Linear diëlectric

A linear diëlectric is a material whose electric polarization density is proportional to the electric field¹, i.e.

⃗ 𝐏 = 𝜖 0 𝜒 𝑒 ⃗ 𝐄

where $𝜒 𝑒$ is the empirically determined electric susceptibility. The permittivity of a linear diëlectric is then

𝜖 = 𝜖 0 (1 + 𝜒 𝑒) = 𝜖 0 𝜖 𝑟

⃗ 𝐃 = 𝜖 ⃗ 𝐄

Homogenous linear diëlectric

In case a volume $Ω$ is occupied by a homogenous linear diëlectic, i.e. one with constant $𝜒 𝑒$ , we have

𝜌 𝑏 = - 𝜒 𝑒 1 + 𝜒 𝑒 𝜌 𝑓

hence if there is no free charge there is also no bound charge, and Laplace's equation will hold for $⃗ 𝐄$ within $Ω$ .

#state/tidy | #lang/en | #SemBr

Note that $⃗ 𝐄$ is the total electric field, including that caused by the polarized material itself. ↩