Lesson 6.2 • Competency 6.2Complete Lesson

Electric Potential and Equipotential Surfaces

Definition of electric potential V, potential energy U = qV, potential difference ΔV, work done W = qΔV, relationship E = -dV/dr, equipotential surfaces, action of points, and lightning arresters.

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Learning Objectives

Define electric potential V at a point as external work done per unit positive charge from infinity, and calculate V = (1/4πε) (Q/r).
Relate electric field and potential gradient via E = -dV/dr and use it to solve potential differences in uniform and radial fields.
Explain properties of equipotential surfaces, the physical mechanism behind the action of points (corona discharge), and the protective action of lightning conductors.

Core Theory & Concepts

Electric potential is the scalar analog to electric field, representing the electrical potential energy per unit charge. Because the electrostatic force is conservative, the work done moving a charge between two points is entirely independent of the trajectory taken.

Electric Potential

Scalar potential at distance r from point charge Q: V = (1 / 4πε) (Q / r). Positive for positive charges; negative for negative charges.

V = \frac{1}{4\pi \varepsilon_0 \varepsilon_r} \frac{Q}{r}

Potential Gradient

Electric field strength equals the negative derivative of potential with respect to distance: E = -dV/dr. In a uniform field, E = V / d.

E = -\frac{dV}{dr} \implies E = \frac{V}{d} \text{ (uniform field)}

Action of Points (Corona Discharge)

On any charged conductor, potential V is uniform, which forces surface charge density σ ∝ 1/r. At sharp points with tiny radius r, σ and E = σ/ε become intense enough to ionize surrounding air molecules.

\sigma \propto \frac{1}{r}, \quad E = \frac{\sigma}{\varepsilon_0}

Common Misconceptions

Misconception

If the electric potential V at a point in space is zero, the electric field E at that point must also be zero.

Physical Clarification:Potential V is a scalar sum, whereas electric field E is a vector sum. At the midpoint between equal and opposite charges (+q and -q), V = +kq/d - kq/d = 0, but both field vectors point in the same direction, producing a strong non-zero electric field (E = 2kq/d² ≠ 0).

Syllabus Topic Outline

Competency 6.2

1Work done in moving charges and conservative nature of electrostatic field
2Electric potential V = Q / (4πε₀ r) with zero reference at infinity
3Electric potential energy of charge systems: U = (1/4πε) (q₁q₂/r)
4Potential gradient relationship: E = -dV/dr
5Equipotential surfaces: properties, perpendicularity to field lines, zero work
6Surface charge density on curved conductors (σ ∝ 1/r) and action of points
7Lightning conductor construction, ionization discharge, and safe grounding