Skip to content
Know.itKnow.it
Create an animated lesson
On request

Read the answer free. Creating a lesson uses your daily or stored credits; review the language and settings before starting.

What is Coulomb's law?

Class 12 PhysicsNCERT chapter: Electric Charges and Fieldsइसे हिंदी में पढ़ें

Exam-ready answer

Coulomb's law states that the electrostatic force between two point charges at rest is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them. It acts along the line joining them: F = k|q₁q₂|/r², where k = 1/4πε₀ ≈ 9 × 10⁹ N m² C⁻² in vacuum.

Explanation

Coulomb measured the force between small charged spheres using a torsion balance. He found that doubling either charge doubles the force, while doubling the distance cuts the force to one-fourth. Combining both results gives F ∝ q₁q₂/r². The force is repulsive for like charges and attractive for unlike charges, and it always acts along the straight line joining the two point charges.

In SI units the constant of proportionality is written as k = 1/4πε₀, where ε₀ = 8.854 × 10⁻¹² C² N⁻¹ m⁻² is the permittivity of free space. This gives k ≈ 9 × 10⁹ N m² C⁻². From this, one coulomb is the charge that, placed 1 m from an equal charge in vacuum, repels it with a force of 9 × 10⁹ N.

In vector form, the force on q₂ due to q₁ is F₂₁ = (1/4πε₀)(q₁q₂/r₂₁²) r̂₂₁, where r̂₂₁ is the unit vector pointing from q₁ to q₂. By Newton's third law, F₁₂ = −F₂₁. Coulomb's law is an inverse-square law like Newton's law of gravitation, but the electric force can attract or repel and is far stronger: between two protons it is about 10³⁶ times their gravitational pull.

Points to remember

  1. Statement: F = k|q₁q₂|/r², valid for point charges at rest.
  2. k = 1/4πε₀ ≈ 9 × 10⁹ N m² C⁻²; ε₀ = 8.854 × 10⁻¹² C² N⁻¹ m⁻² is the permittivity of free space.
  3. SI unit of charge is the coulomb (C); force is in newton (N).
  4. Like charges repel and unlike charges attract; the force acts along the line joining the charges.
  5. The vector form obeys Newton's third law: F₁₂ = −F₂₁.

Exam tip

State the law in words first, then write F = (1/4πε₀)|q₁q₂|/r² with k ≈ 9 × 10⁹ N m² C⁻². For full marks, add the vector form and mention 'point charges at rest'.

Questions students also ask

What happens to the force if the distance between two charges is doubled?
The force varies as 1/r², so doubling the distance reduces the force to one-fourth of its original value. Halving the distance makes it four times larger. The charges themselves are unchanged, so only the distance factor changes.
How does a medium affect Coulomb's force?
In a medium of permittivity ε, the force becomes F = (1/4πε)|q₁q₂|/r². Since ε = Kε₀, where K is the dielectric constant (relative permittivity), the force in the medium is K times smaller than in vacuum. For water, K is about 80.
How is Coulomb's law similar to Newton's law of gravitation?
Both are inverse-square laws, both depend on the product of two quantities (charges or masses), and both act along the line joining the bodies. The differences: gravity is always attractive, while the electric force can attract or repel and is much stronger.

Chapter labels help you find the topic in your textbook. Check your own edition: chapter names and order can change. These are Know.it explanations, not official NCERT solutions.