Electric flux

Prof. Dr. Thorsten Jungmann (last updated 2025-09-03)

Electric flux (German: elektrischer Fluss) describes the total quantity of electric field lines that pass through a given area. It is a measure of how much electric field passes through an area.

1 Quantity symbol and unit

The quantity symbol is the Greek capital letter $\Psi$ (‘Psi’).
The unit is the coulomb ($\mathrm{C}$) or the ampere second ($\mathrm{As}$), as the two are equivalent. Electric flux is defined mathematically as the surface integral of the electric flux density:

$$\Psi =\underset{A}{\int }\vec{D}\cdot \mathrm{d}\vec{A}$$

Only the part of the electric flux that is normal to the area contributes.

2 Practical and worked examples

• In a parallel-plate capacitor with a homogeneous field, the electric flux is $\Psi =D\cdot A$, where $A$ is the plate area.
• Gauss’s law uses the electric flux: the flux through a closed surface equals the enclosed free electric charge.
• In high-voltage insulators, the electric flux is used to calculate the field distribution.
• In electret microphones, a constant electric flux density is stored.

3 Typical orders of magnitude

• Small capacitors: nanoampere seconds ($\mathrm{nAs}$) to microampere seconds ($\mu \mathrm{As}$).
• Power capacitors: milliampere seconds ($\mathrm{mAs}$).
• High-voltage applications: ampere seconds ($\mathrm{As}$) to kiloampere seconds ($\mathrm{kAs}$).

4 Example phrasings

• ‘The electric flux through the capacitor plate is $2.5\mu \mathrm{As}$.’
• ‘According to Gauss’s law, the electric flux through the enclosing surface is equal to the enclosed electric charge.’

5 Related quantities

• Electric flux density ($\vec{D}$): $|\vec{D}|=\frac{\mathrm{d}\Psi }{\mathrm{d}A}$ describes the local distribution of the flux
• Electric charge ($Q$): According to Gauss’s law, $\oint \vec{D}\cdot \mathrm{d}\vec{A}=Q$ applies
• Electric field strength ($\vec{E}$): Linked via the permittivity: $\vec{D}=\epsilon \cdot \vec{E}$
• Capacitance ($C$): In capacitors, the flux determines the stored electric charge.

6 Relevant components

Capacitor, insulator, electret microphone.