課程名稱︰電磁學一
課程性質︰必修
課程教師︰張宏鈞、江衍偉、林怡成、林晃巖
開課學院：電機資訊學院
開課系所︰電機工程學系
考試日期（年月日）︰2012/06/22
考試時限（分鐘）：100min
是否需發放獎勵金：是（如未明確表示，則不予發放）
試題 :
Final Exam (10:20am-12:00noon)
1.(5%) What is the definition of the magnetization vector in a magnetic
material in terms of magnetic dipole moments?
2.(5%) For a material medium with permittivity ε, permeability μ, and
conductivity σ, what is its complex intrinsic impedance?
3.(8%) Find the unit vector normal to the surface y = x^2 at the point (3,9,3)
4.(27%) Consider a source consisting of an infinite sheet lying in the xy-plane
in free space. A uniformly distributed current Js(t) flows on this
infinite plane sheet.
(a)(20%) The source generates sinusoidally time-varying uniform plane waves
propagating in the ±z-direction in free space. Consider the +z
propagatiion having the following characteristics: f = 200MHz and
polarization is left circular with the electric field at z = 0+ and
t = 0 having an x-component equal to -2E0 and a y-component equal to
1.5E0. Please write the expressions for the electric-and magnetic-
field intensities for this wave.
(b)(7%) What is the expression for Js(t).
5.(20%) Consider a uniform electromagnetic wave propagating in a uniform
material with intrinsic impedance expressed as η = |η|exp(jθ) along
the negative z-direction.
The electric field at z = 0 is found to be H(0,t) = H0cosωt ax H/m,
where ω is the angular frequancy. The propagation constant of the
wave is expressed as γ = α + jβ.
(a) Give the expression for H(z,t). (4%)
(b) Give the expression for E(z,t). (6%)
(c) Give the expression for the instantaneous Poynting vector. (4%)
(d) What is the time-varying power flow per unit area along the z-direction?
(6%)
6.(15%) Consider two infinitely long, straight-line charges of equal and
opposite uniform and passing through x = b and x = -b, respectively,
as shown in the figure. If the potential is zero at the point (0,b,0)
and is 1V at (b,b,0), what are the values for the potential at the
points (2b,b,0) and (b,2b,b), respectively?
第六題的圖與課本FIGURE 5.14(b)完全同
7.(20%) Consider a coaxial-line structure.
The inner conductor has a ring-shape cross-section, that is, it is a
solid cylindrical conductor of radius a with that part of r < r0
removed and replaced by air, where the radius r0 < a. A current I(Amp)
flows with uniform volume density J = J0 az (Amp/m^2) along the
infinitely long inner conductor and returns with uniform surface
density in the opposite direction along the surface of an infinitely
long, perfectly conducting cylinder of radius b(>a) and coaxial with
the inner conductor.
Please find the internal inductance per unit length of the inner
conductor.
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