# Permittivity

Permittivity describes the effect of material in determining the electric field in response to electric charge. For example, one can observe from laboratory experiments that a particle having charge

gives rise to the electric field

where

is distance from the charge,

is a unit vector pointing away from the charge, and

is a constant that depends on the material. Note that

increases with

, which makes sense since electric charge is the source of

. Also note that

is inversely proportional to

, indicating that

decreases in proportion to the area of a sphere surrounding the charge – a principle commonly known as the *inverse square law*. The remaining factor 1/

is the constant of proportionality, which captures the effect of material. Given units of

/

for

and

for

, we find that

must have units of farads per meter (

/

). (To see this, note that

.)

Permittivity (

,

/

) describes the effect of material in determining the electric field intensity in response to charge.

In free space (that is, a perfect vacuum), we find that

where:

The permittivity of air is only slightly greater, and usually can be assumed to be equal to that of free space. In most other materials, the permittivity is significantly greater; that is, the same charge results in a weaker electric field intensity.

It is common practice to describe the permittivity of materials relative to the permittivity of free space. This *relative permittivity* is given by:

Values of

for a few representative materials is given in Appendix 10.1 . Note that

ranges from 1 (corresponding to a perfect vacuum) to about 60 or so in common engineering applications. Also note that relative permittivity is sometimes referred to as *dielectric constant*. This term is a bit misleading, however, since permittivity is a meaningful concept for many materials that are not dielectrics.

## Additional Reading

- “Permittivity” on Wikipedia.
- Appendix 10.1 (“Permittivity of Some Common Materials”).
- “Inverse square law” on Wikipedia.

Ellingson, Steven W. (2018) Electromagnetics, Vol. 1. Blacksburg, VA: VT Publishing. https://doi.org/10.21061/electromagnetics-vol-1 CC BY-SA 4.0

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