AcademyElectric Charge and Fields

Academy

Conductors and Insulators

Level 1 - Physics topic page in Electric Charge and Fields.

Principle

Conductors and insulators differ by how freely charge can move through the material.

Notation

\(q_{\mathrm{free}}\)
mobile charge in a material
\(\mathrm{C}\)
\(q_{\mathrm{bound}}\)
charge bound to atoms or molecules
\(\mathrm{C}\)
\(\vec E\)
electric field
\(\mathrm{N\,C^{-1}}\)
\(\vec F\)
electric force on a charge
\(\mathrm{N}\)
\(\sigma\)
surface charge density
\(\mathrm{C\,m^{-2}}\)

Method

Derivation 1: Use charge mobility

The same electric force law acts in both material types, but the response differs because the charges have different freedom to move.

Force on a charge
\[\vec F=q\vec E\]
Conductor response
\[q_{\mathrm{free}}\ \text{moves through the material}\]
Insulator response
\[q_{\mathrm{bound}}\ \text{shifts only locally}\]

Derivation 2: Electrostatic equilibrium in a conductor

If a conductor is at rest electrostatically, its free charges have stopped drifting. That is only possible when the net electric force on free charges inside the conducting material is zero.

No drift in equilibrium
\[\vec F_{\mathrm{free}}=0\]
Use electric force
\[q\vec E=0\]
Interior field
\[\vec E=0\quad\text{inside conducting material}\]
Excess charge
\[Q_{\mathrm{excess}}\ \text{resides on the surface}\]

Rules

These are the material rules used in electrostatic problems.

Charge force
\[\vec F=q\vec E\]
Conductor equilibrium
\[\vec E=0\quad\text{inside conducting material}\]
Surface charge
\[\sigma=\frac{\Delta Q}{\Delta A}\]
Insulator response
\[\text{bound charges polarize locally rather than flowing through the body}\]

Examples

Question
A neutral metal sphere is placed in an external electric field and left to settle. What is the field inside the metal?
Answer
Free charges move until the interior electric force vanishes. In electrostatic equilibrium,
\[\vec E=0\]
inside the conducting material.

Checks

  • Conductors have mobile charge; insulators can still contain charged particles.
  • \(\\vec E=0\) applies inside conducting material in electrostatic equilibrium, not inside every cavity or nearby space automatically.
  • Excess charge on an isolated conductor moves to surfaces.
  • Polarization can occur without changing the net charge of the object.