Understanding Coulomb's Law: Calculating Force Between Two Point Charges in Different Mediums

Coulomb’s Law – Force between two point charges

Note:- This law is strictly applied to a stationary point charges.

Consider two point charges q1 and q2, both are placed in vacuum (or in air or in free space) and separated by a distance r.

Due to charge there is interaction between the charges. Interaction means force between the charges.

This force may be attractive or repulsive in nature. If both the charges are of same nature that is both are positive or both are negative then repulsive force act.

If one charge is positive and other is negative then attractive force act between them.

According to Coulomb’s law, interaction (force) acting between two point charges is

(i) directly proportional to product of magnitude of charges

[latex]F \propto q_{1} \times q_{2} \text{ ……………(i)} [/latex]

and (ii) inversely proportional to square of distance (i.e separation ) between the charges.

[latex]F \propto \frac{1}{r^{2}} \text{……………(ii)} [/latex]

combining both equations

[latex]F \propto \frac{q_{1} \times q_{2}}{r^{2}} [/latex]

[latex]F = k \frac{q_{1} q_{2}}{r^{2}} [/latex]

Here k is a constant of proportionality and also known as electrostatic force constant for coulomb law.

[latex]k = \frac{1}{4\pi \varepsilon _{0}} \text{…..(This is for Air / Vacuum / free space)} [/latex]

The value of k is different for different type of medium.

[latex]k = \frac{1}{4\pi \varepsilon } \text{ …..(This is for medium only)} [/latex]

[latex]where \hspace{1cm} \varepsilon = \varepsilon_{0} \times \varepsilon_{r} [/latex]

Here ℇ <sub>0</sub>  is known as absolute electrical permittivity of air/vacuum/free space between the two charges.

Here ℇ is known as absolute electrical permittivity of the dielectric medium between the two charges.

Here ℇr is known as relative electrical permittivity.