State Coulomb's law. Write it in vector form and show that the forces between two charges obey Newton's third law.

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 = kq₁q₂/r², with k = 1/4πε₀ = 9 × 10⁹ N m² C⁻², acting along the line joining the charges.
3. 3 · Draw the figure. [q₁ and q₂ a distance r apart; unit vector r̂₁₂ from q₁ to q₂; for like charges, F₂₁ on q₂ pointing away from q₁ and F₁₂ on q₁ pointing away from q₂]
4. 4 · Write the vector form. F₂₁ = k(q₁q₂/r²) r̂₁₂ is the force on q₂ due to q₁.
5. 5 · Show equal and opposite. F₁₂ = k(q₁q₂/r²) r̂₂₁ and r̂₂₁ = −r̂₁₂, so F₁₂ = −F₂₁.
6. 6 · Close in one line. The two forces are equal, opposite and along the same line, as Newton's third law requires.

Scoring tip: Name the unit vector and its direction (from q₁ to q₂). Many answers lose the vector-form mark by leaving out r̂.