Short on time? This page is the recap. For the figures, derivations and worked examples, use the full study guide. This topic is part of the calculus-based Physics C: E&M course.
Recap
- Flux describes how much of a quantity passes through an area. Electric flux is proportional to the number of field lines crossing a surface.
- The area vector A has the size of the area and points perpendicular to the surface. For an open surface you choose one side; for a closed surface it points outward.
- Flux is a scalar with a sign. Unit: N·m²/C.
- In a uniform field, the net flux through any closed surface is zero: every line that enters also leaves.
Key relationships
| Situation | Flux |
|---|---|
| Uniform E, flat surface | Φ_E = E·A = EA cos θ |
| Angle α given between E and the surface | θ = 90° − α, so Φ_E = EA sin α |
| Components, surface in the xy-plane, A = A k̂ | Φ_E = E_z A |
| E varies, or the surface curves | Φ_E = ∫E·dA (strips with constant E) |
| Closed surface | Φ_E = ∮E·dA, outward dA |
| Curved open surface in uniform E | same size as the flux through the flat area across its rim |
Assumptions behind the results
- “Uniform” means the same size and direction at every point of the surface.
- In the strip method, E must be constant along each strip; choose strips perpendicular to the direction in which E changes.
- Signs depend on the stated area vector. Always say which way A points.
Mistakes to avoid
- Angle from the surface. θ is measured from the normal.
- Dropping the sign. Entering field lines give negative flux on a closed surface.
- Inward normals on closed surfaces. Always outward.
- One value of E for a varying field. Integrate instead.
- Curved area for a dome in a uniform field. Use the flat rim area, πR².
- “Zero net flux means zero field.” A uniform field gives zero net flux through a closed surface, yet E is not zero.
Quick self-check
- A uniform 200 N/C field makes 60° with the area vector of a 0.50 m² flat surface. Flux? (+50 N·m²/C)
- What is the flux through a surface parallel to the field? (Zero)
- A cube of side 0.10 m has two faces perpendicular to a uniform 400 N/C field along +x. Flux through each of these faces, and the net flux? (+4.0 N·m²/C on the +x face, −4.0 N·m²/C on the −x face; net zero)
Next: practice questions.