Читать книгу Introduction To Modern Planar Transmission Lines - Anand K. Verma - Страница 146

It is noted above that the charge and current create the electric and magnetic flux fields, described by the flux densities They also create the force field described by the electric and magnetic field intensities . The flux density parameters are related to the force field intensity parameters by the following constitutive relations:

(4.1.7)

where ε₀ and μ₀ are the permittivity and permeability of the free space. The permittivity of any medium is its ability to store electric energy, such as a capacitor. Therefore, it is identified as the capacitance of the free space. Any dielectric material medium can store more electric energy through the mechanism of electric polarization. The electric dipole is created during the process of polarization and the total induced charge is shown as electric flux density . Chapter 6 presents a detailed discussion of material polarization. The electric polarization of material under the influence of an external electric field gives a higher value of permittivity as compared to the permittivity of the free space. This is known as the relative permittivity ε_r of a medium. It is also known as the dielectric constant of a medium. The permittivity of a medium is ε = ε₀ε_r. For an isotropic dielectric medium, ε_r is a scalar quantity. However, for an anisotropic medium, it is a tensor quantity.

Likewise, the free space has also an ability to store magnetic energy. It is expressed as its permeability. Magnetic material is magnetized by the process of magnetization under the influence of an external magnetic field. Thus, magnetic material stores more magnetic energy as compared to the free space. The ability of a magnetic material to store magnetic energy is expressed through its relative permeability. The permeability of the medium is μ = μ₀μ_r. The permittivity ε₀ and permeability μ₀ of the free space are the primary physical constants ε₀ = 8.854 × 10⁻¹² F/m, μ₀ = 4π × 10⁻⁷ H/m. Again, for the isotropic magnetic medium, the relative permeability μ_r is a scalar quantity, and for an anisotropic medium, it is a tensor quantity.

It is interesting to note that the velocity of EM‐wave and the characteristic (intrinsic) impedance of the free space are given in terms of these primary constants,

(4.1.8)

A material medium with a finite conductivity dissipates energy in the form of heat. The finite conductivity of a medium is due to the presence of free charge carriers. The free space is considered as a lossless medium because it has no free charge carrier. The conduction current flows through a medium under the influence of an external electric field. The conduction current density () in a medium is related to the electric field intensity () by Ohm’s law:

(4.1.9)

where σ is the conductivity of a conducting medium. The conductivity (σ) of the isotropic conducting medium is a scalar and for an anisotropic conducting medium it is a tensor. As free space has no conductivity, there is nothing like the relative conductivity of a medium. However, sometimes the conductivity of a medium is expressed in terms of the conductivity of copper.

In summary, the electrical properties of a material are described by the relative permittivity (ε_r), relative permeability (μ_r), and conductivity (σ). A material can have all three properties at a time, or it can have one predominant property at a time. Assuming the case of one predominant property at a time, all materials are classified into three basic categories.