110年 - [非官方正解]110 國立臺灣大學_碩士班招生考試_電信工程研究所甲組:電磁學及電磁波#113085

科目：研究所、轉學考(插大)◆電磁學 | 年份：110年 | 選擇題數：40 | 申論題數：0

試卷資訊

所屬科目：研究所、轉學考(插大)◆電磁學

選擇題 (40)

1.Which of the following statements is not correct? (A)(B)(C)(D)

2.Which of the following statements is not correct? (A) A curl-less vector field can be expressed as the gradient of a scalar field. (B) A divergence-less vector field can be expressed as the curl of a vector feld. (C) A curl-lJess and divergence-less vector field is a constant vector field. (D) A smooth and rapidly decaying vector field can be expressed as the sum of a curl-less vector field and a divergence-less vector field.
3.A charged particle at rest is released in a region of uniform electric field in the y direction and uniform magnetic field in the z direction. Which of the following statements is not correct? (A) The motion of the particle in the y direction is periodic. (B) In average, the particle moves with a constant speed in the x direction. (C) The kinetic energy of the particle increases with time. (D) The magnetic field does no work on the particle.

4. For an ideal electric quadruple, what is the relation between the electric field strength E and the distance r in the far field? (A)(B) (C) (D)

5.Consider two long parallel wires of radius a, separated by a distance d. If d□ a, find the capacitance per unit length. (A)(B) (C) (D)

6. In the static case, consider an interface between the free space and a perfect conductor with some charges on the surface. Which of the following statements is not correct? (A) The electric field in the free space near the surface is proportional to the surface charge density. (B) There is no electric field in the conductor. (C) The surface charge would experience no electric force. (D) The electric potcntial is the same in the conductor, even near sharp edges.

7.An uncharged metal sphere is placed in an otherwise uniforn electric field . Find the induced surface charge density. (A) Zero everywhere on the sphere. (B) ε0E0cosθ (C) 2ε0E0cosθ (D) 3ε0E0cosθ

8.What does ρ in the Gauss's lawmean? (A) The free volume charge density. (B) The free surface charge density. (C) The sum of the polarization volume charge density and the free voiume charge density. (D) The sum of all surface charge density and volume charge density.

9.What does in the Ampcre's lawmean? (A) The free volume current density. (B) The free surface current density. (C) The sum of the polarization current density, the magnetization current density, and the free current density. (D) The sum of all surface current density and volume current density.

10. Consider a uniformly polarized dielectric sphere where the polarization inside the sphere is . Find the displacement ficld inside the sphere. (A)0 (B) (C)(D)

11. A short solenoid (length I, radius a, ni turns per unit length) lies on the axis of a very one solenoid (length /, radius b, na turns per unit length), where a＜b. What is the total magnetic flux through the long solenoid if a steady current / flows in the short aD solenoid? (A) μ0πa2n1n2ll (B) μ0πb2n1n2ll(C) μ0πa2n12ll(D)μ0πabn1n2ll
12. Which of the following statements is not correct in general? (A) Diamagnetism could be related to the orbital motion of electrons. (B)Paramagnetism could be related to the electronic spin. (C) Ferromagnetism becomes obvious above the Curie temperature. (D) Antiferromagnetism vanishes above the Neel temperature.

13. Consider a sheet current source at z = 0. The medium on either side of the sheet is free space. Which of the following statements for the region z ＞0 is not correct? (A) There will be a wave propagating in the +z direction. (B) The electric field and magnetic field are in phasc. (C) The instantaneous power flow out of an arbitrary closed surface is zero. (D) The average power flow is half of the peak power flow.

14. Consider a sheet current source at z =0. The medium on either side of the sheet is perfect dielectric. Assume the dielectric constant is higher in the z ＞0 region. Which of the following statcments is not correct? (A) The power flux is higher in the z＞0 region. (B) The power flux is higher in the z ＜0 region. (C) The power flux is the same in both regions (D) There is no power flux in both regions.

15. Assume the relation holds in a medium, where ε is a constant. What do we not imply for that medium? (A) The medium is linear. (B) The medium is isotropic. (C) The medium is nondispersive. (D) The medium is lossless.
複選題
16. Assume two electromagnetic waves (frequency fA and fB) enters a nonlinear material whose polarization field includes a term that is proportional to the square of the clectric field. Which of the following frequencies could one possibly observe at the output of the nonlincar material? (A) fA+ fB(B) 2fA (C) 2fB (D) All of the above.

17. Consider a situation that region 1 (z ＜0) is free space and region 2 (z ＜0) is an anisotropic lossless nonmagnetic material described by the following reiationship.
 
 For a uniforn piane wave with the electric field incident on the interface z =0 form region I. What is the electric field of the reflected wave?(A) (B)(C) (D) None of the above.

18. Following the previous question, what is the electric field of the transmitted wave? (A) (B)(C)(D) None of the above.
19. A randomly polarized electromagnetic wave in free space is incident on a lossless medium with a diclectric constant of 3. At what incident angle does the reflected wave become linearly polarized? (A) 0 degree (B) 30 degrees (C) 60 degrees(D) None
20. Assume the electron density is 106 cm-3 in a certain layer of ionsphere. Which of the following frequency of electromagnetic waves that could pass through that layer? (A) 12 MHz (B) 8 MHz (C) 4 MHz (D) 1 MHz

21.If V/m. Find (z，t). (A)mA/m (B)mA/m (C)mA/m (D)m/Am

22. In an air-filled parallel-plate waveguide with dimension a = 4 cm, according to the expression of electric field distribution,
E= E0(sin25πx+3sin50πx)sin(8x109πt)
What is the value of phase constantβ2 of propagation wave? (A) 7.5 (B) 23.5 (C) 29.2 (D) 74 radm

23. Consider a parallel-plate waveguide (plates at y=0and y=b planes), with wave propagating in the +z direction. For the lowest-order TM mode, if the instantaneous field expression for the z-component of the clectric field at (x, y, z) = (x, b/4. 0) is Ez(t) = E0cos wt, what is the corresponding expression for Ez(t) at (x, y, z) = (x. b/2, d)? (A)2E0cos(wt-βd)(B)(C)2E0sin(wt-βd)(D) sin(wt-βd)

24. Find the spacing d for a parallel-plate waveguide having a dielectric of ε =4ε0, and u= u0 such that 5 GHz is the cutotr frequency of the dominant mode. (A) 1(B)1.5 (C)2 (D) 2.5 cm

25. A wave in air is incident upon a soil surface at θ1 =40°. If soil has εr = 2.2 and μr=1, determine Γ⊥and τ⊥. (A)Γ⊥=-0.48,τ⊥=0.52(B)Γ⊥=-0.27,τ⊥=0.52(C)Γ⊥=0.27,τ⊥=0.73(D)Γ⊥.=-0.48,τ⊥=0.73

26. The magnetic field in a given dielectric medium is given by = y6cos(2z)sin(2x107t -0.1x) (A/m), where x and z are in meters. Determine the phase velocity of the electromagnetic wave. (A) 2x108 (m/s) (B) 3x108 (m/s) (C) 5x108(m/s) (D) 1.5x108 (m/s)

27. The magnetic field associated with a uniform plane wave propagating in the +z-direction in free space is given by  = H0 cos(6πx107t -0.2πz)y (A/m) . Find the instantaneous power fow across a surface of area Im2 in the z=0 plane at t=(1/8)μs(A)0 W (B)1 W (C)1.5 W (D)3 W

28. The electric field of a plane wave is given by(zt) = x3 cos(ωt-kz) + y4 cos(ωt-kz) (V/m). Determine the polarization state of the corresponding electromagnetic wave. (A)Lincar Polarization (B) Right-Hand Circular Polarization (C) Left-Hand Circular Polarization (D)Elliptical Polarization

29. The general expression of the voltage on a lossless transmission line in the sinusoidal steady state is Which one of the following statements is wrong?(A)The current can be expressed as，where Z0 is the characteristic impedance of the transmission line. (B) If B is zero, there is no standing wave on the transmission line. (C) The first term and the second term represent the waves going in the +z and -z directions, respectively. (D) ω /vp is the propagation constant.

30. A 50-Ω transmission line is terminated by a load. Which one of the following statements is wrong? (A)Ifthe load impedance is 0Ω and the electrical length of the transmission line is 90 degree, the input impedance is ∞. (B) If the load impedance is 100 Ω and the electrical length of the transmission line is 90 degree, the input impedance is 20Ω. (C) Ifthe load impedance is 200Ω and the electrical length of the transmission line is 180 degree, the input impedance is 200Ω. (D) If the load impedance is 30 Ω and the electrical length of the transmission line is 360 degree, the input impedance is 30Ω.

31. For the system impedance of Zo, what is the component which can match the impedance at point A to point B along the constant VSWR circle as shown in Fig. 1?
  (A)A series capacitor. (B) A series resistor. (C) A series transmission line with characteristic impedance of Zo. (D)A shunt short-circuited transmission line with characteristic impedance of Zo.
32. Which one cannot allow TEM wave propagation? (A) Rectangular metal waveguide. (B)Coaxial cable. (C) Parallel-plate waveguide. (D)Stripline. 
33. If the load is a pure inductor L, which statement is WRONG? (A) A refected wave is resulted since the boundary condition at load is violated. (B) The inductor is initially open, hence the voltage at the load will be Vo at t =T+. (C) The reflccted wave will be of positive voltage for t > T. (D)The voltage at the load will be zero as t tends to infinity.
34. If the load is a scries resistor R = Zo and inductor L, which statement is WRONG? (A) The current at the load should be continuous versus t, due to the presence of L. (B) The inductor is initially open, hence the voltage at the load will be Vo at  t =T+. (C) The reflected wave will be of positive voltage for t> T. (D)The voltage at the load will be zero as t tends to infinity.
35. If the load is a pure capacitor C, which statement is WRONG? (A) The voltage at the load should be continuous versus t, due to the presence of C. (B) The capacitor is initially short, hence the voltage at the load will be O at t=T+. (C) The reflected wave will be of positive voltage for t much larger than T. (D)The voltage at the load will be zero as t tends to infinity.
36. If the load is a shunt connection of capacitor C and resistor R =Zo, which statement is WRONG? (A)The voltage at the load should be continuous versus t, due to the presence of C. (B) The capacitor is initially short, hence the voltage at the load will be zero at t=T. (C) The reflected wave will be of positive voltage for t much larger than T. (D) The voltage at the load will be Vo/2 as t tends to infinity.

37. Design a transmission line of characteristic impedance Zo and length , as shown in the Fig. 3, to match a resistive load RI = 300 Ω to a lossless transmission line of characteristic impedance Zo = 75 Ω 
(A)Z1= 150Ω,=λ/8 (B) Z1= 187.5Ω,=λ/8 (C) Z1= 150Ω,=λ/4 (D) Z1= 187.5Ω,=λ/4 (E)Z1= 150Ω, =λ/2

38. A 50-Ω transmission line is connected to a load of impedance ZL = 35 + j80Ω. Find the position d and length  of a short-circuited stub required for impedance matching, as shown in the Fig. 4.
(A)d= 0.016λ,= 0.076 (B) (C)d= 0.266λ,= 0.0761； (D) (E) It is impossible to match the load using the single-stub matching circuit.

39. Figure 5 shows a power divider of power ratio PL1/PL2 =1, where PL1 and PL2 are the power delivered to the loads Rei and Riz, respectively. The loads have resistance RiI = 750 and RL2 = 300 , and the characteristic impedance of the transmission line is Z0 = 50 Ω . Find the characteristic impedances Z1 and Z2 of the quarter-wavelength transmission linesso that the impedance is matched from the source.
(A) Z1=61.2Ω,Z2 = 122.5Q； (B)Z1= 122.5Ω, Z2=61.2Ω； (C)Z1=86.62Ω,Z2=173.2Ω； (D) Z1= 173.2Ω,Z2 =86.6Ω； (E) It is impossible to match the loads by using the quarter-wavelength transformers.

40. A 50-Ω transmission line is connected to a load of impedance ZL = 35 + j80Ω. Design a double-stub matching circuit shown in the Fig. 6. Short-circuited stubs are used and the position of the second stub is d =λ/8.
(A) (B)(C)(D)(E) It is impossible to match the load using the double-stub matching circuit.

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