25.11
Susceptibility, Permittivity and Dielectric Constant
When placed in an external electric field, a dielectric material gets polarized. The charge density in the dielectric material is given by the sum of…
In a polarized dielectric, the total charge density is the sum of the bound and free charge densities. Recalling the expression for bound charge density and rewriting the total charge density in terms of the total electric field gives the expression for electric displacement in terms of polarization.
In the case of linear dielectrics, the polarization is proportional to the total electric field. The constant of proportionality is called the electric susceptibility of the material, and the permittivity of free space makes the electric susceptibility dimensionless.
For an applied electric field, if electric susceptibility increases, the polarization increases.
Substituting the expression for polarization implies that the electric displacement is also proportional to the total electric field.
The new constant of proportionality is the permittivity of the material. The ratio of the material's permittivity to the permittivity of free space gives the relative permittivity, also known as the dielectric constant.
This estimates the ability to store charge for a given electric field. Materials with higher dielectric constants are used in capacitors to increase energy storage.
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Q1: What is electric susceptibility and how does it relate to polarization?
Electric susceptibility is a dimensionless constant that describes a material's tendency to become polarized in an external electric field. For linear dielectrics, polarization is directly proportional to the applied electric field, with electric susceptibility as the constant of proportionality. Materials with higher electric susceptibility exhibit greater polarization for the same electric field strength.
Q2: How is permittivity different from the dielectric constant?
Permittivity is the proportionality constant between electric displacement and the total electric field in a material. The dielectric constant, or relative permittivity, is the ratio of the material's permittivity to the permittivity of free space. The dielectric constant is always greater than 1 for any medium, while free space has a dielectric constant of exactly 1.
Q3: What role does the dielectric constant play in capacitor energy storage?
The dielectric constant estimates a material's ability to store charge for a given electric field. Materials with higher dielectric constants are used in capacitors to increase energy storage capacity. The presence of a dielectric medium in a capacitor always increases the energy storage, thereby increasing the capacitance compared to a capacitor with no dielectric.
Q4: How does total charge density relate to bound and free charge in a dielectric?
In a polarized dielectric, the total charge density is the sum of bound charge density and free charge density. The bound charge density can be expressed in terms of polarization, while the total charge density can also be written in terms of the total electric field. This relationship leads to the expression for electric displacement in terms of polarization.
Q5: Why is electric susceptibility dimensionless?
Electric susceptibility is made dimensionless by dividing the proportionality constant between polarization and electric field by the permittivity of free space. This normalization allows for consistent comparison of material polarization tendencies across different systems. The dimensionless nature makes electric susceptibility a pure material property independent of unit systems.
Q6: What happens to electric displacement when electric susceptibility increases?
When electric susceptibility increases for a given applied electric field, the polarization increases proportionally. Since electric displacement is also proportional to the total electric field through the material's permittivity, an increase in electric susceptibility results in increased electric displacement. This demonstrates how material properties directly affect the electric field behavior within dielectrics.
Q7: How does the dielectric constant relate to capacitance with and without a dielectric medium?
The dielectric constant is the same proportionality constant that relates the capacitance of a capacitor with a dielectric medium to its capacitance without one. A capacitor with a dielectric always has greater capacitance than the same capacitor with vacuum or air between its plates. The ratio of these capacitances equals the dielectric constant of the material used.