Define electric field at a point. Derive an expression for the electric field due to a point charge, and state four properties of electric field lines.

1. 1 · Define the field. E = F/q₀: the force on a small positive test charge at the point, per unit charge. Unit N C⁻¹.
2. 2 · Set up the derivation. Place a small test charge q₀ at P, a distance r from a point charge q.
3. 3 · Use Coulomb's law. Force on q₀: F = kqq₀/r², along the line from q to P.
4. 4 · Divide by q₀. E = F/q₀ = q/(4πε₀r²), radially outward for +q and inward for −q.
5. 5 · Draw the field lines. [A +q with 8 radial lines pointing out; a −q with 8 radial lines pointing in; a dipole with curved lines from + to −]
6. 6 · State four properties.
   • They start on + charges and end on − charges.
   • The tangent gives the direction of E.
   • Crowded lines mean a strong field.
   • Two lines never cross.
7. 7 · Close in one line. So the field of a point charge falls as 1/r², and field lines picture both its direction and its strength.

Scoring tip: Write the definition with the words 'unit positive test charge'. Examiners look for 'positive' and for the unit N C⁻¹.