What is an equipotential surface? State three of its properties and show that E = −ΔV/Δr.

1. 1 · Define. An equipotential surface is one on which every point is at the same potential.
2. 2 · Draw two examples. [Point charge: dashed concentric circles crossed by radial field lines. Uniform field: parallel dashed lines at right angles to straight field lines]
3. 3 · Three properties.
   • No work is done in moving a charge along it.
   • E is at right angles to it at every point.
   • Two equipotential surfaces never intersect.
4. 4 · Relate E and V. Move a unit positive charge a small distance Δr along E: ΔV = EΔr cos 180° = −EΔr.
5. 5 · Write the result. E = −ΔV/Δr: the field is the negative potential gradient, pointing the way V falls.
6. 6 · Close in one line. So field lines always cross equipotentials at right angles, from high to low potential.

Scoring tip: Draw the field lines solid and the equipotentials dashed, and make them meet at right angles.