110年 - 110 國立中山大學碩士暨碩士專班招生考試_光電系碩士班:電磁學#104298

1. (16%) Please derive the boundary conditions for static D and H across an interface of two media.

(a) polarization P in each region (10%) and

(b) capacitance C of the capacitor (10%).

(a) Write down the Maxwell's equations in phasor form. (12%)

(b) In a simple and nonconducting source-free medium, please derive the homogenous vector Helmholtz's equation for H. (8%)

(a) What is the value of k_z? (4%)

(b) What is the corresponding H field? (6%)

(c) Please find out the time-average power flow per unit area normal to the direction of propagation. (6%)

5. (8%) For a transmission line system shown in Fig. 2, please find out the input impedance .

(a) For a uniform waveguide with arbitrary cross section as shown in Fig. 3(a), please derive the two- dimensional (2-D) vector phasor expression of transverse magnetic field components in terms of are 2-D vector phasors for E_z and H_z. (10%)

(b) For an air-filled metallic rectangular waveguide with the transverse dimensions a = 5.0cm and b = 3.0cm as shown in Fig. 3(b), if the operation wavelength is λ = 5.0cm, find out the modes which can appear on this waveguide. (10%)

110年 - 110 國立中山大學碩士暨碩士專班招生考試_光電系碩士班:電磁學#104298

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