Download Homework-08

Fields and Waves 1 – ECSE-2100 – Professor Schubert
Homework-08
1. This question concerns the Poynting vector of sunlight. Sunlight has an optical radiation power
density of about 1.0 kW / m2 at the Earth’s surface.
(a) What is the meaning of the Poynting vector? What are the units of the Poynting vector?
What is the approximate direction of the Sun’s Poynting vector at the Earth’s equator?
(b) Assuming that solar radiation is harmonic and linearly polarized, what is the direction and
amplitude of the electric field of solar radiation at the Earth’s surface at the equator?
�⃗-field)?
(c) What is the direction and amplitude of the associated magnetic field (𝐻𝐻
(d) The radius of Venus’ and Earth’s orbit around the Sun is 108 × 106 km and 150 × 106 km,
respectively. What is the solar radiation power density on Venus?
(e) What is the time it takes for transporting solar energy from the Sun to the Earth, that is,
how long is solar energy en route (in transit) between Sun and Earth?
2. A point-like EM-radiation source (f = 5 GHz) is initially located in air. The EM-wave power
density (i.e. power per unit area) is 1 mW/m2 at a distance of 100 m from the source.
(a) Sketch the experimental setup and label all objects. What is the power emitted by the
radiation source? What is the power density at a distance of 200 m?
(b) Next, the source is put into seawater with resistivity ρ = 0.25 Ω m and relative permittivity
εr = 25. What is the value of the attenuation constant α? At which distance z has the
attenuation term e–αz a value of e–1? What do we learn from this question?
(c) Next, the radiation source is put into fresh water with resistivity ρ = 1 000 Ω m and relative
permittivity εr = 25. Determine the attenuation constant α. What is the power density of a
point-like EM-radiation source with power of 100 W at a distance of 10 m from the source?
3. What kind of EM-wave is obtained when superimposing the following pairs of EM-waves?
Assume that |Ex0| = |Ey0|. Sketch the waves. Give a detailed answer.
and
Ey = Ey0 cos (k z – ω t)
(a) Ex = Ex0 sin (k z – ω t)
and
Ey = Ey0 sin (k z – ω t – π/2)
(b) Ex = 2 Ex0 sin (k z – ω t)
4. How the type of interaction is called that occurs between the following pairs of EM-waves?
Sketch the waves. Describe what wave results from the superposition of the two waves.
(a) Ex = Ex0 sin (k z – ω t)
and
Ex = Ex0 sin (k z – ω t – π)
and
Ex = Ex0 sin (k z – ω t – 2π)
(b) Ex = Ex0 sin (k z – ω t)
5. Determine if the following statements are (i) true, (ii) false, or (iii) impossible to determine due
to lack of information. Explain each of your answers with a few words.
(a) D'Alembert's solution of the wave equation can have any waveform. Any waveform can be
produced by the superposition of multiple harmonic waveforms.
(b) The relative permittivity εr and relative permeability µr of a material generally depend on
the frequency of an EM-wave, whereas εr and µr of vacuum never depend on the frequency.
(c) EM-wave pulses propagating in vacuum never disperse (i.e. the pulse shape never distorts
and never broadens as the EM-wave propagates), whereas EM-wave pulses propagating in a
material generally disperse (i.e. the pulse shape generally distorts and broadens).
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