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2.3: 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 $$q$$ gives rise to the electric field ${\bf E} = \hat{\bf R} ~ q ~ \frac{1}{4\pi R^2} ~ \frac{1}{\epsilon}$ where $$R$$ is distance from the charge, $$\hat{\bf R}$$ is a unit vector pointing away from the charge, and $$\epsilon$$ is a constant that depends on the material. Note that $${\bf E}$$ increases with $$q$$, which makes sense since electric charge is the source of $${\bf E}$$. Also note that $${\bf E}$$ is inversely proportional to $$4\pi R^2$$, indicating that $${\bf E}$$ decreases in proportion to the area of a sphere surrounding the charge – a principle commonly known as the inverse square law. The remaining factor $$1/\epsilon$$ is the constant of proportionality, which captures the effect of material. Given units of V/m for $${\bf E}$$ and C for $$Q$$, we find that $$\epsilon$$ must have units of farads per meter (F/m). (To see this, note that 1 F $$=$$ 1 C/V.)

Permittivity

Permittivity ($$\epsilon$$, F/m) 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 $$\epsilon = \epsilon_0$$ where: $\epsilon_0 \cong 8.854 \times 10^{-12} ~\mbox{F/m}$ 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: $\epsilon_r \triangleq \frac{\epsilon}{\epsilon_0}$ Values of $$\epsilon_r$$ for a few representative materials is given in Appendix A1. Note that $$\epsilon_r$$ 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.