9. Given a scalar function V =, please evaluate the rate of the increase of V at the point (1,2,0) along the vector of â_z:
(A) e³
(B) 0
(C) π/2
(D) None of the above

1. In the following cross-section figure, four straight current-carrying wires are devised out of the page. IA = I, IB = 3I, IC = 2I, ID = 5I If a counter-clockwise Amperian loop enclosing wire A only gives = -μ₀I, what Amperian loop would give= 4μ₀I? (A) A clockwise loop that encloses wires A, B and C only. (B) A clockwise loop that encloses wires B, C and D only. (C) A counter-clockwise loop that encloses wires A and D only. (D) None of the above

2. A circular coil with a radius of R has N turns. A uniform magnetic induction B = B₀sin(ωt) passes perpendicularly through the coil. What is the time-dependent electromotive force produced in the coil? (A) -NπR²B₀ωcos(ωt) (B) NR²B₀cos(ωt) (C) N²πR²B₀ωcos(ωt) (D) None of the above

3. There is a current distribution with the density of J₀ A/m² in the volume between the planes y=a and y=-a. What is the magnetic flux density in the region of -a＜y＜a due to the current distribution? (A)(B) (C)(D) None of the above

4. There is a common boundary in between two magnetic media with permeabilities μ₁ and μ₂ as shown in the following figure. The magnetic field intensity in the medium 1 at the point P has a magnitude H₁ and makes an angle α₁ with the normal, what is the angle α₂? (A) (B)(C)(D) None of the above

5. A rectangular metallic waveguide has dimension of a=3 cm and b=2 cm along x and y directions respectively. Now the waveguide is to transmit 12 GHz signal. How many guided modes can this waveguide support? (A) 1 mode (B) 2 modes (C) 4 modes (D) None of the above

6. A rectangular metallic waveguide has dimension of a and b along x and y directions respectively. Which of the following modes have the same cut-off frequency, assuming the dimensions a = 2b: (A) TE₀₁ & TM₀₁ (B) TE₂₀ & TM₀₁ (C) TE₁₁ & TM₁₁ (D) None of the above

7. Which of the following waveguide can support guided TEM mode: (A) Rectangular waveguide (B) Circular waveguide (C) Microstrip (D) None of the above

8. John tried to find the relation between wave vector and its components kx, ky, kz of guided modes in a hollow metallic waveguide via v² = vx² + vy² + vz² (eq.1), where v² = , and is the velocity of a guided mode in the waveguide. He used the formula vi =, i = x, y, z (eq.2), and then obtained (eq.3), which is different from the usual understanding of k² = kx² + ky² + kz² (eq.4). Which of the following statement is correct: (A) The eq.1 is not correct. (B) The eq.2 is not valid for the guided modes in this waveguide. (C) The eq.4 is not valid for the guided modes in this waveguide. (D) None of the above

10. Given a material with conductivity of σ, the structure has constant cross section. The cross section area is S, and the distance is L. Please evaluate the resistance between the top and the bottom of this material. (A) (σS)/L (B) (σL)/S (C) L/(σS) (D) None of the above

11. Consider a layer structure of the structure as the figure shown below. This structure has three perfect conductor metal layers, and two insulator layers. One of the insulator layer is composed of Material1, the other insulator layer is composed of Material2 and Material3. The dielectric constant and the dielectric strength of the materials are listed in the Table below. This structure is infinitely extended in y direction; L1＞＞3μm; L2 ＞＞ 3μm; and L1=L2. Applying a voltage Vin between the top perfect conductor and the bottom perfect conductor from 0 V to 20 V, which material will breakdown first? (A) Material1 (B) Material2 (C) Material3 (D) None of the above

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