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. – 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, – Find the standing wave ratio in air – Find the time average Poynting vector in the second medium – Compute the percentages of the time average incident power that are reflected from the interface and transmitted into the material block, respectively.
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: – Make a sketch for the situation and, – Calculate the electric and magnetic field vectors of the resultant wave at an arbitrary position in air.
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. – Write an expression for the electric field phasor of the incident wave, given that the field is a positive maximum at = 0 and = 0. – Calculate the reflection and transmission coefficients. – Write expressions for the electric field phasors of the reflected wave, the transmitted wave, and the total field in the region ≤ 0. – Give the polarisation state of the reflected and the transmitted wave – Determine the percentages of the incident average power reflected by the boundary and transmitted into the second medium.
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, – The reflection and transmission coefficients. – The instantaneous expressions for E and H in the glass medium.
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: – By assuming a cosine reference, what are the instantaneous expressions for!(, ),!(, ), ((, ), ((, )? – 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.
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: – the critical angle – the reflection coefficient. – the transmission coefficient. – the attenuation in dB for each wavelength in air. Draw a diagram to illustrate the physical problem.