15. Please select the closest dB value of the reflection coefficient of a $75 - \Omega$ resistive load in a $50 - \Omega$ system $Z_{0}$.
(A) $-6.9\mathrm{dB}$
(B) $-13.9\mathrm{dB}$
(C) $-1.39\mathrm{dB}$
(D) None of the above.

16. A 5-V dc voltage with $25 - \Omega$ source resistance is applied at $t = 0$ to the input terminal of a $25 - \Omega$ terminated lossless coaxial of $30\mathrm{m}$ length as the figure below. The initial condition of voltage and current of the cable are $0\mathrm{V}$ and $0\mathrm{A}$. The dielectric constant $(\varepsilon_{\mathrm{r}})$ of the insulating material in the cable is 4, and the characteristic impedance of the cable $(Z_0)$ is $50\Omega$. Please select the closest voltage value at $V_{L}$ at 1s. (A) $5\mathrm{V}$ (B) $2.5\mathrm{V}$ (C) $7.5\mathrm{V}$ (D) None of the above.

17. A guided TE mode of frequency $15\mathrm{GHz}$ is excited and propagates in metallic waveguide filled with polyethylene, of which $\varepsilon_{r} = 2.25$. The waveguide is designed with dimensions $a = 2\mathrm{cm}$ (x axis) and $b = 1\mathrm{cm}$ (y axis). If the x component of its electric field is given by $$ E _ {x} = - 5 0 \cos (5 0 \pi x) \sin (1 0 0 \pi y) e ^ {- j \beta z} \mathrm {V / m} $$ Which of the following statements is NOT correct? (A) The mode number is $\mathrm{TE}_{11}$. (B) The guide wavelength is $1.33 \times 10^{-2} \mathrm{~m}$. (C) The cutoff frequency is smaller than $12\mathrm{GHz}$. (D) $E_{z}$ is zero. 

18. Which of the following modes is the dominant mode in an air-filled metallic rectangular resonator for $a > b > d$? where $a, b,$ and $d$ are the dimensions in the x-, y-, and z-directions in respective, and the mode number are $m, n,$ and $p$ accordingly. Hint: Here we choose z-axis as the reference "the longitudinal direction" to define TE modes $(E_z = 0)$ and TM modes $(H_z = 0)$.  (A) $\mathrm{TM}_{110}$ (B) $\mathrm{TM}_{101}$ (C) $\mathrm{TE}_{101}$ (D) $\mathrm{TE}_{011}$

19. A parallel-plate waveguide made of perfectly conducting plates spaced $3\mathrm{cm}$ apart by polyethylene, $\varepsilon_{r} = 2.25$, is operated at frequency of $12\mathrm{GHz}$. Without considering the fringing effect on edges, which of the following supported modes has faster group velocity than others: (A) $\mathrm{TE}_3$ (B) $\mathrm{TM}_2$ (C) $\mathrm{TE}_1$ (D) TEM

20. An engineer intends to design a cubic cavity with side lengths $a = b = d = 25 \mathrm{~mm}$. To achieve the highest possible Q factor, he is evaluating three candidate materials—copper, aluminum, and silver—with electrical conductivities of $\sigma = 5.8 \times 10^{7} \mathrm{~S} / \mathrm{m}, \sigma = 3.5 \times 10^{7} \mathrm{~S} / \mathrm{m}, \sigma = 6.2 \times 10^{7} \mathrm{~S} / \mathrm{m}$, respectively. Which material should be chosen when only conductivity is considered: (A) Copper (B) Aluminum (C) Silver (D) All have the same Q factor. 

1. Consider a particle in a 2D rectangular box. Let the box widths be L and 2L, respectively, in the x- and y-dimensions. Which of the following expressions is the correct first excited state energy? $(h = \text{Planck constant}, m = \text{particle mass})$ (A) $\frac{h^2}{8mL^2}$ (B) $\frac{h^2}{16mL^2}$ (C) $\frac{h^2}{4mL^2}$ (D) $\frac{h^2}{2mL^2}$ (E) $\frac{h^2}{32mL^2}$

2. Consider the EM wave mode with wave vector k and frequency f, in a cavity of temperature T. The average number of photons in the mode, in the limit where $k_{B}T \gg hf$, is given by $(k_{B} = \text{Boltzmann constant}, h = \text{Planck constant})$ (A) $\left[\frac{k_B T}{h f}\right]^2$ (B) $\frac{1}{\left[\exp\left(\frac{k_B T}{h f}\right) - 1\right]}$ (C) $\frac{k_B T}{h f}$ (D) $\exp\left(\frac{-hf}{k_B T}\right)$ (E) $\frac{1}{\left[\exp\left(\frac{hf}{k_B T}\right) + 1\right]}$

3. A muon has a mean lifetime of $2.20 \times 10^{-6}$ s at rest. If it travels at a speed of 0.99c, how far can it travel before decaying? Given that the light velocity $c = 3 \times 10^{8} \, \mathrm{m/s}$. (A) $65\mathrm{m}$ (B) $653\mathrm{m}$ (C) $4632\mathrm{m}$ (D) $6534\mathrm{m}$ (E) $92\mathrm{m}$

4. A beam of ultraviolet light with wavelength $250\mathrm{nm}$ shines on a metal surface and ejects photoelectrons with a maximum speed of 0.004c. Which of the following statements is correct? Given that the light velocity $c = 3\times 10^{8}\mathrm{m / s}$, the Planck's constant $h = 6.626\times 10^{-34}\mathrm{J\cdot s}$, the elementary positive charge $q = 1.6\times 10^{-19}\mathrm{C}$, and the electron mass $m_{e} = 9.11\times 10^{-31}\mathrm{kg}$. (A) The work function of the metal is $0.87\mathrm{eV}$. (B) A wavelength larger than $1.45\mu \mathrm{m}$ can eject electrons from this metal. (C) The photon energy is $4.10\mathrm{eV}$. (D) The threshold frequency is about $1.2 \times 10^{15} \mathrm{~Hz}$. (E) The kinetic energy of the photoelectron is $6.56 \times 10^{-19} \mathrm{eV}$.

5. Find the correct description: (A) The photon energy of light from the Paschen series (transitions from n ≥ 4 to n = 3) of the hydrogen atom is sufficient to induce the photoelectric effect in silver (work function $\approx 4.7$ eV). (B) For n = 4, the radius of the hydrogen atom in the Bohr model is $4a_{0}$, where $a_{0}$ is the Bohr radius. (C) The Balmer series, corresponding to electronic transitions from any higher level ($n \geq 3$) to n = 2, mainly lies in the visible region of hydrogen's atomic spectrum. (D) Rutherford's scattering experiment suggested that the positive and negative charges are uniformly distributed throughout the atom. (E) In the Bohr model, electrons continuously lose energy while orbiting the nucleus and eventually spiral into it.

115年 - 115 台灣聯合大學系統_碩士班招生考試_電機類：電磁學#139672

114年 - 114 台灣聯合大學系統_碩士班招生考試試題_電機類：電磁學#138442

113年 - 113 台灣聯合大學系統_碩士班招生考試試題_電機類：電磁學#138444

112年 - [無官方正解]112 台灣聯合大學系統_碩士班招生考試試題_電機類：電磁學#138446

111年 - 111 台灣聯合大學系統_碩士班招生考試試題_電機類：電磁學#138448

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

110年 - 110 國立臺灣科技大學_碩士班招生試題_電子工程系(丙組)：電磁學#112842

110年 - 110 國立臺灣科技大學_碩士班招生試題_光電工程系：電磁學#111696

110年 - 110 國立臺北科技大學_碩士班招生考試_光電工程系碩士班：電磁學#108271

110年 - [非官方正解]110台灣聯合大學系統_碩士班招生考試_電機類:電磁學#105808