Dielectrics & Polarization

An insulator has no free electrons, but its charges can still shift a little. In a field those tiny shifts add up to charge on its surfaces, and that charge weakens the field inside.

Polar and nonpolar molecules#

Every atom has a positive nucleus surrounded by electrons. What happens in a field depends on whether the centres of positive and negative charge already sit apart.

• Polar materials (water, for example): each molecule has a permanent dipole moment p⃗. Normally they point every which way, so any sizeable volume has zero net dipole moment. A field twists them toward its own direction, while thermal motion keeps scrambling them, so the alignment is only partial.
• Nonpolar materials: the centres coincide and there is no permanent dipole. A field pulls the electron cloud slightly against itself, inducing a small dipole in every atom or molecule.

Either way, a dielectric in a field acquires dipole moment throughout its volume. This is called polarization.

Bound charge on the surfaces#

Line up a slab’s dipoles from left to right. Inside, the head of each dipole sits next to the tail of the next, so the interior stays neutral. But the left face is left with a layer of negative ends and the right face with positive ends. This surface charge is the induced or bound charge: it comes from charges shifted slightly while still bound to their atoms.

For a slab of length l and face area A with bound charge density σ_p, the dipole moment is (σ_pA)l, and dividing by the volume Al:

Dielectric constant#

The bound charges make their own field E⃗_p, opposite to the applied field E⃗₀ in a uniform (homogeneous, isotropic) material. The total field E⃗ = E⃗₀ + E⃗_p points the same way as E⃗₀ but is weaker:

In a very strong field outer electrons are ripped from their atoms and the insulator starts to conduct: dielectric breakdown. The lowest field that causes it is the material’s dielectric strength.