Dielectric Polarization In Polar And Non-Polar Material and Dielectric Constant

Dielectric polarization is the alignment of electric dipoles in a material when exposed to an electric field. This behavior varies between polar materials, which have permanent dipoles, and non-polar materials, where dipoles are induced. The extent of polarization affects a material’s dielectric constant, a key factor in its ability to store electrical energy. Understanding these differences is essential in designing efficient electrical and electronic components.

1.0Dielectrics

• The insulators in which microscopic local displacement of charges takes place in presence of electric fields are known as dielectrics.
• Dielectrics are non-conductors up to a certain value of the field depending on its nature. If the field exceeds this limiting value called dielectric strength they lose their insulating property and begin to conduct.
• Dielectric strength is defined as the maximum value of electric field that a dielectric can tolerate without breakdown. The unit is volt/metre.
• Dimensions $\left[M^1{L}^1{T}^{-3}{A}^{-1}\right]$

2.0Polar Dielectrics

In absence of external field the centres of positive and negative charge do not coincide-due to asymmetric shape of molecules.

•  Each molecule has a permanent dipole moment.
• The dipoles are randomly oriented so the average dipole moment per unit volume of polar dielectric in absence of an external field is nearly zero. In the presence of external field dipoles tends to align in the direction of the field.
• Example: Water, Alcohol, ${\mathrm{CO}}_2,\mathrm{ECl},{\mathrm{NH}}_3$

Note: Dipole moment of polar molecules depends on temperature.

3.0Non-Polar Dielectrics

• In the absence of an external field the centre of positive and negative charge coincides in these atoms or molecules because they are symmetric.
• The dipole moment is zero in normal state.
• In the presence of an external field they acquire induced dipole moments.
• Example: Nitrogen, Oxygen, Benzene, Methane

Note: Induced electric dipole moment of non-polar molecules is independent of temperature.

Polarisation: The alignment of dipole moments of permanent or induced dipoles in the direction applied electric field is called polarisation.

4.0Polarisation Vector

• This is a vector quantity which describes the extent to which molecules of dielectric become polarized by an electric field or oriented in the direction of the field.
• $\vec{P}=\text{ the dipole moment per unit volume of dielectric }=n\vec{p}$

where n is number of atoms per unit volume of dielectric and $\vec{P}$ is the dipole moment of an atom or molecule.

$\vec{P}=n\vec{p}=\frac{qib}{Ad}=\left(\frac{qi}{A}\right)={\sigma }_i=\text{ Induced Surface Charge Density. }$

5.0Dielectric Polarization(Capacitors with Dielectric)

Dielectric polarization in capacitors refers to the alignment of electric dipoles within a dielectric material placed between the capacitor plates, reducing the effective electric field and increasing the capacitor's ability to store charge.

• In absence of dielectric, $E=\frac{\sigma }{{ϵ}_o}$
• When a dielectric is placed between the plates, its dipole molecules align with the electric field.
• ${\sigma }_B={\sigma }_i$ induced (bound) charge density (called bound charge because it is not due to free electrons).The induced charge also produces an electric field.
• Let $E_o,V_o,C_o$ be electric field, potential difference and capacitance in absence of dielectric and E,V,C E, V, C are electric fields,potential difference and capacitance respectively in presence of dielectric.

Electric field in absence of dielectric, $E_O=\frac{V_O}{d}=\frac{\sigma }{{ϵ}_o}=\frac{Q}{{ϵ}_{o}A}$

Electric field in presence of dielectric, $E=E_o-E_i=\frac{\sigma -{\sigma }_b}{{ϵ}_o}=\frac{Q-Q_b}{{ϵ}_o}=\frac{V}{d}$

Capacitance in absence of dielectric, $C_o=\frac{Q}{V_o}$

Capacitance in presence of dielectric, $C=\frac{Q-Q_b}{V}$

The dielectric constant or relative permittivity $(K\text{ or }{ϵ}_r)$,

${ϵ}_r=\frac{E_o}{E}=\frac{V_o}{V}=\frac{C}{C_o}=\frac{Q}{Q-Q_b}=\frac{\sigma }{\sigma -{\sigma }_b}=\frac{ϵ}{{ϵ}_o}$

$\text{ Form }K=\frac{Q}{Q-Q_b}\Rightarrow Q_b=Q\left(1-\frac{1}{K}\right)$

$K=\frac{\sigma }{\sigma -{\sigma }_b}\Rightarrow {\sigma }_b=\sigma \left(1-\frac{1}{K}\right)$

6.0Capacitance in the Presence of Dielectric

$C=\frac{\sigma A}{V}=\frac{\sigma A}{\frac{\sigma }{K{ϵ}_o}\cdot d}=\frac{AK{ϵ}_o}{d}$

Here capacitance is raised by a factor K.

$C=\frac{AK{ϵ}_O}{d}=C_{O}K$

7.0Relation Between Polarization and Induced Surface Charge Density

Equivalent dipole moment of dielectric slab = $q_i\times d$

Electric polarization

$(\vec{P})=\frac{q_i\times d}{V}(V\Rightarrow \text{ volume of dielectric slab })$

$\vec{P}=\frac{q_i\times d}{A\times d}\Rightarrow \vec{P}=\frac{q_i}{A}={\sigma }_i$

$P={\sigma }_i$

It is clear that polarisation is equal to induced surface charge density.

8.0Electric Susceptibility

Polarisation (P)of dielectrics is directly proportional to the electric field (E), i.e.

$P\propto E$

$P={ϵ}_o{\chi }_{e}E$

${\chi }_e=\text{ Electric Susceptibility (constant) }$

$\text{ For vacuum, }{\chi }_e=0$

9.0Dielectric Strength

The maximum electric field strength that a dielectric material can withstand without undergoing electrical breakdown.

$E_{\text{break }}=\frac{V_{\text{break }}}{d}$

$\text{ For Air, }{E}_{\text{break }}=3\times 10^6\mathrm{V}/\mathrm{m}$