We commonly say that opposite electric charges attract and like charges repel. More precisely, charged objects exert an electrostatic force on one another. Because this force can be measured, a key question arises: How does the magnitude of this force depend on the size of the charges and the distance between them?

In the late 18th century, French physicist Charles-Augustin de Coulomb investigated this interaction using a precise instrument called a torsion balance. He discovered that the electrostatic force between two point charges follows a fundamental rule:

• Directly proportional to charge: The force increases as the magnitude of either charge (q₁ or q₂) increases.
• Inverse-square relationship: The force decreases rapidly as the distance (r) between the charges increases—specifically, inverse to the square of the distance (¹⁄_r²).

This mathematical relationship is known as Coulomb's Law:

Where:

• F is the magnitude of the electrostatic force in Newtons (N)
• q₁ and q₂ are the amounts of charge in Coulombs (C)
• r is the separation distance between the centers of the charges in meters (m)
• k is Coulomb's constant (≈ 8.99 × 10⁹ N·m²/C²)

Much like Newton's Law of Universal Gravitation, Coulomb's Law shows how fundamental forces operate across space. However, while gravity is always attractive, the electrostatic force can be either attractive or repulsive depending on the signs of the interacting charges.