COULOMB'S LAW: ELECTRIC FORCE
INTRODUCTION
𝓣he concerned topic is related to electrostatics and is one of the fundamental branches of physics that deals with charges at rest and the forces between them. One of the most important laws in this chapter is Coulomb’s Law, which explains how two electric charges interact with each other. It provides a quantitative relationship between the magnitude of charges, the distance between them, and the force acting between them. Understanding this law is essential for solving numericals and building a strong foundation in topics like electric field and potential.
STATEMENT
𝓒oulomb's law states that the force of attraction or repulsion between two stationary point charges is
❏ directly proportional to the product of the magnitudes of the two charges and
❏ inversely proportional to the square of the distance between them.
❏ This force acts along the line joining the two charges.
If two point charges q₁ and q₂ are separated by distance r, then the force F of attraction or repulsion between them is given by
Where k is a constant of proportionality , called electrostatic force constant.The value of k depends on
❏ The nature of the medium between the two charges and
❏ The system of units chosen to measure F, q₁ , q₂ and r.
For the two charges located in free space and in SI units, we have
where ε₀ (epsilon naught) is called permittivity of free space.Value of ε₀ is
Here, 'F' is called Farad.
In vacuum
In a material medium
Where ε is permittivity of the medium and εᵣ is relative permittivity or dielectric constant of the given material medium .They are related as
COULOMB'S LAW IN VECTOR FORM
𝓒onsider two positive point charges q₁ and q₂ placed in vacuum at distance r from each other . Being like charges , they repel each other.
In vector form , Coulomb's law may be expressed as
= Force on charge q₂ due to q₁
=
Where ,
,is a unit vector in the direction from q₁ to q₂ .
Similarly,
= Force on charge q₁ due to q₂
=
Where, 
, is a unit vector in the direction from q₂ to q₁
IMPORTANCE OF VECTOR FORM
𝓣he vector form of Coulomb's law gives the following additional information :
1. As,
, therefore 
This means that the two charges exert equal and opposite force on each other . So, Coulombian forces obey Newton's third low of motion.
2. As the Coulombian forces act along
,i.e.,along the line joining the centres of two charges, so they are central forces.
LIMITATIONS OF COULOMB'S LAW
𝓒oulomb's law is not applicable in all situations. It is valid only under the following conditions :
1. The electric charges must be at rest.
2. The electric charges must be point charges i.e., the extension of charges must be much smaller than the separation between the charges.
3. The separation between the charges must be greater than the nuclear size(10⁻¹⁵ m), because for distances less than 10⁻¹⁵ m, the strong nuclear force dominates over the electrostatic force.
NUMERICALS
1. In Coulomb's law ,
, what are the factors in which the proportionality constant k depends?
2. In the relation 
, what is the value of k in free space ?
3. Give the SI unit of electrical permittivity of free space.
4. Write down the value of absolute permittivity of free space.
5. Deduce the dimensional formula for the proportionality constant k in Coulomb's law.
6. Write the dimensional formula for the permittivity constant of free space.
7. Two electrically charged particles, having charges of different magnitude, when placed at a distance d from each other, experience a force of attraction F. These two particles are put in contact and again placed at the same distance from each other.
What is the nature of new force between them?
Is the magnitude of the force of interaction between them now more or less than F ?
8. In a medium the force of attraction between two point electrical charges , distance d apart, is F. What distance apart should these be kept in the same medium so that the force between them becomes 3 F ?
9. Two equal charges , distance x apart, exert a force on one another. The change on one of the charges is doubled. What is the ratio of the distance between the two charges now and earlier if the force in the two cases is same?
10. If the distance between two equal point charges is doubled and their individual charges are also doubled, what would happen to the force between them?
11. How does the force between two point charges change, if the dielectric constant of the medium in which they are kept, increases?
12. The dielectric constant of water is 80. What is its permittivity?
13. What is the force between two small charged spheres having charges of 2 × 10⁻⁷ C and 3 × 10⁻⁷ C placed 30 cm apart in air?
14. The electrostatic force on a small sphere of charge 0.4 µC due to another small sphere of charge - 0.8 µC in air is 0.2 N.
(i)What is the distance between two spheres ?
(ii) What is the force on the second sphere due to the first?
15. Explain the meaning of the statement 'electric charge of a body is quantised.'
16. Why can one ignore quantization of electric charge when dealing with macroscopic i.e., large scale charges?
17. When a glass rod is rubbed wuth a silk cloth , charges apoear on both . A similar phenomenon is observed with many other pairs of bodies. Explain how this observation is consistent with the law of conservation of charge.
18. Four point charges Q₁= 2 µC, Q₂ = -5 µC, Q₃ = -2 µC, Q₄ = -5 µC are located at the corners of a square ABCD of side 10 cm. What is the force on a charge of 1 µC placed at the centre of the square ?
19. A polythene piece rubbed with wool is found to have a negative charge of 3.2 × 10⁻⁷ C .
(i) Estimate the number of electrons transferred.
(ii) Is there a transfer of mass from wool to polythene ?
CONCLUSION
Coulomb’s Law plays a crucial role in understanding the behavior of electric charges and forms the backbone of electrostatics. By relating force with charge and distance, it helps us analyze both attractive and repulsive interactions in a clear mathematical way. Mastering its concept, formula, and applications not only improves problem-solving skills but also prepares students for advanced topics in physics. With regular practice of numericals, this concept becomes simple and highly scoring in exams.