Electric charge and electric force

Electric charge is a fundamental scalar property of matter that comes in positive and negative varieties.

Key Definition The smallest indivisible unit is the elementary charge e = 1.60 × 10⁻¹⁹ C, carried by protons (+e) and electrons (−e). All charge is quantized, occurring only in whole-number multiples of e (Q = ne).

Coulomb's Law

• States that the electrostatic force between two point charges is directly proportional to the product of their charge magnitudes and inversely proportional to the square of their separation
• Like charges repel; unlike charges attract
• The force always acts along the line connecting the two charges
• When multiple charges are present, the net force on any one charge is the vector sum of all the individual Coulomb forces — the superposition principle

F = (1 / 4πε₀) · (|q₁||q₂| / r²) = k |q₁||q₂| / r² k = 1 / 4πε₀ ≈ 8.99 × 10⁹ N·m²·C⁻²

Electrostatic Force vs Gravitational Force

• The electrostatic force is enormously stronger than the gravitational force between any pair of charged particles
• Both obey inverse-square laws, so their ratio is independent of the distance between the particles
• Gravity dominates at astronomical scales only because large objects are very nearly electrically neutral, leaving no net charge to produce significant electrostatic forces

Electric Permittivity

• Permittivity measures how easily a material's charge distribution rearranges in response to an external electric field
• Free space (vacuum) has permittivity ε₀ = 8.85 × 10⁻¹² C²·N⁻¹·m⁻² (F·m⁻¹)
• Materials with greater permittivity reduce the net electric field and so weaken the electrostatic force between charges embedded in them

Conductors contain freely moving charge carriers (such as the delocalized electrons in metals); insulators do not, so their charges remain fixed in place.