Question

W hat is polarization in dielectric? Derive the relation where symbols have their usual meaning.

Answer 1

Answer:

Polarization in dielectric medium:

If an external electric field is applied to a dielectric material then the electric field exerts a force on each charged particle in the material, pushes the positive charges along its own direction while the negative charge is displaced in opposite direction. Due to this effect, the centers of positive and negative charges of each atom are displaced from their equilibrium positions. Such a molecule or atom is then called as induced dielectric dipole and this process is known as dielectric polarization.

The induced dipole moment of an individual atom is proportional to the applied electric field E and is given by p = E, where is called atomic polarizability. Its value depends on the detailed structure of the atom.

A lot of little dipoles in the material pointing along the direction of the eternal electric field then the material becomes polarized. A convenient measure of this effect is P = dipole moment per unit volume, which is called Polarization.

Using Gauss's law in dielectric,

The total charge density in the dielectric is = _b + _f , where _b is the bound charge density and _f is the free charge density. Gauss's ;law states that ∇. E = /₀

which implies that ₀ ∇. E = = _b + _f = - ∇. P + _f

Since bound charge density _b = - ∇. P

Therefore, ∇.(₀E + P) = _f,

The expression in the parentheses, designated by the letter D.

             D = (₀E + P)    is known as electric displacement.

In terms of D, Gauss's law becomes ∇. D = _f.

And polarization is proportional to the electric field , P = _0eE,   where _e is called the electric susceptibility of the medium.

In linear dielectric medium, D = ₀E + P = ₀E + _0eE = ₀(1+_e)E

so D is also proportional to the electric field E, that means, D = E

where, = ₀(1+_e).   Here, the new constant is called the permittivity of the material

Finally. = ₀(1+_e) = _0r, therefore the dimensionless quantity _r = /₀ = 1+_eand it is known as relative permittivity or dielectric constant of the material.