(Equation 5.25)

where P_{in} is the incident power density and M is the mass of the object exposed to EM fields.

Figure 5.7.

Calculated average SAR in a prolate
spheroidal model of an average man, as a function of
frequency for several values of permittivity. m is the
permittivity of muscle tissue.

(Equation 5.26)

(Equation 5.27)

Figure 5.8.

Relative absorption cross section in prolate
spheroidal models of an average man, a rabbit, and a
medium-sized rat--as a function of frequency for E
polarization.

Figure 5.9.

Comparison of relative scattering cross
section (RSC) and relative absorption cross section (RAC) in
a prolate spheroidal model of a medium rat--for planewave
irradiation, E polarization.

E_{1p} = E_{2p} (Equation 5.28)

_{1}E_{1n} = _{2}E_{2n} (Equation 5.29)

where E_{lp} and E_{2p} are components parallel to the
boundary, and E_{ln} and E_{2n} are component, perpendicular to the
boundary, as shown in Figure 5.10. It is important to
remember that Equations 5.28 and 5.29 are valid only at a
point on the boundary. From Equation 5.29, we can see that
E_{2n} = _{1} E_{ln} /_{2}; and if _{2} >> _{1}, then E_{2n} << E_{1n}. Thus if E_{ln} is the field in free space and E_{2n} is the field in an absorber, the internal field *at the boundary *will be much weaker than the external field *at the boundary *when _{2} > > _{1} and the fields are normal to the boundary. Also, from Equation 5.28, we see that the external field and the internal field at the boundary are equal when the fields are parallel to the boundary. These two results will be used extensively in explaining relative energy absorption.

Figure 5.10.

Field components at a boundary between two media having different complex permittivities, _{1} and _{2}.

(Equation 5.30)

For the very special case of a lossy dielectric cylinder
in a uniform **H**-field Equation 5.30 can be solved by deducing
from the symmetry of the cylinder and fields that **E **will have
only a component that will be constant around a circular
path, such as the one shown dotted in Figure 5.11. For **E**
constant along the circular path, and **H **uniform, Equation
5.30 reduces to

(Equation 5.31)

Thus, Equation 5.30 shows that **E **is related to the rate
of change of the magnetic flux intercepted by the object; and
Equation 5.31 shows that for the very special case of Figure
5.11, the **E**-field circulates around the **H**-field and is
directly proportional to the radius. For this example the
circulating **E**-field (which produces a circulating current)
would be larger for a larger cross section intercepted by the
**H-**field. The generalized qualitative relation that follows
from Equation 5.30 is that the circulating field is in some
sense proportional to the cross-sectional area that
intercepts the **H**-field. This result is very useful in
qualitative explanations of relative energy absorption
characteristics; however, this qualitative explanation cannot
be used indiscriminantly.

Figure 5.11.

A lossy dielectric cylinder in a uniform magnetic field.

**E**_{in} = **E** _{e}+ **E**_{h} (Equation 5.32)

where

QP1.

**E**_{e} is stronger when **E**_{inc} is mostly *parallel *to the boundary of the object and *weaker *when **E**_{inc} is mostly *perpendicular *to the boundary of the object.

QP2.

**E**_{h} is *stronger *when **H**_{inc} intercepts a *larger *cross section of the object and *weaker *when **H**_{inc} intercepts a *smaller *cross section of the object.

Figure 5.12.

Qualitative evaluation of the internal
fields based on qualitative principles QPl and QP2. **E**_{e}
is the internal **E**-field generated by **E**_{inc}, the
incident **E**-field, and **E**_{h} is the internal
**E**-field generated by **H**_{inc},the incident
**H**-field.

Application of QP1 and QP2 To Planewave SARS

**E**_{e}increases as the magnitude of E_{inc}increases.**E**_{e}decreases as increases.**E**_{h}increases as the magnitude of H_{inc}increases.

**E**_{inc}is slightly lower at 200 MHz and significantly lower at 300 MHz than at the other frequencies.**H**_{inc }is lower at 200 and 300 MHz than at the other frequencies.- The angle of
**E**_{inc }with the z axis is significantly higher at 200 and 300 MHz than at the other frequencies.

Figure 5.13.

Average SAR in a prolate spheroidal model of
an average man as a function of normalized impedance for each
of the three polarizations. (a = 0.875 m, b = 0.138 m, f =
27.12 MHz, = 0.4 S/m, incident **E**-field is 1
V/m.)

Figure 5.14.

Ratio of (SAR)e, to (SAR)_{h} of a 0.07-m^{3}
prolate spheroid for each polarization as a function of the
ratio of the major axis to the minor axis of the spheroid at
27.12 MHz, = 0.4 S/m.

**Go to Chapter 5.2**

**Return to Table of Contents.**

Last modified: June 14, 1997

© October 1986, USAF School of Aerospace Medicine, Aerospace Medical Division (AFSC), Brooks Air Force Base, TX 78235-5301