Coulomb's law opens Class 12 electrostatics. Enter two charges in microcoulombs, the distance between them and the medium to get the force and whether it attracts or repels.
Enter both charges with their signs.
Enter the distance and dielectric constant.
Read the force.
Coulomb's law: F = q₁q₂ ÷ (4πε₀ K r²)
Coulomb's law gives the electric force between two point charges. This calculator takes the two charges in microcoulombs with their signs, the distance between them in metres and the dielectric constant of the medium, and returns the size of the force in newtons and whether it attracts or repels.
It is the opening law of Class 12 electrostatics and appears regularly in board exams, JEE and NEET. Behind everyday effects such as a comb picking up paper bits after running through dry hair, or dust sticking to a TV screen, lies this same law. It also sets the scale for forces inside atoms, where it holds electrons to the nucleus, and for the design of capacitors and electrostatic painting and precipitators.
1. Convert each charge to coulombs. 1 µC = 10⁻⁶ C and 1 nC = 10⁻⁹ C. Keep the signs.
2. Measure the distance r between the charges in metres.
3. Use k = 1 ÷ (4πε₀) ≈ 8.99 × 10⁹ N·m²/C².
4. Compute F = k × q₁ × q₂ ÷ (K × r²), where K is the dielectric constant (1 for vacuum or air).
5. Read the sign: positive means like charges and repulsion, negative means unlike charges and attraction.
6. Quote the magnitude of F in newtons with the direction in words.
The force is proportional to each charge and falls off as 1 ÷ r². Double the distance and the force becomes a quarter; halve it and the force becomes four times larger. The square appears because the field spreads out over the surface of a sphere, whose area grows as 4πr². That is also why k is written as 1 ÷ (4πε₀). The form is the same as Newton's law of gravitation, but the electric force is vastly stronger and can repel as well as attract.
Placing charges in a material other than vacuum reduces the force by the dielectric constant K, also called relative permittivity. The material's molecules polarise, lining up so that their own charges partly cancel the field between q₁ and q₂. Air has K very close to 1, so it is treated as vacuum. Water has K near 80, which is why salts like NaCl dissolve so easily: the attraction between Na⁺ and Cl⁻ ions drops about eighty-fold in water.
Coulomb's law as written applies to point charges or to uniformly charged spheres, measured between centres. For charged plates, rods or irregular objects you must add up the contributions of small pieces, which leads to Gauss's law and integration. The law also assumes charges are at rest; moving charges produce magnetic forces too. When several charges act on one, the forces add as vectors, a result called the superposition principle, so you work out each pair and combine them.
In a Class 12 practical, two small metal spheres each carrying +5 µC are held 0.2 m apart in air.
Coulomb's law: F = k q₁ q₂ ÷ (K r²), k = 8.99 × 10⁹ N·m²/C² F = 8.99 × 10⁹ × 5 × 10⁻⁶ × 5 × 10⁻⁶ ÷ (1 × 0.2²) = 5.6172 N
Direction: Positive → the charges repel
Answer: Force 5.6172 N
Forgetting to convert microcoulombs to coulombs by multiplying by 10⁻⁶.
Using the distance instead of the distance squared.
Measuring distance between the surfaces of charged spheres instead of their centres.
Multiplying by the dielectric constant instead of dividing by it.
Adding forces from several charges as plain numbers instead of as vectors.
Class 12 electrostatics numericals and JEE and NEET preparation.
Estimating forces in electrostatic painting, printers and dust precipitators.
Understanding why ionic compounds dissolve in water.
Rough models of forces between ions in chemistry and biology.
Explaining static electricity effects in dry winter weather.
What happens if the distance doubles?
The force becomes one quarter.
Why is the force weaker in water?
Water's dielectric constant of about 80 reduces the force by that factor.