19. One air-filled rectangular waveguide is connected to the other rectangular waveguide filled with a dielectric characterized by the dielectric constant εᵣ. Both waveguides have identical dimensions with a=2b. What's the exact expression for the frequency range over which single-mode operation will occur in both waveguides?
(A)
(B)
(C)
(D) none of the above

1. A circular disk of radius a is uniformly charged with ρs C/m². If the disk lies on the z=0 plane with its axis along the z-axis, What is the electric field that at point (0, 0, h)? (A)(B) (C) (D)

2. The linear electric quadrupole is a set of three charges as shown in the following figure. The separation s is again much smaller than the distance r to the point P. What is the potential V at the point of P: (A)(B)(C)(D)

3. There is a sector of a spherical shell with the cross section as shown in the figure (where 0≤α＜2π) What is the resistance between the top and bottom bases of the sector? (Assume that the electrical conductivity of the sector material is σ) (A) R = (B) R = (C) R =(D) R =

4. A parallel-plate capacitor has plates of area A separated by a distance s. Its dielectric has a conductivity σ=a+bx, where x is the distance to one plate and a uniform relative permittivity εᵣ. With an alternating voltage with the angular frequency ω across the electrodes, there is a current I flowing through the dielectric. What is the electric field in the capacitor? (A) (B)(C) (D)

5. The plane boundary defined by z=0 separates air (z ≥ 0) from a block of iron (z ≤ 0), of which μ = 5000μ₀. If = x̂4 - ŷ6 + ẑ12 is the magnetic field in air, what is the magnetic field in iron: (A) = x̂0.0008 - ŷ0.0012 + ẑ12 (B) = x̂4 - ŷ6 + ẑ60000 (C) = x̂4 - ŷ6 + ẑ0.0024 (D) = x̂20000 - ŷ30000 + ẑ12

6. Which material type in the following has negative magnetic susceptibility, thus the direction of the induced magnetic dipole moment is opposite to the corresponding applied magnetic field: (A) Paramagnetic material (B) Diamagnetic material (C) Ferromagnetic material (D) None of the above material have negative magnetic dipole moments

7. Which following equation is not one of the Maxwell's equations: (A) (B)(C) (D)

8. The plates of a parallel-plate capacitor has areas of 10 cm² each and are separated by 1 cm. The capacitor is filled with a dielectric material with ε = 4ε₀, where ε₀ = 8.85 × 10⁻¹² F/m, and the voltage across it is given by V(t) = 30cos(2π×10⁶t) (V). What is the displacement current? (A) Id = 2.4πε₀ × 10⁷sin(2π × 10⁷t) ( A ) (B) Id = 2.4πε₀ × 10⁹cos(2π × 10⁷t) ( A ) (C) Id = 2.4πε₀ × 10⁹sin(2π × 10⁷t) ( A ) (D) None of the above.

9. Considering a plane electromagnetic wave traveling in a material with a permittivity ε and a permeability μ, what is the phase velocity of the wave? (A) (B)  (C) με (D) none of the above.

10. The instantaneous expression of the electric field of a plane wave in vacuum is given by (z,t) = âx E₀cos(ωt - βz). The intrinsic impedance (also called the wave impedance) is η₀. What is the instantaneous expression of the Poynting vector? (A) (B)(C) (D) none of the above.

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