Electric field strength

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

The electric field strength (German: elektrische Feldstärke) describes how strong the electric field is at a particular point and thus characterizes the spatial distribution of the force that an electric field exerts on an electric charge.

Vector quantity in a homogeneous field → scalar quantity

This is a vector quantity. In this script, however, it is conventionally treated 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 field strength is $E$.

Its dimension (unit) is volt per metre, abbreviated with the unit symbol $V/m$.

$$[E]=V/m$$

(read: ‘The dimension of E is volt per metre.’)

Alternatively, the electric field strength can also be given in newtons per coulomb: $[E]=N/C$, as both units are equivalent. This shows the close relationship with the forces acting on the charges in the field.

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

2 Practical and worked examples

2.1 Force on an electric charge

The force on a point charge in the electric field is described by:

$$\vec{F}=q\cdot \vec{E}$$

where:

• $\vec{F}$ the force on the electric charge
• $q$ the electric charge
• $\vec{E}$ the electric field strength

2.2 Parallel-plate capacitor

The electric field strength between the plates of a capacitor is stated, for example, as follows:

$$E=\frac{U}{d}=\frac{12\mathrm{V}}{2\mathrm{mm}}=6kV/m$$

2.3 Breakdown strength of air

The breakdown field strength of air under standard conditions is:

$$E_{\mathrm{bd}}\approx 3MV/m$$

The distance to a high-voltage line carrying 380 kV must therefore be at least approx. 13 cm to prevent breakdown. Of course, in practice safety margins many times higher are applied.

3 Typical orders of magnitude

While electric field strengths of a few $V/m$ to $kV/m$ occur near charged objects in the household, electric field strengths of several $MV/m$ can be reached in capacitors. During lightning discharges, field strengths of over $100MV/m$ occur briefly.

4 Example phrasings

• ‘The electric field strength between the capacitor plates is $150kV/m$.’
• ‘At a field strength of $3MV/m$, breakdown occurs in air.’
• ‘The permissible electric field strength in the insulation must not exceed $2MV/m$.’
• ‘At a distance of $10,\mathrm{cm}$ from the charged sphere, the field strength is $500V/m$.’

5 Related quantities

• The breakdown strength of insulators is stated as an electric field strength.

• The electric field strength is linked to the voltage and the distance:

$$E=\frac{U}{d}$$

• The electric force on an electric charge in the field:

$$F=q\cdot E$$

• The electric flux density and the electric field strength are related via the permittivity:

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

6 Relevant components

• Capacitor: determination of the field strength between the electrodes
• Insulator: testing of the breakdown strength