Work done in moving charge Q given by ∆ W = Q ∆ V Equipotential surfaces.

The idea

Electric potential V at a point is the work done per unit positive charge in bringing a small positive test charge from infinity to that point. The work done W in moving charge Q through a potential difference ΔV is W = QΔV. This applies whether the field is uniform or non-uniform, provided ΔV is the potential difference between the start and end points. For example, moving 2.0 C through a potential difference of 5.0 V requires W = 2.0 × 5.0 = 10 J. Equipotential surfaces are surfaces on which V is constant; they are always perpendicular to electric field lines. In a uniform field, they are parallel planes; around a point charge, they are concentric spheres. The equation links energy transfer to potential difference and charge, and is central to understanding capacitors, particle accelerators and circuits.

What earns the marks

• State that electric potential V is work done per unit positive charge: V = W/Q, with the test charge brought from infinity.
• Use W = QΔV to calculate energy transferred when charge Q moves through a potential difference ΔV, ensuring consistent signs for energy gain or loss.
• Define an equipotential surface as a surface where the electric potential is constant, so ΔV = 0 between any two points on it.
• Explain that equipotential surfaces are always perpendicular to electric field lines, and sketch them for a uniform field (parallel planes) and a radial field (concentric spheres).
• Relate the direction of motion to work done: if a positive charge moves to a higher potential, work is done on the charge; if it moves to a lower potential, the field does work.

Common mistakes and how to put them right

• Confusing electric potential V with electric potential energy.

  Put it right: Divide or multiply by Q as appropriate.

• Using W = QΔV with ΔV as a magnitude and ignoring the sign of the charge or the potential change, leading to incorrect energy direction.

  Put it right: Include signs or state clearly whether energy is gained or lost.

• Drawing equipotential surfaces that cross or are not perpendicular to field lines.

  Put it right: Equipotentials must be perpendicular to field lines everywhere and can never intersect.

Exam tips

• When calculating work done, write the equation W = QΔV, substitute values with units, and state the direction of energy transfer (work done on or by the field).
• For equipotential sketches, always draw field lines first, then add equipotentials perpendicular to them, labelling values of potential if given.
• If a question asks about moving a charge along an equipotential, immediately state that ΔV = 0, so W = 0, and explain that the electric force is perpendicular to the displacement.