Electric flux density

Prof. Dr. Thorsten Jungmann (last updated 2026-05-04)

The electric flux density (German: elektrische Flussdichte, also Verschiebungsdichte) describes the electric displacement in a material under the influence of an electric field. It takes into account the material properties of the medium and describes the resulting electric displacement.

Vector quantity in a homogeneous field → scalar quantity

This is a vector quantity. In this script, however, it is treated by convention as a scalar quantity in the context of the homogeneous field (for a detailed justification).

1 Quantity symbol and unit

The quantity symbol of the electric flux density is $\vec{D}$ or $D$ (as a scalar quantity).

Its dimension (unit) is coulomb per square metre, abbreviated with the unit symbol $C/{\mathrm{m}}^2$.

$$[D]=C/{\mathrm{m}}^2$$

(read: ‘The dimension of D is coulomb per square metre.’)

Alternatively, the electric flux density can also be given in ampere-seconds per square metre: $[D]=As/{\mathrm{m}}^2$, since both units are equivalent.

To denote a position-dependent electric flux density, the quantity symbol $\vec{D}(\vec{r})$ is used for the flux density vector, since the electric flux density is a vector quantity. Without the vector property, the magnitude is meant.

2 Practical and worked examples

2.1 Parallel-plate capacitor with dielectric

The electric flux density between the plates of a capacitor with a dielectric is given, for example, as follows:

$$D=\epsilon \cdot E={\epsilon }_0\cdot {\epsilon }_r\cdot E=8.85\cdot 10^{-12}F/m\cdot 4\cdot 50kV/m=1.77\mu C/{\mathrm{m}}^2$$

where:

• $\epsilon$ the permittivity
• ${\epsilon }_0$ the electric field constant (${\epsilon }_0\approx 8.8542\cdot 10^{-12}F/m$)
• ${\epsilon }_r$ the relative permittivity of the dielectric (dimensionless)
• $E$ the electric field strength

3 Typical orders of magnitude

While electric flux densities from a few $nC/{\mathrm{m}}^2$ to $\mu C/{\mathrm{m}}^2$ occur in air capacitors, electric flux densities of several $mC/{\mathrm{m}}^2$ can be reached in capacitors with high-permittivity dielectrics. In electret microphones, permanent flux densities of about $10\mu C/{\mathrm{m}}^2$ are stored.

4 Example phrasings

• ‘The electric flux density in the capacitor is $2.5\mu C/{\mathrm{m}}^2$.’
• ‘At a flux density of $1mC/{\mathrm{m}}^2$, the saturation of the dielectric is reached.’
• ‘The stored flux density in the electret material is $15\mu C/{\mathrm{m}}^2$.’
• ‘An electric flux of $50\mathrm{nC}$ emerges through the boundary surface.’

5 Related quantities

• The electric flux density is linked to the electric field strength via the permittivity:

$$\vec{D}={\epsilon }_0\cdot {\epsilon }_r\cdot \vec{E}=\epsilon \cdot \vec{E}$$

• The electric flux $\Psi$ that passes through any area $A$ is equal to the surface integral of the electric flux density $D$. Only the part of the electric flux that is normal to the area $A$ contributes.

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

• Gauss’s law connects the electric flux density with the free electric charge:

$$\oint \vec{D}\cdot d\vec{A}=Q$$

• The displacement current as the rate of change of the electric flux density over time:

$$I_D=\frac{d}{dt}\underset{A}{\int }\vec{D}\cdot d\vec{A}$$

• The energy density stored in the electric field:

$$w=\frac{1}{2}\vec{D}\cdot \vec{E}$$

6 Relevant components

• Capacitors: determination of the charge distribution and capacitance
• Dielectrics: characterization of the material properties
• Electret microphones: permanent storage of electric flux density