Dielectric

A dielectric is a material whose electrons are tightly bound to their atoms — they don’t migrate when an Electric field is applied. The material can still respond to a field, but only through polarization: bound electrons shift slightly relative to their nuclei, creating microscopic dipoles. No net charge flows.

This is the defining contrast with a conductor, where outer-shell electrons are loosely bound and free to migrate as a current.

Permittivity

A dielectric is characterized by its Permittivity $ϵ={ϵ}_r{ϵ}_0$, where the relative permittivity ${ϵ}_r>1$ measures how strongly the medium polarizes. Some examples:

Material	${ϵ}_r$
Vacuum	1 (exact)
Air	1.0006
Teflon (PTFE)	2.1
Quartz	3.8
Glass	4–10
Mica	5.4
Water	80

Water’s huge ${ϵ}_r$ comes from its permanent molecular dipole (oxygen pulls electrons from hydrogens), which reorients with the field.

Why dielectrics matter

Three practical reasons engineers care:

1. Capacitors. The capacitance $C=ϵA/d$ for a parallel-plate capacitor scales linearly with ${ϵ}_r$ of the filling material. A dielectric multiplies the capacitance for the same physical size.
2. Transmission lines. The phase velocity on a TEM line filled with dielectric is $u_p=c/\sqrt{{ϵ}_r}$ — signals travel slower in dielectric, which sets the wavelength and propagation timing.
3. Insulation. A perfect dielectric has $\sigma =0$ (no current flow), so it isolates conductors at different potentials. Real dielectrics have small but nonzero $\sigma$, leading to gradual leakage.

Three idealizations

The Electromagnetics conventions:

• Linear: $\mathbf{P}$ proportional to $\mathbf{E}$. Holds at moderate field strengths.
• Isotropic: $\mathbf{P}$ parallel to $\mathbf{E}$ (no directional preference). Crystals like quartz are anisotropic, with $ϵ$ a tensor.
• Homogeneous: $ϵ$ doesn’t vary with position. Composite materials and graded dielectrics violate this.

Together: $\mathbf{D}=ϵ\mathbf{E}$ with $ϵ$ a position-independent scalar.

Dielectric breakdown

Even an ideal dielectric breaks down at high enough field. The threshold is the dielectric strength $E_{\text{ds}}$ — beyond it, bound electrons ionize and a conduction avalanche begins. The material’s resistivity collapses, often with permanent damage. See Polarization (dielectric) for typical strength values.

This sets the maximum operating voltage for capacitors: $V_{\max }=E_{\text{ds}}\cdot d$, where $d$ is dielectric thickness. The trade-off in capacitor design: high ${ϵ}_r$ packs more capacitance into less volume, but the dielectric strength may be lower (or its breakdown more catastrophic) than a simpler material.

Compared with a conductor

Property	Conductor	Dielectric
Free electrons	Many	Effectively none
$\sigma$	Very large	Very small
$\mathbf{E}$ inside	$\approx 0$ in equilibrium	$\mathbf{E}=\mathbf{D}/ϵ$, nonzero
Surface charge	${\rho }_s={ϵ}_0{E}_n$	Bound polarization charges $-\nabla \cdot \mathbf{P}$
Current	$\mathbf{J}=\sigma \mathbf{E}$	$\mathbf{J}=0$ ideally

The duality is striking: both materials respond to applied $\mathbf{E}$, but the response mechanism is different. Conductors expel the field by moving charges to the surface; dielectrics partially cancel it by polarizing internally.