# Introduction to Polarization

What are the Different Types of Polarization?  In electromagnetism, polarization density or electric polarization or polarization is the density of electric dipole moment in a dielectric material. It occurs when a non-polar molecule is placed in an electric field. The electric field lines then pass through the molecules and try to align themselves according to the direction of electric field. The electric field then attract the negative charged particles present in the molecule towards positive plate and conversely the positive charged particles of the molecules towards the negative plate. This whole procedure will cause distortion in the non-polar molecule and as a result we will be able to see the formation of a new dipole.

Polarization also decides the response of an object when it is placed in an electric field. Relatively it is also responsible for the changes that the electric field undergoes when an unknown substance is placed inside the field. Different materials exhibit different polarization. The interaction between the material and their polarizability give rise to many other different forces of nature. Being quite common quantity in the field of electromagnetism, electric polarization extensively explains the drift of charged particles or simple the displacement that a charged particle cover which then result into the formation of an opposing alternating current in the electric field.

# Definition of Polarization

When an external electric field is applied to a dielectric material, it causes the charged particles inside the material to show a bit of displacement. These charged elements, can be any particle, are initially bound to the molecule and are not allowed to move freely unlike free electron which move freely inside a conductor to conduct electric charge. These charged particles are then attracted by the applied filed and like charges repel whereas unlike charges are attracted towards the direction of field. As a result of this theory, positive particles are displaced in the direction of the field whereas the negative particles are displaced opposite the direction of the field. However, being bound by the molecule, they still remain inside the molecule and the molecule remains at its initial position.

For a specific volume ΔV of the material, the dipole moment is Δp, the polarization density P is given as

P=Δp/ΔV

As we are familiar with the density, this formula is similar to the basis of density. As the dipole moment do not remain constant throughout the material, a change is observed in it. Hence the derivative will better explain the polarization density which is given as

P=dp/dV

The SI unit is given as coulombs per square meter. This definition of polarization density, dipole moment per unit volume, is commonly used in almost all the numerical problems. The charge which appear due to polarizing density is called as bound charge.

## Gauss’s law

Gauss’s law is also implacable in the concepts of polarization. As gauss’s law states that for a given closed charged surface, the total electric flux is equal to the charge enclosed by the object divided by the permittivity. Thus for a given volume V enclosed by a surface S, the bound charge Q, as defined earlier, inside the object is equal to flux of P through S with negative sign

$$-Q_b=\oiint P \cdot d A$$
Differential form
After applying divergence theorem on the above formula, gauss’s law for the field P can be easily written in the differential form as
$$-\rho_b=\nabla \cdot P$$
Where $\nabla . P$ is the divergence in the field $\mathrm{P}$ through a given surface containing bound charge density $\rho_b$.
Relationship between fields of $P$ \& $E$
Homogenous, isotropic dielectrics
In a linear, homogenous, non-dispersive and isotropic dielectric medium, the polarization is aligned with the electric field. The flow of displaced electrons is in line with the electric field applied externally. Also it is proportional to the electric field strength $\mathrm{E}$
$$P=X \varepsilon_o E$$
Where $\xi_g$ is the vacuum permittivity acting as electric constant and $X$ is the electric susceptibility of the medium.
Anisotropic dielectrics
In anisotropic dielectrics, the polarization density and the electric field are not evenly distributed. As a result of which, polarization density and electric field are not in the same direction.
For solving queries related to these materials, following expression is used. In such cases, the relationship between the $i$-th component of polarization and $f$-th component of electric field is observed
$$P_i=\sum_j \varepsilon_o X_{i j} E_j$$
This relation explains that a material can polarize in $x$ direction when a filed is applied in the $z$ direction. This case of anisotropic material is best described by the field of crystal optics.

# Types of polarization

There are two types of polarization of molecules

## Induced polarization

Induced polarization is the induced dipole when an induced electric field is applied on a material. The induced dipole moment or simply the induced moment is directly proportional to the strength of the electric field. In simple words this is the simple form of polarization where dipole is induced as a result of induced electric filed. This relation can be stated as

μ=αF

Where α is the constant of proportionality and is called induced polarizability constant.

## Orientation polarization

When a polarized molecule is produced as a result of induced electric field, the dipolar molecule tends to align itself according to the direction of the field. This is called orientation polarization and is given as

P_o=4πN_o α_o/3

Where αo is proportionality constant and is called as orientation polarizability.

Thus we conclude in orientational polarization, the orientation of the atom is somehow changed keeping the original state of the atom constant. Temperature has some effect on this type of polarization. Thermal energy in dipole molecules results in the elimination of net dipole moment.

# Types of dielectric polarization

Dielectric polarization is further categorized into 4 categories

## Electric polarization

When the center of positive charge and the center of negative charge in an atom are separated due to the effect of electric field, this phenomenon is known as atomic polarization or electric polarization. The relationship between induced dipole and applied electric field is a direct relation. Increment in one quantity is followed by the increment in other.

## Ionic polarization

In any ionic compound where atoms are bound together by ionic bonds, when an external electric field is applied, the atom breaks resulting in the formation of its constituents that are cations and anions. These cations and anions after separation move far from each other and align themselves in opposite side of the atom, result in some valuable net dipole. However, in the absence of any electric field, the net dipole remains zero.

## Orientational polarization

We have already discussed it above.

## Space-charge polarization

This type of polarization occurs when an external electric field causes the charges to accumulate between two plates or between two regions within a material. Thus a charge imbalance is observed because of insulating property of dielectric in the electric field. It generally occurs in compound dielectric materials.