Direct Energy, 2018a

26 2.2 Capacitors
2.2.3 Permittivity and Related Measures
For historical reasons, the permittivity may be expressed by dierent measures.
The electric susceptibility χ e , relative permittivity ɛ r , index of refraction
n, and permittivity ɛ all describe the ability of a material to store
energy in the electric eld. Electric susceptibility is a unitless measure
related to the permittivity by
χ e = ɛ − 1 (2.9)
ɛ 0
and relative permittivity is another unitless measure dened by
ɛ r = ɛ
ɛ 0
. (2.10)
With some algebra, we can write the material polarization in terms of the
relative permittivity or the electric susceptibility.
−→ P =(ɛr − 1)ɛ 0
−→ E = ɛ0 χ e
−→ E (2.11)
Scientists studying optics often use index of refraction, another unitless
measure which represents the ratio of the speed of light in free space to the
speed of light in the material.
n =
c
| −→ v |
=
speed of light in free space
speed of light in material
(2.12)
Since electromagnetic waves cannot travel faster than the speed of light
in free space, index of refraction of a material is greater than one, n > 1.
Assuming a material is a good insulator and μ = μ 0 , which are typically
safe assumption for optics, the relationship between index of refraction and
permittivity simplies to
n = √ ɛ r . (2.13)
Table 2.1 lists relative permittivities of some insulators used to make
capacitors or piezoelectric devices. The values are all approximates. See
the references cited for more detailed information.
In the denitions of Section 1.6.3 and in Table 2.1, permittivity is
treated as a scalar constant, but in some contexts a more complicated
description is needed. In a crystalline material, a voltage applied along one
crystallographic axis may induce charge separation throughout the material
more easily than a voltage of the same size applied along a dierent axis.