Dielectrics

Physics 101F

Introduction and Molecular Theory

• Dielectric are the insulators which are highly resistant to the flow of an electric current e.g. air, wax, glass etc.

• Dielectrics are broadly divided into two groups – Polar and Nonpolar Dielectrics.

• If the center of the gravity of positive charges coincides with the centre of gravity of negative charges, the molecule does not posses dipole moment and is said to be nonpolar. E.g. Oxygen, Nitrogen and Hydrogen.

….continue

• When such a molecule is placed in an electric field, the centre of positive and negative charge get displaced. The positive charge in the direction of electric field and negative charge in opposite direction of electric filed. The molecule is said to be polarized and is called induced dipole. The dipole acquired by the molecule is called induced dipole moment. As soon as the external field removes induced dipole moment disappears.

….continue• In some dielectric like water, HCl etc. the centre of

gravity of positive charge does not coincide with the centre of gravity of negative charges. These asymmetric molecule posses an intrinsic dipole moment and dielectric is said to be polar dielectric.

• In the absence of electric field the molecules are oriented in random direction, therefore the net dipole moment per unit volume is zero.

• In the presence of electric field, the molecular dipole expresses a torque that tends to align them with the filed direction. The dielectric is said to be polarized and the phenomenon is called polarization of dielectric.

Polarization

• The alignment of dipoles of the permanent or induced dipoles along the external field is termed as polarization of a dielectric.

• Types of Polarization – (a) Electronic Polarization, (b) Ionic Polarization, (c) Orientation Polarization

• (a) Electrical Polarization – When Dielectric is placed in an electric filed, the electron clouds of the constituent atoms or molecules experiences a displacement with reference to heavy fixed nucleus. This causes induced induced dipole moment and phenomenon is called Electronic Polarization. It is independent of temperature.

….continue• (b) Ionic Polarization - In the presence of

external field the ions in ionic molecules like NaCl are displaced from their equilibrium position causing an alteration in their intrinsic dipole moment. It is called Ionic Polarization. This is also independent of Temperature and have values less than Electronic Polarization.

• (c) Orientation Polarization – Polar Dielectrics have molecules which has intrinsic dipole moments but due to random orientation of these dipoles there is no net moments on the dielectrics.

• When such a polar dielectrics is placed in an electric field, the molecular dipoles rotate about their axis of symmetry to align with external field. This is strongly temperature dependent.

• The net Polarization in a dielectric is taken to be a sum of all the above three polarization probabilities.

Fig. Orientation polarization in water molecule

Displacement Vector, Electric Susceptibility, Dielectric Coefficient, Permittivity and

various relation between these

• Displacement Vector D is defined as a vector quantity whose surface integral over any charged surface, the flux of D, is equal to the free charge only within the surface. It is given by the following relation.

D = ε0 E + P

Here E is electric field intensity and P is dielectric polarization.

….continue• The electric susceptibility may be defined as the

ratio of polarization vector to the electric intensity in the dielectric.

Gauss’s Law in Dielectrics•The total flux passing through a closed The total flux passing through a closed surface is proportional to the charge surface is proportional to the charge enclosed within that surface.enclosed within that surface.•Gauss’s Law can be used to determine the Gauss’s Law can be used to determine the electric field of a charge distribution if electric field of a charge distribution if there is a high degree of symmetrythere is a high degree of symmetry

Example - Long straight line of chargeExample - Long straight line of charge

• Looking at the diagram (b), we can Looking at the diagram (b), we can determine that the problem has a determine that the problem has a cylindrical symmetrycylindrical symmetry..

• Therefore cylindrical coordinates Therefore cylindrical coordinates are appropriate.are appropriate.There are three surfaces to consider. The There are three surfaces to consider. The upper upper and lower circular surfacesand lower circular surfaces have normals parallel have normals parallel to the z axis which are perpendicular to the electric to the z axis which are perpendicular to the electric field, thus field, thus contribute zero to the fluxcontribute zero to the flux..

The integral to be evaluated is that of the The integral to be evaluated is that of the cylinder cylinder of height of height . The . The charge enclosed is charge enclosed is ..

Example - Long straight line of chargeExample - Long straight line of charge

Since the field has radial symmetry, it is also Since the field has radial symmetry, it is also constant at a fixed distance of r.constant at a fixed distance of r.