Diëlectric

Linear diëlectric

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

⃗𝐏=𝜖0𝜒𝑒⃗𝐄

where 𝜒𝑒 is the empirically determined electric susceptibility. The permittivity of a linear diëlectric is then

𝜖=𝜖0(1+𝜒𝑒)=𝜖0𝜖𝑟

and the Electric displacement is given by

⃗𝐃=𝜖⃗𝐄

Homogenous linear diëlectric

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

𝜌𝑏=−𝜒𝑒1+𝜒𝑒𝜌𝑓

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

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tidy | en | SemBr

Footnotes

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