Define electric field at a point. Derive an expression for the electric field due to a point charge q at a distance r from it. Draw the graph of E against r.

1. 1 · Define the field. Electric field is the force per unit positive test charge: E = F/q₀, unit N C⁻¹.
2. 2 · Set up. Point charge q at O; small test charge q₀ at P, a distance r away.
3. 3 · Use Coulomb's law. F = (1/4πε₀)(q q₀/r²) r̂.
4. 4 · Divide by q₀. E = F/q₀ = (1/4πε₀)(q/r²) r̂: radially outward for positive q.
5. 5 · Draw the graph. [E on the vertical axis, r on the horizontal axis; a curve falling steeply towards the r-axis, labelled E ∝ 1/r²]
6. 6 · Real life. Air breaks down when E reaches about 3 × 10⁶ N C⁻¹, which is how lightning starts.
7. 7 · Close in one line. The field of a point charge is radial and falls as the inverse square of distance.

Scoring tip: Say 'small positive test charge' in the definition. Both words, small and positive, carry marks.