Skip to content

Electric Flux

Source lecture(s): SC134 Lec4

Intuition

Flux counts how many field lines pierce a surface—open surfaces measure flow, closed surfaces measure enclosed sources.

Formal Definition

\[\Phi_E = \int \vec{E}\cdot d\vec{A}\]

Mathematical Formulation

Closed surface: \(\oint \vec{E}\cdot d\vec{A} = q_{\text{enc}}/\varepsilon_0\) Uniform field through flat area: \(\Phi = EA\cos\theta\).

Derivation

Parallel-plate model visualizes field lines; Gauss's law turns flux into enclosed charge.

Worked Example

Cube in uniform \(E\) parallel to edges has zero net flux if no charge inside.

Common Mistakes

  • Counting every field line instead of piercing component.
  • Confusing open vs closed surface formulas.

Quiz

Q1. What is the net flux through a closed surface with no enclosed charge?

Answer

Zero.