Definition

Uniform field, flat surface

Φ_{E} = E A cos θ

Statement

Field strength times the area facing the field, with θ measured from the surface normal.

Symbols and units

$Φ_{E}$	electric flux	N·m²/C
$E$	field strength	N/C
$A$	area of the surface	m²
$θ$	angle from the surface normal	degrees

When it applies

Uniform field through a flat surface.

Don't use when

Only for a uniform field through a flat surface — a non-uniform field or a curved surface needs the general integral definition instead.

Derivation

Face-on, every line through the area counts, so flux is field times area:

Φ_{E} = E A

Tilt the surface by θ and its shadow across the field shrinks:

A_{effective} = A cos θ

Hence:

Φ_{E} = E A cos θ = E \cdot A

Worked examples

Tilted panel

E = 500 N/C through an area of 0.20 m², at three orientations:

Φ_{E} = E A cos θ = 100, 50, 0 N m^{2} /C

For θ = 0°, 60° and 90° respectively.

Watch out for

θ is measured from the normal, not from the surface itself. Edge-on means θ = 90° and zero flux.

Connects to