Coulomb's law

Coulomb's law gives the force between two point charges:

F = k q₁q₂ / r², with 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. In a medium, the force becomes smaller.

The force acts along the line joining the charges: repulsive for like charges, attractive for unlike.

Example: two charges of 1 µC each, 1 m apart, in air: F = 9 × 10⁹ × 10⁻⁶ × 10⁻⁶ / 1² = 9 × 10⁻³ N.

It is an inverse square law, like gravity. Triple the distance and the force becomes 1/9. Double one charge and the force doubles.

The forces obey Newton's third law: the force on q₁ due to q₂ is equal and opposite to the force on q₂ due to q₁, even when the charges are of different sizes.

Superposition: with many charges, the force on one charge is the vector sum of the forces from each of the others, each found as if the rest were absent. Draw every force as an arrow first.

Example: one charge feels 3 N to the east from one neighbour and 4 N to the north from another. The total is √(3² + 4²) = 5 N.

With symmetric arrangements (equal charges at the corners of a square or an equilateral triangle), look for forces that cancel before calculating anything.

The electric force between an electron and a proton is about 10³⁹ times their gravitational pull. Electric forces hold atoms, molecules and solids together.