2.2 Electric Potential Due to a Point Charge

Potential from a point charge

The electric potential due to a point charge is V = kQ/r, where k = 1/(4πε₀), Q is the source charge, and r is the distance from it. Unlike the electric field, potential is a scalar — it has no direction, only magnitude and sign, which matches the sign of Q.

Reference point and superposition

V is defined so that it equals zero at infinity, making point-charge potential absolute (no arbitrary constant needed). For multiple charges, potentials add algebraically (not as vectors): V_total = kΣ(qᵢ/rᵢ). This scalar addition makes potential often easier to work with than the field directly.

Sign and behavior near charges

A positive charge creates positive potential everywhere around it, decreasing toward zero as r → ∞; a negative charge creates negative potential. As r → 0, |V| → ∞ near a point charge. Equipotential surfaces around an isolated point charge are concentric spheres centered on the charge.

Key terms

Formula for potential due to a point charge

V = kQ/r, where k = 1/(4πε₀), Q is source charge, r is distance from it.

Is electric potential a scalar or vector?

Scalar — it has magnitude and sign but no direction.

Reference point for point-charge potential

V is defined to be zero at r = infinity.

How do potentials from multiple charges combine?

By algebraic (scalar) superposition: V_total = kΣ(qᵢ/rᵢ).

Shape of equipotential surfaces around a point charge

Concentric spheres centered on the charge, since V depends only on r.

Try an AP-style question

What is the potential 3 m from a 6 nC point charge? (k = 9 × 10⁹)

1. 54 V
2. 18 V
3. 6 V
4. 2 V