Fundamentals of Electromagnetics - RF/Microwave Interaction with Biological Tissues - page 56

is obtained. The derivation involves an approximation. It has been men-
tioned that a more accurate value of 0.0051 mK can be obtained without
this approximation. Prove this assertion.
1.18. Calculate the brightness of a blackbody radiator at a temperature of
6,000 K and a wavelength of 0.5 mm.
1.19. When the brightness is expressed in terms of unit wavelength, the wave-
length for the peak brightness is not the same as when brightness is
expressed in terms of unit bandwidth. The quantitative relation for the
l p T product when brightness is expressed in terms of unit wavelength is
obtained by maximizing (1.42) and simplifying. Prove that it yields the
value 0.0029 mK [15].
1.20. Show that the arc plot of a dielectric with a single relaxation time (Cole-
Cole diagram, Eqn. 1.52), obtained by representing e≤(w) as a function
of e¢(w), is a semicircle. Verify that a given point on the semicircle cor-
responds to a given frequency while the summit corresponds to wt= 1
and find the points for w = 0 and w =•. Observe the disadvantage: w
does not appear in it. Any material with a single relaxation time, char-
acterized by e s and e • gives the same arc plot. Observe that it is there-
fore essential to supply the magnitude of t in addition to the arc plot.