- Elecromagnetism 1 (170.4 KiB) Viewed 24 times
Elecromagnetism
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Elecromagnetism
Elecromagnetism
4.1 an 4.8. A wireless computer network transmits data across the space between nodes as a modulation of a 2.45 GHz (microwave) carrier signal. The signal is able to pass through a brick wall that is 100 mm thick. Recent measurements have determined that the dielectric function at microwave frequencies for the material of a typical building brick is E = Ereal + i Eimag = 5.86 + 0.68 i, and the relative permeability is unity. (a) With reference to the electric and magnetic fields and relevant boundary conditions, explain what happens to the 2.45 GHz radiation when it encounters the surface of a brick wall, at normal incidence. (Suggested answer length: 150 words.) (14 marks) (b) Show that about 17% of the energy that strikes the brick surface at normal incidence is reflected. (Since Ereal > Eimag for brick, it is satisfactory at the interface to suppose that E Ereal.) (8 marks) (c) (i) Show that the standard plane wave solution for 2.45 GHz radiation as it propagates through the bulk of a brick can be given by E = Eo exp[-kimagz] exp[i(kreal2 – wt)] ez. where kreal = nreal w/c ~ Ereal w/c and kimag = Nimag W/C Eimagw/2cVE real. (12 marks) (ii) Explain the physical interpretation of the two exponential terms in the expression for E in part (c) (i). (Suggested answer length: 100 words.) (4 marks) (d) Show that in passing perpendicularly through 100 mm of brick only about 16% of the incident energy emerges. (Multiple reflections can be ignored but transmission across both interfaces must be taken into account.) (12 marks)
4.1 an 4.8. A wireless computer network transmits data across the space between nodes as a modulation of a 2.45 GHz (microwave) carrier signal. The signal is able to pass through a brick wall that is 100 mm thick. Recent measurements have determined that the dielectric function at microwave frequencies for the material of a typical building brick is E = Ereal + i Eimag = 5.86 + 0.68 i, and the relative permeability is unity. (a) With reference to the electric and magnetic fields and relevant boundary conditions, explain what happens to the 2.45 GHz radiation when it encounters the surface of a brick wall, at normal incidence. (Suggested answer length: 150 words.) (14 marks) (b) Show that about 17% of the energy that strikes the brick surface at normal incidence is reflected. (Since Ereal > Eimag for brick, it is satisfactory at the interface to suppose that E Ereal.) (8 marks) (c) (i) Show that the standard plane wave solution for 2.45 GHz radiation as it propagates through the bulk of a brick can be given by E = Eo exp[-kimagz] exp[i(kreal2 – wt)] ez. where kreal = nreal w/c ~ Ereal w/c and kimag = Nimag W/C Eimagw/2cVE real. (12 marks) (ii) Explain the physical interpretation of the two exponential terms in the expression for E in part (c) (i). (Suggested answer length: 100 words.) (4 marks) (d) Show that in passing perpendicularly through 100 mm of brick only about 16% of the incident energy emerges. (Multiple reflections can be ignored but transmission across both interfaces must be taken into account.) (12 marks)
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