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THE UNIVERSITY OF QUEENSLAND
SCHOOL OF ELECTRICAL ENGINEERING and COMPUTER SCIENCE
ELEC3100 FUNDAMENTALS OF ELECTROMAGNETICS
Week 9 - Problems to Solve
Problem 1
The principal investigator of UQ Photonics group decides to characterise newly arrived concrete blocks
non-destructively by using a monochromatic low-frequency electromagnetic probe with frequency at
= 1 GHz. To get a rough idea what’s going on, researchers decide to treat the low-frequency wave
as a uniform plane time-harmonic field with rms electric field intensity !" = 1 V/m. The lab technician
manages to run the transmission-type experiments in air. Now, this wave passes through the air and
eventually impinges on the flat surface of a bulky concrete block perpendicularly. The concrete block
material parameters are given as # = 6,
= 2.5 ⋅ 10$% S/m and # = 1.
(a) Now, you need to determine if the concrete block is a good dielectric, good conductor, or
quasi conductor, and find electric and magnetic fields in both media,
(b) Find the standing wave ratio in air
(c) Find the time average Poynting vector in the second medium
(d) Compute the percentages of the time average incident power that are reflected from the
interface and transmitted into the material block, respectively.
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Problem 2
A TEM wave propagating in air for y>0 is incident obliquely on a perfect electric conductor screen
occupying the plane y=0.The complex rms electric field intensity vector of the wave is given by
= '((*+√%-)3 (V/m).
You need to:
(a) Make a sketch for the situation and,
(b) Calculate the electric and magnetic field vectors of the resultant wave at an arbitrary position
in air.
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Problem 3
A 200-MHz left-hand circularly polarised plane wave with an electric field modulus of 5 V/m
is normally incident in air upon a dielectric medium with ! = 4 and occupying the region
defined by
≥ 0.
(a) Write an expression for the electric field phasor of the incident wave, given that the
field is a positive maximum at
= 0 and
= 0.
(b) Calculate the reflection and transmission coefficients. (c) Write expressions for the electric field phasors of the reflected wave, the transmitted
wave, and the total field in the region ≤ 0. (d) Give the polarisation state of the reflected and the transmitted wave
(e) Determine the percentages of the incident average power reflected by the boundary
and transmitted into the second medium.
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Problem 4
A perpendicularly polarised wave in air is obliquely incident upon a planar glass-air interface
at an incidence angle of 30○. The wave frequency is 600 THz (1 THz = 1012 Hz), which
corresponds to green light, and the index of refraction of the glass is 1.6. If the electric field
amplitude of the incident wave is 50 V/m, determine,
(a) The reflection and transmission coefficients.
(b) The instantaneous expressions for E and H in the glass medium.
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Problem 5
A uniform plane wave in air with () = 510 ⋅ $%&' is incident normally onto an interface at = 0 with a lossy medium having a dielectric constant of 2.5 and a loss tangent of 0.5.
You need to demonstrate to your tutor:
(a) By assuming a cosine reference, what are the instantaneous expressions for !(, ), !(, ), ((, ), ((, )?
(b) How do you find expressions for the time average Poynting vectors in the two media,
i.e., air and the lossy medium, respectively?
Hint: obtain expressions for a and
for a lossy medium first.
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Problem 6
An electromagnetic wave from an underwater source with perpendicular polarization is
incident on a water-air interface at q)
= 20°. Using ! = 81 for fresh water find:
(a) the critical angle
(b) the reflection coefficient.
(c) the transmission coefficient.
(d) the attenuation in dB for each wavelength in air.
Draw a diagram to illustrate the physical problem.
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