Conductors & Charge Distributions

You’ll be able to

Describe the electric field and charge arrangement inside and on a conductor in equilibrium
Explain why charge concentrates at sharp points on a conductor
Analyze the uniform field between parallel charged plates

A conductor in electrostatic equilibrium

Give a conductor some excess charge and its free electrons rearrange almost instantly until everything is still — electrostatic equilibrium. In this state three things are always true: the electric field inside the conducting material is zero (any leftover field would keep pushing charges until it canceled), all the excess charge sits on the outer surface, and the field just outside is perpendicular to the surface. If the field had a component along the surface, charges would slide until it vanished.

Why lightning rods are pointed

On an irregular conductor, charge does not spread evenly — it piles up where the surface curves most sharply. At a sharp point the surface charge density, and therefore the field just outside, becomes very large. That is exactly what a lightning rod exploits: its point concentrates charge enough to ionize the surrounding air and guide a strike safely to ground. The same effect makes charge leak (“corona discharge”) from sharp edges.

Uniform field between parallel plates

E = V / d

Two large parallel plates with a voltage V across a gap d produce a nearly uniform field V/d, pointing from the positive plate to the negative plate. This is the geometry of a parallel-plate capacitor.

Worked example

Two parallel plates are 0.020 m apart with a potential difference of 100 V across them. Find the electric field between the plates and the force it exerts on an electron there. (e = 1.6 × 10⁻¹⁹ C)

1.Field between the plates: E = V/d = 100 / 0.020 = 5.0 × 10³ N·C⁻¹.
2.The field is uniform, so the force on any charge is F = qE.
3.For an electron: F = (1.6 × 10⁻¹⁹ C)(5.0 × 10³ N·C⁻¹).
4.Multiply: 1.6 × 10⁻¹⁹ × 5.0 × 10³ = 8.0 × 10⁻¹⁶ N.

Answer: E = 5.0 × 10³ N·C⁻¹ and the force on the electron is 8.0 × 10⁻¹⁶ N, directed toward the positive plate (opposite the field, since the electron is negative).

Checkpoint

Two parallel plates are separated by 0.020 m with a potential difference of 100 V between them. What is the magnitude of the (uniform) electric field between the plates?

Tip

The field between parallel plates is uniform, so the force on a charge is the same everywhere in the gap — unlike the point-charge field, it does not weaken with distance from a plate. That constant force gives charged particles a constant acceleration, like projectile motion.

Checkpoint

Inside the material of a solid metal conductor in electrostatic equilibrium, the electric field is:

On the exam

Lock in the conductor facts: field zero inside, excess charge on the surface, field perpendicular just outside, and charge densest at sharp points. These appear on nearly every electrostatics free-response question.

Answer the 2 checkpoints as you read.