Electrostatic Potential and Potential Energy

Lesson

Part 1 — a single number at every point that tells you how much work it takes to bring a charge there.

In this lesson you will

Define electric potential and potential difference, and describe equipotential surfaces
Derive the potential of a point charge and compare V and E with distance
Find the potential of a system of charges and of a dipole

Radii r, 2r, 3r carry V, V/2, V/3.

Concept

Potential and potential difference

The potential difference between A and B is the work done per unit positive charge in moving a test charge from A to B without acceleration: $V_B - V_A = \dfrac{W_{AB}}{q_0}$ The potential at a point is the work done per unit charge in bringing a test charge from infinity (where V = 0) to that point: $V = W/q_0$ . Unit: volt (1 V = 1 J C⁻¹). Potential is a scalar.

The electrostatic force is conservative, so W does not depend on the path taken.
A positive charge moves naturally from high to low potential.

Diagram

Equipotential surfaces

An equipotential surface joins points at the same potential:

No work is done in moving a charge along an equipotential.
The field is everywhere perpendicular to equipotentials (otherwise a component of E along the surface would do work).
E points from higher to lower potential; equipotentials are closer together where E is stronger. Two equipotentials never intersect.
Point charge: concentric spheres; uniform field: parallel planes perpendicular to E.

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