Coulomb’s law, named after French physicist Charles-Augustin de Coulomb, describes the electrostatic interaction between two point charges. This law quantifies the force of attraction or repulsion between charges and provides insights into how the strength of this interaction depends on the charges’ magnitudes and the distance between them.

Mathematically, Coulomb’s law is expressed as:

F=k⋅r2q1​⋅q2​​

Where:

• $F$ is the magnitude of the electrostatic force between two charges.
• $k$ is Coulomb’s constant, a proportionality constant that depends on the medium between the charges. In vacuum, $k$ is approximately 8.9875×109 N m2/C28.9875×109N m2/C2.
• q1​ and q2​ are the magnitudes of the charges.
• $r$ is the distance between the charges.

Key points about Coulomb’s law:

1. Inverse Square Law: Coulomb’s law follows an inverse square relationship, meaning that the force between charges decreases as the square of the distance between them increases. This reflects the spreading of the electric field in three-dimensional space.
2. Attraction and Repulsion: Like charges (positive-positive or negative-negative) repel each other, resulting in a positive force. Unlike charges (positive-negative) attract each other, resulting in a negative force.
3. Magnitude of Force: The force is directly proportional to the product of the charges and inversely proportional to the square of the distance. Larger charges or smaller distances lead to stronger forces.
4. Superposition Principle: If there are multiple charges present, the total force on a charge is the vector sum of the individual forces due to each charge.
5. Vector Nature: The force between charges is a vector quantity, meaning it has both magnitude and direction. It follows the line connecting the charges and is attractive if the charges have opposite signs and repulsive if they have the same sign.
6. Unit of Charge: In SI units, charge is measured in coulombs (C). The elementary charge $e$ is the charge of a single proton or electron and is approximately 1.602×10−19 C1.602×10−19C.
7. Permittivity: Coulomb’s constant $k$ includes the electric permittivity of the medium between the charges. Different materials have different permittivities, affecting the strength of the electric field and force between charges.

Coulomb’s law is fundamental to understanding the behavior of charged particles in various physical and chemical systems. It provides the basis for the study of electrostatics, the behavior of charged particles in electric fields, and the interactions between charged particles in different contexts.