Coulomb’s Law is a fundamental principle in physics that describes the electrostatic interaction between charged particles. The interaction between two fixed point charges results in either attraction or repulsion, with the amount of the force being directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

 Let ‘r’ represent the separation between two point charges, denoted as q1 and q2.Coulomb’s law states that the amount of the mutual force, denoted as F, acting on two charges, q1 and q2, is given by the equation 

F = (|q1| × |q2|) / r×r, where r represents the distance between the charges. 

The equation can be expressed as F = K (|q1| × |q2|) / r×r, where K represents a constant of proportionality. The determination of the value of K is contingent upon the specific medium in which two point charges are situated. In the International System of Units (SI).  The value of K, which represents the electrostatic constant in vacuum or air, is equal to the reciprocal of 4πε0.The constant ε0, which has a value of 8.85 × 10^–12 C^2/N-m^2, is commonly referred to as the “permittivity” of free space. Therefore, the equation for the force (F) between two point charges (q1 and q2) separated by a distance (r) can be expressed as

F = 1/(4πε0) (|q1| × |q2|) / r×r   …. (2)

, where ε0 is the permittivity of free space. This equation is approximately equal to 9 × 10^9, as denoted by equation (2).

2.1 The Permittivity of a Medium

If the medium separating the two point charges q1 and q2 is not a vacuum or air. The electrostatic force between two charges can be expressed as

F = 1/(4πε) (|q1| × |q2|) / r×r   …. (3)

where ε0 represents the vacuum permittivity and εr denotes the relative permittivity.

 In equation (3), the symbol ε represents the product of ε0 and εr, which is commonly referred to as the ‘absolute permittivity’ or simply ‘permittivity’ of the medium. The term εr, on the other hand, denotes a dimensionless constant known as the ‘relative permittivity’ of the medium. It is important to note that εr remains constant for a certain media. The symbol εr is occasionally referred to as the “dielectric constant” or “specific inductive capacity” of the medium.

2.2 COLOUMB’S LAW AS A VECTOR

The vector representation of Coulomb’s law can be expressed as follows:

Vector F = K (|q1| × |q2|) / r×r   …. (4)

where K represents the Coulomb constant, q1 and q2 denote the magnitudes of the charges, and r represents the distance between the charges.

The unit vector originates from the source of the force. To illustrate, in order to determine the force acting on q2, the reference point of the unit vector is located at q1. It is imperative to indicate the signs of the charges clearly in equation (4). In the context where F represents the magnitude of the force, the expression “Vector F = + (F × unit vector)” denotes a repulsive force, while the expression “Vector F = – (F × unit vector)” signifies an attractive force.