Spread the love

Electric Polarization | What Is Electric Polarization

Electric Polarization | What Is Electric Polarization :- When a non-polar dielectric material is placed in an external electric field $\displaystyle {{\overrightarrow{E}}_{0}}$ , the centre of positive charge experiences a force in the direction of the electric field $\displaystyle {{\overrightarrow{E}}_{0}}$ , while the centre of negative charge experiences a force in the direction opposite to the electric field $\displaystyle {{\overrightarrow{E}}_{0}}$ .

The electric field $\displaystyle {{\overrightarrow{E}}_{0}}$ increases the separation between the centers of the positive and negative charges, while the attractive force between the positive and negative charges tends to reduce the distance between them. Thus, the molecule gets distorted and behaves like an electric dipole, and in equilibrium each molecule possesses a dipole moment.

Similarly, a polar dielectric also becomes polarized when placed in an electric field. In the absence of an external electric field, the molecules of the dielectric are randomly oriented, so their resultant dipole moment is zero. However, when an electric field is applied, each dipole (molecule) tends to align itself along the direction of the electric field. As a result, the polar dielectric acquires a net dipole moment.

The extent of polarization depends on the strength of the applied electric field $\displaystyle {{\overrightarrow{E}}_{0}}$ (which tends to align the molecules along the direction of the electric field) and on the thermal energy (which opposes the alignment of the molecules along the direction of the electric field).

Therefore, when a dielectric material (polar or non-polar) is placed in an external electric field, the positive and negative charges present in its molecules or atoms are slightly displaced relative to each other in opposite directions. As a result, electric dipoles are formed (or aligned), and a net electric dipole moment per unit volume is produced in the material. This phenomenon is called electric polarization.

Effect of an External Electric Field on a Dielectric Slab

(Electric Polarization | What Is Electric Polarization)

Suppose a non-polar dielectric slab PQRS is placed between the two plates of a capacitor in a uniform electric field $\displaystyle {{\overrightarrow{E}}_{0}}$ .

Let us assume that in the presence of an external electric field $\displaystyle {{\overrightarrow{E}}_{0}}$ , each molecule becomes uniformly polarized, and the distance between the centers of the positive and negative charges is . Therefore, the dipole moment of each molecule will be p = qx. If the number of molecules per unit volume is , then the dipole moment per unit volume (polarization) is P = Np = Nqx.

Polarization ( $\displaystyle \overrightarrow{P}$ )

It is a vector quantity that indicates the extent to which a molecule or an atom can be polarized in the direction of the electric field in the presence of an external electric field. The polarization vector $\displaystyle \overrightarrow{P}$ is defined as the dipole moment produced per unit volume (total dipole moment density). It is given as follows –

$\displaystyle \overrightarrow{P}$ = Dipole moment per unit volume

⇒ $\displaystyle \overrightarrow{P}=N\text{ }\vec{p}=Nq\vec{x}$

Unit of Polarization (m^-3)C-m= C-m^-2

Substances whose molecules or atoms become polarized in the direction of an external electric field are called linear isotropic dielectrics. The induced dipole moments of different molecules combine to give the dielectric a net dipole moment in the presence of the external field.

For linear isotropic dielectrics, the polarization vector is proportional to the resulting (reduced) electric field. Hence, the polarization vector can also be expressed as follows :-

$\displaystyle \overrightarrow{P}=\varepsilon {{\chi }_{e}}\overrightarrow{E}$ …..(1)

Where χ_e is a dimensionless constant called the electric susceptibility. The value of χ_e varies for different dielectric materials. For vacuum, χ_e = 0.

After polarization, the total charge within the dielectric (enclosed by the dashed line) is zero, because the positive charge of one dipole is positioned near the negative charge of another dipole, canceling each other out. However, a layer of charge is induced on the surface of the dielectric.

This charge is called the induced charge (Q_i) or polarization charge, and due to the induced charge, the surface charge density is called the induced surface charge density (σ_i).

Again

$\displaystyle P=N\text{ }p=\frac{{{Q}_{i}}d}{Ad}=\frac{{{Q}_{i}}}{A}={{\sigma }_{i}}$ …..(2)

The induced charge Q_i generates a new electric field $\displaystyle {{\overrightarrow{E}}_{p}}$ , which is in the opposite direction to the applied electric field $\displaystyle {{\overrightarrow{E}}_{0}}$ .

∴ Effective electric field in a polarized dielectric

$\displaystyle E={{E}_{0}}-{{E}_{p}}$ …..(3)

Also

$\displaystyle {{E}_{p}}=\frac{{{\sigma }_{i}}}{\varepsilon }=\frac{1}{\varepsilon }\frac{{{Q}_{i}}}{A}=\frac{P}{\varepsilon }$ …..(4)

Dielectric Constant

(Electric Polarization | What Is Electric Polarization)

The ratio of the applied electric field $\displaystyle {{\overrightarrow{E}}_{0}}$ to the resulting electric field E( $\displaystyle E={{E}_{0}}-{{E}_{p}}$ ) is called the dielectric constant of the given material. It is denoted by K.

$\displaystyle K=\frac{{{E}_{0}}}{E}$ …..(5)