State Coulomb’s Law.

Short Answer

Coulomb’s Law explains the force between two electric charges. It states that the electric force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. This means the force increases when charges are bigger and decreases when they are farther apart.

The force can be attractive or repulsive. Like charges repel each other, while unlike charges attract. Coulomb’s Law helps us calculate the strength of this force and understand how electric charges interact in different situations.

Detailed Explanation

Coulomb’s Law

Coulomb’s Law is one of the most important principles in electrostatics. It describes how two charged objects interact with each other. This law was discovered by the French scientist Charles-Augustin de Coulomb in the 18th century. It gives a mathematical and conceptual way to understand the electric force between two charges.

According to Coulomb’s Law, the force between two point charges depends on three main factors:

  1. The amount of charge on each object
  2. The distance between them
  3. The medium between the charges

The law can be stated as follows:
The force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.

Direct proportionality to charges

If the amount of charge on one or both objects increases, the electric force between them also increases. For example, if one charge is doubled, the force also doubles. If both charges are doubled, the force becomes four times stronger. This shows that larger charges exert a stronger influence on each other.

Inverse square relationship with distance

Coulomb’s Law also says that the force becomes weaker as the distance between the charges increases. The force decreases with the square of the distance. This means if the distance is doubled, the force becomes one-fourth. If the distance is tripled, the force becomes one-ninth. This inverse square rule is similar to the law of gravitation.

This relationship shows that even a small change in distance can greatly affect the strength of the electric force.

Nature of the electric force

Coulomb’s Law also explains whether the force is attractive or repulsive.

  • If both charges are positive, they repel each other.
  • If both are negative, they also repel each other.
  • If one charge is positive and the other is negative, they attract each other.

The force acts along the straight line joining the two charges. This is called a central force because it acts directly toward or away from the center of the charges.

Mathematical form

Coulomb’s Law can be written in mathematical form as:

F = k (q₁ × q₂) / r²

Here,

  • F is the electric force,
  • q₁ and q₂ are the charges,
  • r is the distance between them,
  • k is the Coulomb constant, whose value in air or vacuum is approximately 9 × 10⁹ N m²/C².

This formula helps us calculate the exact force between two charges placed at a certain distance.

Role of the medium

The medium between the charges can also affect the force. Coulomb’s Law works best in air or vacuum. If the charges are placed in water, glass, or other materials, the force becomes weaker because these materials reduce electric interaction. This is why the law sometimes includes a factor called the permittivity of the medium.

Applications of Coulomb’s Law

Coulomb’s Law is used in many areas of physics, especially in electricity and magnetism. Some common applications are:

  • Understanding the behavior of charged particles
  • Designing electrical equipment
  • Explaining how charges behave in conductors and insulators
  • Studying atomic structure, because electric force holds electrons around the nucleus
  • Calculating forces in electrostatic machines and instruments

Without Coulomb’s Law, it would be very difficult to study electric fields, electric potential, or charge interaction.

Conclusion

Coulomb’s Law clearly explains how two electric charges influence each other. It shows that the electric force depends on the size of the charges, the distance between them, and the nature of the medium. The force can be attractive or repulsive and follows an inverse square relationship with distance. This law forms the foundation of electrostatics and is essential for understanding many electrical concepts in physics.