15
Coupling of Electromagnetic Fields into Biological Systems
Short dipole
Near
field
r
Far
field
Reactive
Radiative
θ
energy
energy
transfer
transfer
FigurE 1.6 Flow of electromagnetic energy from a dipole antenna: Arrows represent the direction of energy flow at successive instants in time.
Invoking the Poynting vector shows that the quasistatic and induction terms represent energy that is stored in the field during one quarter of a cycle and is returned to
the antenna during the next quarter of the cycle without net or average outward flow.
In the near zone, the energy exchange is largely reactive; only the 1/r terms contribute
to an average outward flow of energy. The energy transfer characteristics are illustrated
in Figure 1.6, in which the arrows represent the direction of energy flow at successive
instants in time (Lin 2000). Power density in the near zone is not as uniquely defined
as in the far zone, since the electric and magnetic fields and their ratios vary from point
to point. Furthermore, the angular distribution actually depends on the distance from
the antenna. It is necessary to individually arrive at a quantitative determination of the
power density at all points.
1.8.3 Far Field of a Dipole Antenna
At points far from the dipole antenna, r is large and terms involving 1/r 2 and 1/r 3 in
Equations 1.26 through 1.28 can be neglected in comparison with terms involving 1/r.
Thus, in the far field only two field components remain, which are given by
E θ = j[ηiβℓ/(4πr)] e j(ω t−βr) sin θ
(1.36)
H ϕ = j[(iβℓ/(4πr)] e j(ω t−βr) sin θ
(1.37)
The wave impedance in the far zone is defined by the ratio E θ /H ϕ , which is the same as
the intrinsic impedance η = (μ/ε) 1/2 of the medium. Also, E θ and H ϕ are in time phase
and at right angles to each other. Thus, the electric and magnetic fields in the far field of
a dipole are related in the same fashion as in a plane wave. Further, from the Poynting
Coupling of Electromagnetic Fields into Biological Systems
Short dipole
Near
field
r
Far
field
Reactive
Radiative
θ
energy
energy
transfer
transfer
FigurE 1.6 Flow of electromagnetic energy from a dipole antenna: Arrows represent the direction of energy flow at successive instants in time.
Invoking the Poynting vector shows that the quasistatic and induction terms represent energy that is stored in the field during one quarter of a cycle and is returned to
the antenna during the next quarter of the cycle without net or average outward flow.
In the near zone, the energy exchange is largely reactive; only the 1/r terms contribute
to an average outward flow of energy. The energy transfer characteristics are illustrated
in Figure 1.6, in which the arrows represent the direction of energy flow at successive
instants in time (Lin 2000). Power density in the near zone is not as uniquely defined
as in the far zone, since the electric and magnetic fields and their ratios vary from point
to point. Furthermore, the angular distribution actually depends on the distance from
the antenna. It is necessary to individually arrive at a quantitative determination of the
power density at all points.
1.8.3 Far Field of a Dipole Antenna
At points far from the dipole antenna, r is large and terms involving 1/r 2 and 1/r 3 in
Equations 1.26 through 1.28 can be neglected in comparison with terms involving 1/r.
Thus, in the far field only two field components remain, which are given by
E θ = j[ηiβℓ/(4πr)] e j(ω t−βr) sin θ
(1.36)
H ϕ = j[(iβℓ/(4πr)] e j(ω t−βr) sin θ
(1.37)
The wave impedance in the far zone is defined by the ratio E θ /H ϕ , which is the same as
the intrinsic impedance η = (μ/ε) 1/2 of the medium. Also, E θ and H ϕ are in time phase
and at right angles to each other. Thus, the electric and magnetic fields in the far field of
a dipole are related in the same fashion as in a plane wave. Further, from the Poynting