Electric Potential
One number at every point that encodes the whole field.
Lesson at a glanceShow the key points
- V_B − V_A = (U_B − U_A)/q (29.7), in volts.
- V_A = (U_A − U_P)/q (29.8) with V = 0 at a reference point (usually infinity): work per unit charge by an external agent.
- Point charge V = Q/4πε₀r (29.9); potentials add as scalars.
A field is a vector at every point. Potential describes the same field with just one number at every point, which makes many problems far easier.
Potential difference
Move a test charge q from A to B while the other charges stay fixed. If the electric potential energy changes by U_B − U_A:
Conversely, taking a charge q through a potential difference V_B − V_A changes its potential energy by q(V_B − V_A).
Potential at a point
Choose a reference point P where V = 0 (usually infinitely far from all the charges). Then
Potential is a scalar: potentials from several charges simply add.
Potential of a point charge
Bringing q from infinity to distance r from Q changes the energy by Qq/4πε₀r, so
+4.0 µC and −6.0 µC are 10 cm apart. Find the potential at the midpoint.
An electron is accelerated from rest through a potential difference of 500 V. What kinetic energy and speed does it gain?
- 1V_B − V_A = (U_B − U_A)/q, in volts.
- 2Potential at a point: external work per unit charge to bring a test charge from the reference point (usually infinity).
- 3Point charge V = Q/4πε₀r; potentials add as scalars.
Check yourself
Keep exploring
Hand-picked videos, simulations and readings that explain this idea from a different angle.