Charge is quantised, conserved and additive; two point charges exert a force along the line joining them, proportional to the product of charges and inversely proportional to the square of their separation.
How it's asked: Number of electrons in a given charge, force after identical spheres touch and separate, effect of a dielectric medium, and the net force from several charges by vector superposition.
Why this is true
All charge comes in whole-number multiples of the electronic charge e = 1.6 × 10⁻¹⁹ C, because it is carried by electrons and protons; ordinary charging simply moves electrons from one body to another, which is why total charge is conserved. The force between two point charges falls as 1/r², like gravity, but can be attractive or repulsive and is enormously stronger. Forces from several charges add as vectors (superposition), because each pair interaction is unaffected by the others. In a medium of dielectric constant K the molecules polarise and partly shield the charges, so the force falls to 1/K of its value in vacuum. When two identical conducting spheres touch, symmetry forces them to share the total charge equally.
Key points
Key formulae
Coulomb's law
F = q₁q₂/(4πε₀r²)
Quantisation
q = ne
In a medium
F = q₁q₂/(4πε₀Kr²)
Sharing between identical spheres
q' = (q₁ + q₂)/2
Electrostatic versus gravitational force
| Feature | Electrostatic | Gravitational |
|---|---|---|
| Dependence on r | 1/r² | 1/r² |
| Nature | Attractive or repulsive | Always attractive |
| Depends on medium | Yes (÷K) | No |
| Relative strength (two protons) | About 10³⁶ times stronger | Much weaker |
Common traps
- Keep the sign of each charge when sharing: +6 μC and −2 μC give +2 μC each, not +4 μC each.
- Net force from several charges is a vector sum — add components, not magnitudes.
Worked example
Two identical small metal spheres carry +6 μC and −2 μC and attract with force F at separation r. They are touched together and returned to the same separation. What is the new force?
High-yield
F ∝ q₁q₂/r², reduced by K in a medium; identical spheres in contact share (q₁ + q₂)/2 each.
Quick check
Q1.The number of electrons that must be removed from a neutral body to give it a charge of +1.6 μC is:
Q2.Two point charges in air repel with force F. When the space is filled with a liquid of dielectric constant 4 (same separation), the force becomes: