Antennas. Yi Huang

Antennas - Yi Huang


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≈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 Magnetic Field

      Whilst charges can generate an electric field, currents can generate a magnetic field. The magnetic field, H (in A/m), is the vector field that forms closed loops around electric currents or magnets. The magnetic field from a current vector I is given by the Biot–Savart law as

      (1.23)equation

      where

        is the unit displacement vector from the current element to the field point and

       r is the distance from the current element to the field point.

       I, and H follow the right‐hand rule, that is H is orthogonal to both I and , as illustrated by Figure 1.12.

      Like the electric field, the magnetic field exerts a force on electric charge. But unlike an electric field, it employs force only on a moving charge, and the direction of the force is orthogonal to both the magnetic field and the charge's velocity:

      where

       F is the force vector produced, measured in Newtons;

       Q is the electric charge that the magnetic field is acting on, measured in Coulombs (C);

       v is the velocity vector of the electric charge Q, measured in meters per second (m/s);

       μ is the magnetic permeability of the material. Its unit is Henries per meter (H/m). The permeability of free space is(1.25)

      In Equation (1.24), Qv can actually be viewed as the current vector I and the product of μH is called the magnetic flux densityB (in Tesla), the counterpart of the electric flux density. Thus,

      (1.26)equation

      Again, in an isotropic material (properties independent of direction), B and H are in the same direction and μ is a scalar quantity. In an anisotropic material, B and E may be in different directions and μ is a tensor.

      Like the relative permittivity, the relative permeability is given as

      (1.27)equation

Material Relative permeability Material Relative permeability
Superalloy ≈1 × 106 Aluminum ≈1
Purified iron ≈2 × 105 Air 1
Silicon iron ≈7 × 103 Water ≈1
Iron ≈5 × 103 Copper ≈1
Mild steel ≈2 × 103 Lead ≈1
Nickel 600 Silver ≈1

      Combining Equations (1.17) and (1.24) yields

      (1.28)equation

      This is called the Lorentz force. The particle will experience a force due to the electric field of QE and the magnetic field Qv × B.

      1.4.3 Maxwell’s Equations


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