私立中原大學八十八學年度研究所招生考試命題紙

所組別 :電子工程學系甲組 科目 :電磁學 考試時間 : 05月01日第2節


  1. Solve the following conceptual problems if possible using equation or derived formulas instead of statement (儘量以方程式或導出公式回答下列觀念題):

    2. (1)、Write the differential form of Maxwell's equations.
    (2)、Under which conditions from Maxwell's eqs. does the electromagneto statics constitute and state all the four equations in the integral form.
    (3)、Derive Lenz's law from Faraday's induction law and explain it.
    (4)、Explain the significance of displacement current, which must be added to Amperes'law.
    (5)、Why do we need constitutive relations (or material equations ) for materials and what are the sources in the electromagnetic model ?
    (6)、Derive the nonhomogeneous wave equation for vector magnetic potential and explain the Lorentz condition.
    (7)、Derive the Source-free wave equation for the time-varying electric field and the Helmholtz's equation in phasor form is of advantage, why?
    (8)、Write the equation, which obtains Hall electric field for the semiconductor sample in Hall measurement, and what phenomenon acts on any current-carrying loop situated in a uniform magnetic field.
    (9)、Derive, the magnetic wave lags behind the electric wave by π/4 and write the formula of skin-depth.
    (10)、In what way does the wave impedance in a waveguide depend on frequency for a propagating TEM, TM and TE wave, respectively? Explain the Poynting's vector of general electromagnetic wave.

    (each for 5 pts. )

  2. Two arbitrary shape of electrode are immersed in the lossy dielectrics with permittivity ε and permeability μ, connected to supply voltage V
    3. (1)、Under what condition, derive its relaxation time τR
    (2)、Prove current flux-lines are normal to the surface of conducting electrode.
    (3)、If the voltage is put away, derive the discharging process of the charged electrode.
    (4)、Two layers of lossy dielectrics, such as ε1, s1 andε2, s2 are inserted between two electrodes (i.e. parallel conducting plates). Find the relation of two media that exists no surface charge density ρs =0 at the interface of the two.( each for 5 pts. )

  3. An infinitely large dielectrics in electric field E, which is uniformly polarized with polarization vector Po. If the cliclectrics is duy with a spherical cavity, its radius b; to find is the electric field at center of the sphere Ec .( 15 pts. )

  4. Determine the force FI between a very long, straight wire and a conducting elliptic loop with short and long radius a and b, that carry respective currents I1and I2 , as shown in <Fig>. (15pts.)
Hint:


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