2.9 Electric Potential

Electric Potential Defined

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). Unlike electric field, potential doesn't depend on the test charge placed there — it's a property of the source charge's configuration and the location in space.

Potential from a Point Charge

For a point charge Q, V = kQ/r, where r is distance from the charge. Potential decreases with distance and can be positive or negative depending on the sign of Q. Potentials add algebraically (as scalars) when multiple charges contribute to a point — no vector components needed.

Potential Difference and Equipotentials

Potential difference (ΔV) between two points relates to work: W = -qΔV, or the work done by an external force moving charge q equals qΔV. Equipotential surfaces connect points of equal V; electric field lines are always perpendicular to them, and no work is done moving a charge along an equipotential.

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, decreases as 1/r, sign depends on the source charge.

Combining potentials from multiple charges

Add algebraically as scalars (with sign), unlike electric fields which require vector addition.

Equipotential surface

A surface where all points have the same electric potential; electric field is always perpendicular to it, and no work is done moving charge along it.

Work and potential difference

W = qΔV; work done by an external force moving charge q through potential difference ΔV.

Try an AP-style question

A 2 C charge moves through a potential difference of 5 V. What is the change in its potential energy?

1. 0.4 J
2. 7 J
3. 10 J
4. 2.5 J