Electric charge and Coulomb’s law

Charge and the force between charges

Electric charge is a basic property of matter. There are two kinds, positive and negative; like charges repel and unlike charges attract. The SI unit of charge is the coulomb (C).

Three key properties of charge:

• Quantisation: any charge is a whole-number multiple of the electron charge, q = ne, where e = 1.6 × 10⁻¹⁹ C.
• Conservation: the total charge of an isolated system never changes. Charge can move from one body to another (for example when rubbing a glass rod with silk) but it is not created or destroyed.
• Additivity: charges add like ordinary numbers, taking signs into account.

Coulomb’s law: the force between two point charges is F = k q₁q₂ / r², where k = 1/(4πε₀) ≈ 9 × 10⁹ N m² C⁻² and ε₀ = 8.854 × 10⁻¹² C² N⁻¹ m⁻² is the permittivity of free space. The force acts along the line joining the charges. In a medium of dielectric constant K the force becomes F/K.

Superposition principle: when many charges act on one charge, the net force is the vector sum of the forces from each charge taken separately.

Worked example: charges 2 μC and 3 μC are 0.3 m apart in air. F = 9 × 10⁹ × (2 × 10⁻⁶)(3 × 10⁻⁶) / (0.3)² = 0.6 N (repulsive).

Key points

• e = 1.6 × 10⁻¹⁹ C; 1 C corresponds to 6.25 × 10¹⁸ electrons.
• F ∝ q₁q₂ and F ∝ 1/r² (inverse-square law).
• k = 9 × 10⁹ N m² C⁻² in vacuum; force in a medium = vacuum force ÷ K.
• Coulomb forces obey Newton’s third law: equal and opposite.

Exam tips

• Ratio questions are common: “if r is halved, F becomes four times”.
• Always convert μC to C (× 10⁻⁶) and cm to m before substituting.
• For three or more charges, draw each force as a vector before adding.

Common mistakes

• Forgetting to square the distance.
• Adding forces as plain numbers when they point in different directions.
• Thinking a body becomes positive by gaining protons; it actually loses electrons.