Advanced Electromagnetism Notes Material Properties Dielectrics, Polarization, and Permittivity
Dielectrics are materials whose dominant charges in atoms and molecules are bound negative and positive charges that are held in place by atomic and molecular forces and they are not free to travel. i.e. Dielectrics do not contain any free charges.
When external forces (fields) are applied, these bound negative and positive charges do not move to the surface of the material as in conductors, but their respective centroids can shift slightly in position relative to each other, thus creating numerical electrical dipoles.
The formation of electric dipoles is usually referred to as orentational polarization. For each dipole, their moment is given by:
Where Q is the magnitude of the charge and l is the distance/length of the dipole.
The total dipole moment is given by the following equation:
Where Ne is the electric dipoles per unit volume, Îv is total volume, and NeÎv is the total number of electric dipoles.
Electric polarization vector can be defined as the dipole moment per unit volume. Or in terms of an equation:
Where the P with the bar over it represents surface charge density which is bound. Within a volume an integral number of positive and negative pairs with an overall zero net charge must exist.
Assuming an average dipole moment of
The electric polarization vector can be written as:
Electric polarization for dielectrics can be produced by any of the following mechanisms.
Dipole or Oriental Polariziation: This polarization is evident in material that, in the absence of an applied field and owing to their structure, possess permanent dipole moments that are randomly oriented. However, when an electric field is applied these diples tend to align with the applied fields (polar.) For example, water is a good polar material
Ionic or Molecular Polarization: Evident in materials such as salt that posses anions (+ve) and cations (-ve) and that tend to displace themselves when an electric field is applied.
Electronic Polarization: Exists when an applied electric field displaces the electric cloud center of an atom relative to the center of the nucleus.
If the charges in a material, in the absence of an applied electric field are averaged in such a way that anion and cation charges cancel each other throughout the material, then there are no individual dipoles formed and the total dipole moment and electric polarization vector are zero. However, when an electric field is applied, it exhibits a net nonzero polarization. Such a material is referred to as nonpolar material.
Polar materials are those whose charges in the absence of an applied electric field are distributed so that there are individual dipoles formed each with a dipole moment but with a net total dipole moment and electric polarization vector of zero. This is usually due to the random orientation of the dipole. Typical dipole moments are on the order of 10^-30 Coulomb-meters.
Materials that, in the absence of an applied electric field, posses a net dipole moment and electric polarization vector with a nonzero value are referred to as electrets.
When an electric field is applied to a nonpolar or polar dielectric material, the charges in each medium are aligned in such a way that individual dipoles with nonzero dipole moments are formed within the material.
When we see the material on a macroscopic scale, we can say the following:
On the lower surface, there exists a net positive surface charge density.
On the upper surface there exists a net negative surface charge density.
The volume density inside the material is zero because the positive and negative of adjacent dipoles cancel each other out.
In this figure, a DC source is connected and remains across two parallel plates separated by distance s. Half of the space between the two plates is occupied by dielectric and half is filled with air (i.e. free space.)
Assume five free charges on each part of the plates separated by free space. The same number appears on the part of the plates separated by dielectric material Because of the realignment of bound charges in dielectric material and formation of electric dipoles and cancellation of adjacent opposite charges, a polarization electric vector is formed within the dielectric material.
The net effect is that between the lower and upper surfaces of the dielectric there is a net electric polarization vector directed from the upper toward the lower surfaces, in the same direction as the applied electric field, whose amplitude is given by:
The electric flux density for free space is given by:
The electric flux density is related in the dielectric portion assuming free space is:
Where Ï is the electric susceptibility.
Where Δ_s is the static permitivty whose relative value Δ_sr is given by:
referred to as the relative permittivity (dielectric constant).
The index of refraction: n=âΔr
The dielectric constant of a dielectric material is a parameter that indicates the relative (compared to free space) charge (energy) storage capabilities of a dielectric material. The larger its value, the greater its ability to store charge.
Up next: FUCKING MAGNETISM AND HOW IT WORKS!