Coulomb’s Law: Definition, Formula, & Constant

Contents

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Key learnings:

Coulomb’s Law Definition: Coulomb’s law defines the force between two stationary, electrically charged particles, known as the electrostatic force.
Electrostatic Force: The electrostatic force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.
Coulomb’s Law Formula: The formula for Coulomb’s law is F = k * (Q1 * Q2) / d², where F is the force, Q1 and Q2 are the charges, d is the distance, and k is Coulomb’s constant.
Coulomb’s Constant: Coulomb’s constant (k) in a vacuum is approximately 8.99 x 10⁹ N m²/C², and it varies with the medium.
Historical Background: Charles-Augustin de Coulomb formalized Coulomb’s law in 1785, building on earlier observations by Thales of Miletus.

What is Coulomb’s Law?

Coulomb’s law (also known as Coulomb’s inverse-square law) is a law of physics that defines the amount of force between two stationary, electrically charged particles (known as the electrostatic force). Coulomb’s law was discovered by Charles-Augustin de Coulomb in 1785. Hence the law and the associated formula was named after him.

Coulomb’s Law Definition

Colomb’s law states that the magnitude of the electrostatic force of attraction or repulsion between two electrically charged bodies is directly proportional to the product of the charge of the charged bodies and inversely proportional to the square of the distance between the center of the charged bodies.

This inverse-square relationship is why the law is also referred to as Coulomb’s inverse-square law.

This concept can be confusing when first introduced. Looking at the formula for Coulomb’s Law below can help you visualize the relationship between charge and distance, and how this influences the electrostatic force (electrostatic force is the electric force between charged bodies at rest. This is also known as the Coulomb force).

Coulomb’s Law Formula

Let us imagine, Q₁ and Q₂ are the electrical charges of two objects.
d is the distance between the center of the objects.

The charged objects are placed in a medium of permittivity ε_oε_r

Then we can write the force ‘F’ as:

The equation above is the formula for Coulomb’s Law. This formula allows us to calculate the electrostatic force that two charges exert on each other.

Statement of Coulomb’s Law

If you would prefer a video explanation, you can watch the video below:

Coulomb’s First Law

Coulomb’s first law states that objects with like charges repel each other, while objects with opposite charges attract each other.

Coulomb’s Second Law

Coulomb’s second law states that the force of attraction or repulsion between two electrically charged objects is directly proportional to the magnitude of their charge and inversely proportional to the square of the distance between them. Hence, according to the Coulomb’s second law,

Where,

‘F’ is the repulsion or attraction force between two charged objects.
‘Q₁’ and ‘Q₂’ are the electrical charged of the objects.
‘d’ is distance between center of the two charged objects.
‘k’ is a constant that depends on the medium in which charged objects are placed. In S.I. system, as well as in M.K.S. system k=1/4πε_oε_r. Hence, the above equation becomes.

The value of ε_o = 8.854 × 10^-12 C²/Nm².

Hence, Coulomb’s law can be written for medium as,

Then, in air or vacuum ε_r = 1. Hence, Coulomb’s law can be written for air medium as,

The value of ε_r would change depends on the medium. The expression for relative permittivity ε_r is as follows;

Principle of Coulomb’s Law

If we have two charged bodies, one positively charged and one negatively charged, they will attract each other at a certain distance. Increasing the charge of one body, while keeping the other unchanged, increases the attraction force.

Similarly, if we increase the charge of the second body keeping the first one unchanged, the attraction force between them is again increased. Hence, the force between the charged bodies is proportional to the charge of either body or both.

By keeping the charges fixed at Q₁ and Q₂, bringing them closer increases the force between them, while moving them apart decreases the force.

If the distance between the two charge bodies is d, it can be proved that the force acting on them is inversely proportional to d².

This development of force between two same charged bodies is not the same in all mediums. As we discussed in the above formulas, ε_r would change for various medium. So, depends on the medium, creation of force can be varied.

Limitations of Coulomb’s Law

Coulomb’s law is valid if the average number of solvent molecules between the charged particles is large.
Coulomb’s law is valid, if the point charges are at rest.
It is difficult to apply the Coulomb’s law when the charges are in arbitrary shape. Hence, we cannot determine the value of distance ‘d’ between the charges when they are in arbitrary shape.

Who Invented Coulomb’s Law?

Coulombs law was first observed in 600 BC by Greek philosopher Thales of Miletus. if two bodies are charged with static electricity, they will either repulse or attract each other depending upon the nature of their charge. This was just an observation but he did not establish any mathematical relation for measuring the attraction or repulsion force between charged bodies.

After many centuries, in 1785, Charles Augustin de Coulomb who is a French physicist published the actual mathematical relation between two electrically charged bodies and derived an equation for repulsion or attraction force between them. This fundamental relation is most popularly known as Coulomb’s law.