The electric flux density is also called the electric displacement, hence, the symbol D. It is also a vector. In an isotropic material (properties independent of direction) D and E are in the same direction and ε is a scalar quantity. In an anisotropic material, D and E may be in different directions if ε is a tensor.
If the permittivity is a complex number, it means that the material has some loss. The complex permittivity can be written as
(1.20)
The ratio of the imaginary part to the real part is called the loss tangent, that is
(1.21)
It has no unit and is also a function of frequency and temperature.
The electric field E is related to the current density J (in A/m2), another important parameter, by Ohm’s law. The relationship between them at a point can be expressed as
(1.22)
where σ is the conductivity, which is the reciprocal of resistivity. It is a measure of a material’s ability to conduct an electrical current and is expressed in Siemens per meter (S/m). Table 1.3 lists conductivities of some common materials linked to antenna engineering. The conductivity is also a function of temperature and frequency.
Table 1.3 Conductivities of some common materials at room temperature
| Material | Conductivity (S/m) | Material | Conductivity (S/m) |
|---|---|---|---|
| Silver | 6.3 × 107 | Graphite | ≈105 |
| Copper | 5.8 × 107 | Carbon | ≈104 |
| Gold | 4.1 × 107 | Silicon | ≈103 |
| Aluminum | 3.5 × 107 | Ferrite | ≈102 |
| Tungsten | 1.8 × 107 | Sea water | ≈5 |
| Zinc | 1.7 × 107 | Germanium | ≈2 |
| Brass | 1 × 107 | Wet soil | ≈1 |
| Phosphor bronze | 1 × 107 | Animal blood | 0.7 |
| Tin | 9 × 106 | Animal body | 0.3 |
| Lead | 5 × 106 | Fresh water | ≈10−2 |
| Silicon steel | 2 × 106 | Dry soil | ≈10−3 |
| Stainless steel | 1 × 106 | Distilled water | ≈10−4 |
| Mercury | 1 × 106 | Glass | ≈10−12 |
| Cast iron | ≈106 | Air | 0 |
1.4.2
