D.2.16 (HL)—Work in electric fields

Use potential difference

External work on a charge equals its change in electric potential energy. Keep the sign of $q$ and calculate final potential minus initial potential. Work by the field has the opposite sign.

Worked example — moving between equipotentials

A $+2.0\,\mathrm{C}$ charge moves from $40\,\mathrm{V}$ to $20\,\mathrm{V}$. Then $W_{\mathrm{on}}=(2.0)(20-40)=-40\,\mathrm{J}$. Its electric potential energy falls by $40\,\mathrm{J}$; if free, that energy can become kinetic energy.

Connect to kinetic energy

If only the electric field does work, $W_{\rm field}=-q\Delta V_e$, and the change in kinetic energy equals this work. A positive charge moving to lower potential can gain kinetic energy; a negative charge may gain kinetic energy moving to higher potential.

Use endpoints

Because electrostatic fields are conservative, the work between two points does not depend on the path. Motion along an equipotential has $\Delta V_e=0$ and therefore zero work by the field.

Common trap

Check which agent’s work the question asks for and keep the charge sign. Do not assume that moving a negative charge toward lower potential necessarily increases its kinetic energy.