2.1 Electric Potential

Defining Electric Potential

Electric potential (V) is the electric potential energy per unit charge at a point in space: V = U/q. It's a scalar quantity measured in volts (J/C). Potential exists independent of any test charge placed there — it's a property of the field created by source charges.

Potential from a Point Charge

For a point charge Q, V = kQ/r, where r is distance from the charge. Potential decreases with distance for positive Q and increases (toward zero) for negative Q. Since potential is scalar, potentials from multiple charges add algebraically (not vectorially like fields).

Potential Difference and Work

The potential difference ΔV between two points equals the work per unit charge done by an external force moving a charge between them: ΔV = -W_field/q. Moving a positive charge from high to low potential means the field does positive work; potential decreases in the direction of E.

Key terms

Electric potential (V)

Electric potential energy per unit charge at a point; V = U/q, measured in volts.

Potential due to a point charge

V = kQ/r; scalar quantity that falls off as 1/r.

Scalar vs. vector: potential and field

Electric field is a vector; electric potential is a scalar, so multiple potentials just add algebraically.

Potential difference (ΔV)

Work per unit charge done by an external force moving a charge between two points: ΔV = -W_field/q.

Direction of E relative to V

The electric field points in the direction of decreasing electric potential.

Try an AP-style question

In a uniform field E = 500 V/m, what is the potential difference over 0.02 m along the field?

1. 25,000 V
2. 0.04 V
3. 250 V
4. 10 V