Section 6.2 · Problems · 7 of 8
Problem 6.2.7: Finding parameters of a biological tissue
Finding parameters of a biological tissue
#A uniform plane time-harmonic electromagnetic wave of frequency propagates in the positive -direction through a nonmagnetic biological tissue of unknown parameters. According to the measurements, the wave amplitude is reduced to its value for every centimetre travelled, and the phase constant of the wave amounts to . Determine the permittivity and conductivity of the tissue.
Adapted from: B. M. Notaroš, Electromagnetics, Problem 9.25.
This is the inverse problem: and are measured and the medium is unknown. With the wave number (field ) of Eq. (6.2.3),
so the real part of gives and the imaginary part gives .
gives , that is per centimetre. Also rad/s.
, and the forward calculation with these values returns . Further, and , against . In the statement the phase constant is sometimes called the "propagation constant", and some texts write for .
Phantom liquids for testing mobile phones are mixed to the average head tissue of the standards, and at : the "measured" tissue is exactly of this kind. The power density falls as , to within , so a phone heats a skin layer of about a centimetre (Exercise 6.2.11).