1.5 Electric Flux

What is electric flux?

Electric flux (Φ) measures the amount of electric field passing through a surface. For a flat surface in a uniform field, Φ = E · A · cos(θ), where θ is the angle between the field vector and the surface's normal vector. Flux is a scalar, measured in N·m²/C, and can be positive, negative, or zero depending on orientation.

Flux through non-uniform fields or curved surfaces

For surfaces that are curved or fields that vary, flux is found by integrating: Φ = ∫E·dA, summing E·dA over infinitesimal area elements. Each dA vector points along the surface's outward normal. This integral form is essential for Gauss's Law and situations where E isn't constant across the surface.

Orientation matters

Flux is maximized when the field is parallel to the area's normal vector (θ = 0°) and zero when the field is parallel to the surface itself (θ = 90°, since cos 90° = 0). Field lines entering a closed surface count as negative flux, while lines exiting count as positive, based on the outward normal convention.

Key terms

Electric flux (uniform field)

Φ = E·A·cos(θ), where θ is the angle between E and the surface's normal vector.

Electric flux (general/integral form)

Φ = ∫E·dA, integrating the dot product of E and the area vector over the surface.

Normal vector

A vector perpendicular to a surface, used to define orientation and the sign of flux through that surface.

Units of electric flux

N·m²/C (newton-meters squared per coulomb).

Flux when E is parallel to the surface

Zero — since θ = 90° between E and the normal, cos(90°) = 0.

Try an AP-style question

A uniform 200 N/C field passes perpendicularly through a 0.5 m² surface. What is the flux?

1. 100 N·m²/C
2. 200 N·m²/C
3. 0
4. 400 N·m²/C