State Coulomb's law. Write it in vector form and show that the forces two charges exert on each other are equal and opposite.

1. 1 · State the law. The force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.
2. 2 · Write the formula. F = (1/4πε₀) q₁q₂/r², with 1/4πε₀ = 9 × 10⁹ N m² C⁻².
3. 3 · Draw the figure. [Origin O; q₁ at position vector r₁ and q₂ at r₂; arrow r₂₁ from q₁ to q₂; forces F₂₁ on q₂ and F₁₂ on q₁ along the joining line]
4. 4 · Write the vector form. F₂₁ = (1/4πε₀)(q₁q₂/r₂₁²) r̂₂₁, where r̂₂₁ is the unit vector from q₁ to q₂.
5. 5 · Show equal and opposite. F₁₂ = (1/4πε₀)(q₁q₂/r₁₂²) r̂₁₂. Since r̂₁₂ = −r̂₂₁, F₁₂ = −F₂₁.
6. 6 · Close in one line. Coulomb forces are equal, opposite and along the joining line, as Newton's third law requires.

Scoring tip: Name the unit vector clearly (from q₁ to q₂). Many students lose the vector-form mark by leaving out r̂.