Short Answer:

Coulomb’s law is a basic law in electricity that explains how two electric charges interact. It states that the force between two charges is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them. The force acts along the line joining the two charges.

This force can be either attractive or repulsive depending on the type of charges. Like charges repel each other, and unlike charges attract each other. Coulomb’s law helps in understanding electric forces between particles and is fundamental in studying electric fields and electrostatics.

Detailed Explanation:

Coulomb’s law

Coulomb’s law is a very important principle in electrostatics. It was discovered by French physicist Charles-Augustin de Coulomb in 1785. This law helps to calculate the electric force between two charged particles at rest. It is similar in form to Newton’s law of gravitation, but instead of mass, it deals with electric charge.

Coulomb’s law gives a clear mathematical expression to describe how strongly two charged particles attract or repel each other. It is a quantitative law and is used as a starting point to understand many electrical phenomena in physics and engineering.

Statement of Coulomb’s law

Coulomb’s law states:

“The magnitude of the electrostatic force between two point charges is directly proportional to the product of the magnitudes of the charges, and inversely proportional to the square of the distance between them. The force acts along the line joining the charges.”

Mathematical formula:

F=k⋅∣q1⋅q2∣r2F = k \cdot \frac{{|q_1 \cdot q_2|}}{{r^2}}F=k⋅r2∣q1⋅q2∣

Where:

F = electrostatic force between the charges (in newtons)
q₁ and q₂ = magnitudes of the two point charges (in coulombs)
r = distance between the two charges (in meters)
k = Coulomb’s constant = 8.99×109 Nm2/C28.99 \times 10^9 \, \text{Nm}^2/\text{C}^28.99×109Nm2/C2

The sign of the force depends on the nature of the charges:

If charges are like (both positive or both negative), the force is repulsive.
If charges are unlike (one positive and one negative), the force is attractive.

Nature of electrostatic force

It is a central force: Acts along the line joining the two charges.
It is a conservative force: The work done is stored as potential energy.
It follows the inverse square law: As the distance increases, the force decreases rapidly.
It can act in vacuum or any medium: In a medium, the formula becomes:

F=14πε⋅∣q1⋅q2∣r2F = \frac{1}{4\pi \varepsilon} \cdot \frac{{|q_1 \cdot q_2|}}{{r^2}}F=4πε1⋅r2∣q1⋅q2∣

where ε is the permittivity of the medium.

Importance of Coulomb’s law

Foundation of electrostatics: It is the base for all electric field calculations.
Electric field and potential: The electric field due to a point charge is derived using Coulomb’s law.
Helps in understanding atomic structure: Explains how electrons are bound to the nucleus.
Used in designing electrical components: Such as capacitors, insulators, and electrostatic sensors.

Limitations of Coulomb’s law

It is applicable only to point charges or spherical charged bodies.
It assumes the charges are at rest.
It does not work accurately when charges are in motion or at very short distances (quantum effects dominate).
It assumes a uniform medium between the charges.

Conclusion:

Coulomb’s law explains the electrostatic force between two stationary electric charges. The force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. It plays a key role in the study of electric fields, charge interactions, and is a basic concept in both physics and electrical engineering.