Permittivity and permeability of free space

Other SI electrical units are determined from the first four via the fundamental constants eo and tiQ, the permittivity and permeability of free space respectively. The ampere is defined in terms of the force between two straight parallel infinitely long conductors placed a metre apart, and once this has been defined the coulomb must be such that one coulomb per second passes along a conductor if it is carrying a current of one ampere. 

The absolute permittivity and absolute permeability of free space are denoted by So and Ha respectively. The sources of the electromagnetic-field vectors D, E, B, and H are the charge density, pQr, t), and the current density, due to charges in motion, J(r, /). The radius vector of a point with co-ordinates x, y, and z is denoted hy r = ix + Jy + kz, and the time is denoted by t. The use of the tilde, on the field variables in equations (1)—(6) is to emphasize that these equations describe the electromagnetic field in free space. Quantities without the tilde will have meanings to be defined below. 

The ratio c/u is always greater than 1, and is called the index of refraction of the material (through which the wave travels at the speed u). Note that though c is popularly called the velocity of light, it is the same for any electromagnetic wave. It can be shown that c = l/ y/( Xo o)> where x0 is the permeability of free space (vacuum or air) and e0 is the permittivity of free space. x0 and e0 are fundamental constants, since they represent the properties of our universe. 

The transmission boundary-value problem for homogeneous and isotropic particles has been formulated in Sect. 1.4 but we mention it in order for our analysis to be complete. We consider an homogeneous, isotropic particle occupying a domain D with boundary S and exterior (Fig. 2.1). The imit normal vector to S directed into is denoted by n. The exterior domain Ds is assumed to be homogeneous, isotropic, and nonabsorbing, and if t and jM. are the relative permittivity and permeability of the domain Ht, where t = s, i, we have s > 0 and ps > 0. The wave number in the domain Dt is kt = ko, /etPt, where ko is the wave number in the free space. The transmission boundary-value problem for a homogeneous and isotropic particle has the following formulation. 

Often, free-space methods are complementary to use of the waveguide, coaxial, cavity, one-horn interferometer or open-ended coaxial probe. Indeed, due to their heterogeneity, small composite samples arc not representative of the whole material and ffee-space methods are non-destnictive and contactless. They are also suitable for complex permittivity and permeability measurements under high temperature conditions. 

The terms permeability and permittivity of free space have their origins back when scientists viewed space as containing a material-type substance called ether. ... 

In this section we consider the basic properties of the scattered field as they are determined by energy conservation and by the propagation properties of the fields in source-free regions. The results are presented for electromagnetic scattering by dielectric particles, which is modeled by the transmission boundary-value problem. To formulate the transmission boundary-value problem we consider a bounded domain Di (of class with boimdary S and exterior D, and denote by n the unit normal vector to S directed into Ds (Fig. 1.8). The relative permittivity and relative permeability of the domain Dt are et and /it, where t = s,i, and the wave number in the domain Dt is kt = where ko is the wave number in free space. The imbounded... 

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