Dielectrics

Very few $e^-$ available for conduction

• At atomic level, dielectric atom has $e^-$ cloud surrounding $q^+$ (nucleus)
• Electrically neutral

Applying $\vec E$

$$ \vec P = q \vec d $$

• Causes $e^-$ cloud to shift → as a result diploles are formed in the direction of $\vec E$
• Presence of $\vec E$ induces local dipole moment $\vec P$
• Dielectric is said to be polarized

Non-polar Material: Have no dipole until influenced by $\vec E$, then become polarized

• Hydrogen, Oxygen, Nitrogen

Polar Material: Have built-in dipoles that are randomly oriented

• Water, Sulfur, HCl

Linear dielectric medium: when $|\vec P|$ is proportional $|\vec E|$

Isotropic: When $\vec E$ and $\vec P$ have the same direction

Homogenous: If its constitutive parameters ($\sigma, \epsilon, \mu)$ are constants through medium

Polarization: Shows the density of electric dipole moment ($\vec p)$ per unit volume and is given by:

$$ \text{Polarization for linear, isotropic, and homogenous material: }\vec P = X_e \epsilon _0 \vec E $$

• $X _e$ is susceptibility, scalar if isotropic
  • Shows how receptive a material is to polarization
  • Not all materials polarize immediately in the presence of an electric field

Note: Presence of dipoles changes electric flux density $\vec D$

$$ \vec D = \epsilon _0 \vec E + \vec P \newline \vec D = \epsilon _0 \vec E + X _e \epsilon _0 \vec E \newline \vec D = \epsilon _0 \epsilon _r \vec E = \epsilon \vec E $$

• $\vec P$ = electric polarization field