Download 國立彰化師範大學八十八學年度碩士班招生考試試題

國立彰化師範大學九十一學年度碩士班招生考試試題
系所：光電工程技術研究所
☆☆請在答案紙上作答☆☆
碩士班
科目：電磁學
共 2 頁，第 1 頁
[每題 10 分，總分 100 分，請按題目順序作答，答案請註明單位]
1. Explain the following terminologies:
(1) Gauss’s Law, (2) Electric Dipole and Electric Dipole Moment, (3) Equation of Continuity,
(4) Vector Magnetic Potential, (5) Plasma and Plasma Frequency.
2. a) Write the differential form of Maxwell’s equations.
b) Derive the integral form of Maxwell’s equations from the differential form.
c) Explain the physical meaning of the Maxwell’s equations.
3. A spherical distribution of charge  = 0 [1 - (R2/b2)] exists in the region 0  R  b. This charge
distribution is concentrically surrounded by a conducting shell with inner radius Ri (Ri > b) and outer

radius Ro. Determine the electric field intensity E everywhere.
4. The region between two charged concentric spheres is filled with two dielectrics of dielectric constants
5 and 10, as shown in the following figure. Determine the capacitance of the system.
1
 10 9  8.854  10 12 ( F / m) 】
【Note: a = 10 cm, b = 30 cm, c = 20 cm,  0 
36
c
a
b
r1=5
r2=10
5. Consider a very long coaxial cable. The inner conductor has a radius a and is maintained at a potential
V0. The outer conductor has an inner radius b and is grounded. Determine (a) the potential distribution
in the space between the conductors, (b) the electric field intensity in the space between the conductors,
(c) the surface charge density on the inner conductor, and (d) the capacitance per unit length.


6. An uncharged conducting sphere of radius b is placed in an initially uniform electric field E 0  a z E 0 .
Please answer the following:
b 

(a) If V ( R, )   E 0 1  ( ) 3  R cos when R  b after the introduction of the sphere, determine:
R 


(i) the electric field intensity, E ( R, ) , and (ii) the surface charge density, s(), on the sphere;
(b) If the potential is expressed as a sum of two terms: one due to the applied uniform electric field and
the other due to an electric dipole, determine the dipole moment of this electric dipole.
國立彰化師範大學九十一學年度碩士班招生考試試題
系所：光電工程技術研究所
☆☆請在答案紙上作答☆☆
碩士班
科目：電磁學
共 2 頁，第 2 頁
7. A parallel-plate capacitor whose plates are 10 cm square and 0.2 cm apart contains a medium with r =
2 and  = 4  10-5 S/m. To maintain a steady current through the medium a potential difference of 120
V is applied between the plates. Determine (a) the electric field intensity, (b) the volume current density,
(c) the power dissipation, (d) the current, and (e) the resistance of the medium.
8. Consider a p-type semiconductor material of a d (= 200 m)  b (= 100 m) rectangular cross section


in a uniform magnetic field B  2.0 a z (T), as shown in the following figure. A uniform direct
current I  20 (mA) flows in the y-direction. If the hole concentration N = 5  1017 cm-3:

(a) find the volume current density, J ,

(b) find the velocity of the charge carriers (holes), u ,

(c) find the Hall field, E h ,
(d) find the Hall voltage, Vh, (is it positive or negative?)
(e) find the Hall coefficient.
9. Determine the mutual inductance between a very long, straight wire and a conducting circular loop, as
shown in the following figure.
10. The E-field of a uniform plane wave propagating in a dielectric medium is given by



E (t , z )  a x 2 cos (10 8 t  z / 3)  a y sin (10 8 t  z / 3 ) (V / m).
(a) Determine the frequency and wavelength of the wave.
(b) What is the dielectric constant of the medium?
(c) Describe the polarization of the wave.

(d) Find the corresponding H -field.