Section 5.6 · Home exercises · 5 of 7
Home exercise 5.6.5: Wet soil from 100 kHz to 1 GHz
About the home exercises of Section 5.6
Home exercises 5.6.1–5.6.3 belong to the lecture, Home exercises 5.6.4–5.6.7 to the exercise lecture.
Wet soil from 100 kHz to 1 GHz
#A wet soil has , and , independent of frequency.
- Find the loss tangent at , and , and say at each frequency whether the soil acts as a good conductor, a good dielectric or neither.
- At which frequency are the conduction and displacement currents equal?
- At find , , the wavelength in the soil and the distance over which the field falls to .
Strategy
The ratio of conduction to displacement current is , which falls as for constant and . At one frequency the medium is a lossless one with , and .
a)
, so
At the soil is a good conductor (), at neither, at a good dielectric ().
b)
at .
c)
At , . With and ,
Answer
Check
, and .
Remark
In air the wave is long. In the soil it is long, and it falls to in about a quarter wavelength. The same soil passes from conductor to dielectric over four decades of frequency, which is why ground-penetrating radar works at hundreds of MHz while low-frequency signals hardly enter the ground.