to the product of their magnitude and inversely proportional to the square of distance between their centres.

This electrical force can be repulsive or attractive depending upon whether the charges are like or unlike. Also the force always acts along the line joining the centre of the two charges.

Let’s consider two point charges Q₁ and Q₂ held d distance apart in vacuum as shown in Fig.1.

According to Coulomb’s law, the magnitude of electrical force between the charges is given by :

Or,

……………. (1)

Where k is a constant whose value depends upon the medium in which the charges are placed and the system of units employed.

In S.I unit force is measured in newtons, charge in coulombs, distance in meters and the value of k is given by :

Where ϵ₀ = Absolute permittivity of vacuum in air

ϵ_r  = Relative permittivity of the medium in which the charges are placed (for vacuum or air, its value is 1)

The value of  ϵ₀ = 8.854 × 10^-12 F/m and the value of ϵ_r is different for different media.

…………….. (2)

Now,

So,

………… (3) in medium

and,

…………. (4) in air

Absolute Permittivity

Permittivity is the property of a medium that affects the magnitude of force between two point charges. The greater the permittivity of the medium, the lesser the force between the charge bodies placed in it and vice-versa.

Air or vacuum has  a minimum value of permittivity.

The absolute or actual permittivity  of air or vacuum (ϵ₀) is 8.854 × 10^-12 F/m.

The absolute permittivity (ϵ) of all other insulating material is greater than ϵ₀.

The ratio ϵ /ϵ₀ is known as relative permittivity of the material and it is denoted by ϵ_r .

So, ϵ_r = (ϵ /ϵ₀)

Where  ϵ =  absolute permittivity of the material

ϵ₀= absolute or actual permittivity  of air or vacuum

ϵ_r = relative permittivity of the material

Relative permittivity (ϵ_r )of air is equal to 1.