16
Electromagnetic Fields in Biological Systems
vector (P = E × H), one can find the direction and time-average flow of energy per unit
area, which is given by
P = η{[iβℓ/(4πr)] 2 }e j(ω t -βr) sin 2 θ r
(1.38)
Clearly, energy flow in the far zone is real and uniquely defined. It is outgoing in the
radial direction and perpendicular to both E θ and H ϕ . The electromagnetic energy is
hence radiated, and the term radiation zone is synonymous with far field. In the far
field, the intensity of radiated energy (power density) decreases as 1/r 2 with increase in
distance. As in a plane wave, the electric and magnetic fields are outgoing waves with
plane wavefronts independent of its source configuration. Also, in the far zone the field
strengths decrease as 1/r, and only transverse field components appear.
The distance criterion that is most commonly used to distinguish between near and
far zones is that the phase variation of the field from the antenna does not exceed λ/16
(Silver 1949). This boundary occurs at a conservative distance of
R = 2D 2 /λ
(1.39)
where D is the largest dimension of the antenna aperture.
1.9 Coupling of Quasistatic Electric
and Magnetic Fields
As discussed in Section 1.7, for low frequencies where the wavelength is long and time
variation is slow, the induced electric and magnetic fields inside a human body are quasistatic in nature. For all practical purposes, exposures to ELF electric and magnetic
fields always occur in the near-zone inductive region. Moreover, at ELFs the electric and
magnetic field components are decoupled inside a biological body. Indeed, these phenomena arise whenever a biological body or model is small compared to a wavelength.
Also, at ELFs the bulk electrical conductivity is on the order of 0.1 S/m and the relative
dielectric permittivity is about 10 6 . The ratio is
σ/ωε = 3 ×10 7 >>1
(1.40)
Thus, the conduction current is much greater than the displacement current, and biological materials may be considered as conducting media.
1.9.1 Quasistatic Electric Field Coupling
As a model of biological bodies, the induced field inside a spherical model with radius r,
conductivity σ, and dielectric permittivity ε can be considered. For a uniform or constant electric field, E 0 , polarized in the x direction (see Equations 1.13 and 1.15), we have
E 2 = (ωε 0 /σ)E 0 x
(1.41)
Therefore, an applied uniform outside electric field gives rise to a uniform induced
electric field inside the body, which has the same direction as the external field but is
Electromagnetic Fields in Biological Systems
vector (P = E × H), one can find the direction and time-average flow of energy per unit
area, which is given by
P = η{[iβℓ/(4πr)] 2 }e j(ω t -βr) sin 2 θ r
(1.38)
Clearly, energy flow in the far zone is real and uniquely defined. It is outgoing in the
radial direction and perpendicular to both E θ and H ϕ . The electromagnetic energy is
hence radiated, and the term radiation zone is synonymous with far field. In the far
field, the intensity of radiated energy (power density) decreases as 1/r 2 with increase in
distance. As in a plane wave, the electric and magnetic fields are outgoing waves with
plane wavefronts independent of its source configuration. Also, in the far zone the field
strengths decrease as 1/r, and only transverse field components appear.
The distance criterion that is most commonly used to distinguish between near and
far zones is that the phase variation of the field from the antenna does not exceed λ/16
(Silver 1949). This boundary occurs at a conservative distance of
R = 2D 2 /λ
(1.39)
where D is the largest dimension of the antenna aperture.
1.9 Coupling of Quasistatic Electric
and Magnetic Fields
As discussed in Section 1.7, for low frequencies where the wavelength is long and time
variation is slow, the induced electric and magnetic fields inside a human body are quasistatic in nature. For all practical purposes, exposures to ELF electric and magnetic
fields always occur in the near-zone inductive region. Moreover, at ELFs the electric and
magnetic field components are decoupled inside a biological body. Indeed, these phenomena arise whenever a biological body or model is small compared to a wavelength.
Also, at ELFs the bulk electrical conductivity is on the order of 0.1 S/m and the relative
dielectric permittivity is about 10 6 . The ratio is
σ/ωε = 3 ×10 7 >>1
(1.40)
Thus, the conduction current is much greater than the displacement current, and biological materials may be considered as conducting media.
1.9.1 Quasistatic Electric Field Coupling
As a model of biological bodies, the induced field inside a spherical model with radius r,
conductivity σ, and dielectric permittivity ε can be considered. For a uniform or constant electric field, E 0 , polarized in the x direction (see Equations 1.13 and 1.15), we have
E 2 = (ωε 0 /σ)E 0 x
(1.41)
Therefore, an applied uniform outside electric field gives rise to a uniform induced
electric field inside the body, which has the same direction as the external field but is