lvy>試卷(2022/08/11)

# 103 年 - 103 國立中山大學_碩士班招生考試_電機系(戊組)、電波領域：電磁學#110204

【非選題】
1.
1.(20%)

【題組】 (a) (10%) Determine the self-inductance of a toroidal coil of N turns of wire wound on an air frame with mean radius ri and a circular cross section of radius a.

【非選題】
2.【題組】(b) (10%) Obtain an approximate expression assuming a << r1 in the part (a).

【非選題】
3.
2. (20%)A finite line charge of length I carrying uniform line charge density p is coincident with the y- axis.

【題組】 (a) (10%) Determine Vin the plane bisecting the line charge.

【非選題】
4.【題組】

(b) (10%) Determine E from ρ directly by applying Coulomb's law.

【非選題】
5.

3.(30%) The field between the plates in Fig. P3 is a linearly polarized (in the y-direction) uniform plane wave traveling in the z-direction.

【題組】 (a) (10%) Assume that the plates aire perfect electric conductors, then find the E and H field components between the plates. Neglect the edge effects of the finite plates.

【非選題】
6.【題組】(b) (10%) Find the separation d between the plates that creates resonance.

【非選題】
7.【題組】(c) (10%) Derive an expression for the Q of the cavity assuming a conductivity of o for the plates. Neelect any radiation losses through the sides of the cavity.

【非選題】
8.

4.(12%) A uniform plane wave with complex propagation constant propagating in a conductive medium with dielectric constant &, conductivity o and permeability H. Use Maxwell's equations to show that whereη is the intrinsic impedance of the conductive medium.

【非選題】
9.
5.(18%) Briefly answer the following questions:

【題組】 (a) (6%) What is dispersion? Under what situations will plane wave propagation suffer dispersion?

【非選題】
10.【題組】(b) (6%) What is a Smith Chart? What are the situations a Smith Chart can be a very useful tool?

【非選題】
11.【題組】(c) (6%) Describe the skin effect as detailed as possible.

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