97下電磁一期中考

97下電磁一期中考

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Unformatted text preview: Electromagnetics (I) Final Examination June 15,2009 . (1) Write down the Maxwell equations in differential form. (2) What is the advantage of the differential—form Maxwell equations over the integral-form ones? Discuss it briefly. (16%) . (1) What is a phasor? Discuss its usefulness in electromagnetic theory briefly. (2) To compute the time-average Poynting vector, we usually introduce a complex Poynting vector. Please write down the expression of that complex Poynting vector. Is it also a phasor? Explain briefly. (16%) . An infinite plane sheet lying in the z = 0 plane carries a time-varying surface current of density .75 (t) = O.lsin(87rx108t+7z/4)ZiyA/m. The region 2 > 0 is a perfect dielectric of a = 980 and . ,u = #0 , whereas the region 2 < 0 is a perfect dielectric of a = 2.2550 and ,u = #0. Find E(z,t) and H(z,t) in both regions 2 > 0 and z < O. (20%) Consider a uniform plane wave with electric field E(z,t) = E, cos a)(t alga z)5x propagating in a homogeneous perfect dielectric with permittivity a and permeability ,u . (1) Find the instantaneous energy (electric + magnetic) density u(z, t) associated with this uniform plane wave. (2) Show that E xFI — \/:_c‘zz , and explain its physical meaning. (3) Show that u satisfies a #5 ' continuity equation V - (J... a )+ Q— = 0. Discuss the physical meaning briefly. (18%) ,ua at . A steady conduction current is distributed in an inhomogeneous lossy dielectric medium (with conductivity 0'( f) and permittivity 8(7 )) under the influence of an electrostatic field E . (1) Show that in the medium there exist free charges with volume density p f = (Vs — 3 Va) - E . * ‘ or (2) If the volume density of total charges is given by V - 50E , show that in the medium there exist polarization charges with volume density ,0p = [(8—80) Va—VgJ-E . (3) Find the partial a- differential equation satisfied by the corresponding electric scalar potential V ( f ). (15%) . The space between two parallel conducting plates each having an area S is filled with a lossy dielectric whose conductivity varies linearly from 61 at one plate (y=0) to 02 at the other plate (y=d, d<<«/§ ). The permittivity of the dielectric is a constant e. A battery of d-c voltage V0 is applied across the plates, as shown in the following figure. Determine ( 1) the total resistance between the plates, (2) the surface densities of free charges on both plates, and (3) the volume density of free charges between the plates. (4) Draw an equivalent circuit of this system, neglecting the magnetic effect. (5) If the battery is disconnected, what would happen to this system? Give a qualitative description briefly. (Hint. You may consider first the condition of a steady current.) (15%) yr 1 d ...
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