AP® Physics 2: Algebra-Based · Unit 10 · Topic 10.7
Moving a Charge Through a Potential Difference
When a charge moves through a potential difference, the electric force does work on it equal to qDV, and that work becomes kinetic energy. No push from outside is needed — the field itself does the shoving.
A potential difference is an energy hill. Put a charge at the top and the field pushes it down automatically, the same way gravity pulls a dropped ball down a real hill. The charge doesn't need an outside force to speed up — the field supplies the force, and that force does work on the charge as it moves from high potential to low potential (for a positive charge) or low to high (for a negative one, since electrons are pushed toward higher potential).
The work-energy theorem connects the two pictures. The work done by the electric force on a charge q crossing a potential difference DV is W = qDV. Since no other forces act (we usually ignore gravity and friction here), all of that work shows up as kinetic energy: KE_final - KE_initial = qDV. Starting from rest, this becomes 1/2 m v2 = qV, which you solve for speed: v = √(2qV/m). The sign and size of DV tell you how much energy the charge picks up; the charge's own mass tells you how that energy translates into speed.
Because the electric force is conservative, W = qDV only cares about the endpoints, not the route. A charge wandering in loops before reaching its destination gains the exact same kinetic energy as one going straight there. This is the same path-independence you saw with gravitational potential energy, and it's what lets potential difference act as a clean, portable number — a voltage — that works the same everywhere, setting up circuits and capacitors in the rest of the unit.
Key terms
- Potential difference (voltage)
- The work per unit charge needed to move a charge between two points, measured in volts.
- Work-energy theorem
- The net work done on an object equals its change in kinetic energy.
- Conservative force
- A force whose work on an object depends only on starting and ending position, not the path taken.
- Electron volt
- The kinetic energy gained by an electron crossing a 1 volt potential difference, equal to 1.6 x 10−19 J.
Watch it explained
- How it worksHow does the work-energy theorem turn a potential difference into kinetic energy?
- Worked exampleFind the speed of an electron after it falls through a 200 V potential difference from rest.
- Common mistakeWhy doesn't the path a charge takes between two points change the work done on it?
- Going furtherWhat changes about the energy gain if the charge is a proton instead of an electron?
Check yourself
End of topic.