Permittivity

Prof. Dr. Thorsten Jungmann (last updated 2025-09-04)

Electric permittivity (German: elektrische Permittivität) describes the property of a material to conduct an electric field and to store electrical energy. It is the electrical counterpart of permeability in the magnetic field and largely determines the capacitance of capacitors.

Tensor quantity in a homogeneous field with homogeneous material → scalar quantity

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

1 Quantity symbol and unit

The quantity symbol of permittivity is the Greek lower-case letter $\epsilon$ (‘epsilon’).
Its unit is farad per metre or ampere-second per volt-metre:

$$[\epsilon ]=F/m=As/(\mathrm{V}\cdot \mathrm{m})$$

2 Practical and worked examples

The (absolute) permittivity ($\epsilon$) is the product of the relative permittivity ${\epsilon }_r$ of the material and the electric field constant ${\epsilon }_0$:

$$\epsilon ={\epsilon }_r\cdot {\epsilon }_0$$

Electric field constant (${\epsilon }_0$):

$${\epsilon }_0=8.8542\cdot 10^{-12}F/m$$

Relative permittivity (${\epsilon }_r$):
Dimensionless number that indicates how strongly a material increases the electric flux density compared with a vacuum.

2.1 Capacitance of a parallel-plate capacitor

The capacitance of a parallel-plate capacitor depends directly on the permittivity of the dielectric used:

$$C=\epsilon \cdot \frac{A}{d}={\epsilon }_0\cdot {\epsilon }_r\cdot \frac{A}{d}$$

Example: plate area $A=1.0\cdot 10^{-3}{\mathrm{m}}^2$, plate separation $d=0.5\mathrm{mm}$

Air capacitor (${\epsilon }_r=1$):

$$C_1=8.8542\cdot 10^{-12}F/m\cdot 1\cdot \frac{1.0\cdot 10^{-3}{\mathrm{m}}^2}{0.5\cdot 10^{-3}\mathrm{m}}=\underline{17.7\mathrm{pF}}$$

With a ceramic dielectric (${\epsilon }_r=100$):

$$C_2=8.8542\cdot 10^{-12}F/m\cdot 100\cdot \frac{1.0\cdot 10^{-3}{\mathrm{m}}^2}{0.5\cdot 10^{-3}\mathrm{m}}=\underline{1.77\mathrm{nF}}$$

2.2 Electric flux density in the dielectric

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

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

Example: $E=50kV/m$, polyethylene (PE) with ${\epsilon }_r=2.3$

$$D=8.8542\cdot 10^{-12}F/m\cdot 2.3\cdot 50000V/m=\underline{1.02\mu C/{\mathrm{m}}^2}$$

3 Typical orders of magnitude

• Electric field constant ${\epsilon }_0=8.8542\cdot 10^{-12}F/m$
• Vacuum, air: ${\epsilon }_r=1$
• Oil, paraffin: ${\epsilon }_r=2$ to $3$
• Polyethylene: ${\epsilon }_r=2.3$
• Glass: ${\epsilon }_r=5$ to $10$
• Ceramics: ${\epsilon }_r=10$ to $1000$
• Water: ${\epsilon }_r=81$
• Ferroelectrics: ${\epsilon }_r=1000$ to $20000$

4 Example phrasings

• ‘The dielectric has a relative permittivity of ${\epsilon }_r=4.2$.’
• ‘The ceramic material increases the capacitance by a factor of 100.’
• ‘The electric field constant is ${\epsilon }_0\approx 8.85\cdot 10^{-12}F/m$.’
• ‘With a permittivity of $25pF/m$, the flux density is given by $D=\epsilon \cdot E$.’

5 Related quantities

• Electric flux density and electric field strength:

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

• Capacitance of a parallel-plate capacitor:

$$C=\epsilon \cdot \frac{A}{d}$$

• Electric flux:

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

6 Related components

• Capacitor: the dielectric determines the capacitance via the permittivity
• Insulator: the permittivity influences the field distribution and the breakdown strength