1.) The square coil of sides l[m] is shown below connected to a resistor of resistance R [], is placed normal to a time varying magnetic field of flux density
Determine:
The induced voltage (show your work.)
The polarity of the voltage at the terminals a and b of the resistor.Explain
2.) As you have noted the electromagnetic wave equations were all derived using Maxwell’s equations for a point in space. The theory and application of EM wave propagation to transmission lines waveguides, and antennas need you to know them by heart.
Write those 4 equations in mathematical form and state what they say in plain English.
How are these equations modified when we deal with time-harmonic fields? Explain the change.
3.) The ratio of the conduction current density, J [A/m^2], to the displacement current density, [A/m^2], is significant at high frequencies.
(a) Determine the value of their ratio at 1 [GHz] for =8 [F/m], = [H/m],=25 [S/m].
(b) Why do you think this ratio is so relevant? Explain.
4.) A uniform plane wave in air (medium 1) is normally incident to a lossless dielectric (medium 2) with =3,= Suppose that the electric field intensity of the incident wave is
Determine:
The wavelength and the frequency in air and the transmitted wave in the dielectric (medium 2).
The incident field (medium 1)
The reflection coefficient and the transmission coefficient
The total electric field intensity (medium 1)
5.) Consider the superposition of two linearly polarized waves; one polarized in the x-direction; and the other in the y-direction and lagging 90 (or /2), that is, their vector phasors are given by
Under what conditions will the resulting wave be:
Linearly polarized?
Circularly polarized?
Elliptically polarized?
Recall:
Elliptical Polarization exists when and there is a phase difference between and , that is
Linear Polarization (in its most genteral form) is a special case of elliptical polarization when =0, that is
Circular…