課程名稱︰電磁學一
課程性質︰必修
課程教師︰林晃巖
開課學院：電機資訊學院
開課系所︰電機工程學系
考試日期（年月日）︰104/4/17
考試時限（分鐘）：110分鐘
試題 :
Electromagnetics (I) test April 17, 2015
1. The forces experienced by a test charge q at a point in a region of eletric
and magnetic fields E and B, respectively, are given as follows for three
different velocities of the test charge, where v_0 and E_0 are constants.
Please find E and B at that point. (10%)
http://ppt.cc/EdCp
2. In fig. 2, a cylindrical capacitor cinsists of an inner conductor of radius
a and an outer conductor of radius b. The space between the conductors is
free space and the length of the capacitor is L. Fringe effect can be
neglected for L >> a,b.
http://ppt.cc/W0ct
(1) By applying a DC voltage V_0, there will be a charge +Q on the inner
cylinder and -Q on the outer cylinder, please solve the E field in terms
of Q for a < r < b. (10%)
(2) Following (1), please calculate ▽．E and ▽ x E for a < r < b and explain
the results. (5%)
(3) Following (1), please calculate the voltage from the inner cylinder to the
outer cylinder, and show that V_0 is independent of the path of
integration. (5%)
(4) Following (3), please calculate the capacitance by using C = Q/V. (5%)
3. Current I flows along a straight wire from a point charge Q1(t) located at
the origin to a point charge Q2(t) located at (0, 0, 2).
http://ppt.cc/fO0s
(1) Find the line integral of fialong the square closed path C having the
vertices at (2, 2, 0), (-2, 2, 0), (-2, -2, 0), and (2, -2, 0) and
traversed in that order. Please solve it by using Ampere's law and
considering the plane surface S bounded by C except for a slight upward
bulge at the origin to avoid Q1(t) as shown in Fig. 3. (Express the answer
in terms of I.) (5%)
(2) Redo (1) by considering the plane surface S bounded by C except for a
slight downward bulge at the origin to avoid Q1(t). (5%)
(3) If Q2(t) is moved to infinity along z-axis, how does the answer in (1)
change? (10%)
(4) If Q2(t) is slowly moved to the origin (keeping I constant) along z-axis,
how does the answer in (1) gradually change? (10%)
-kx 8
4. For the electric field E = E_0 e cos(2·10 t - y)a_z in free space (J = 0),
please find
(1) The value(s) of k for which the field satisfies both of Maxwell's curl
equations. (10%)
(2) The magnetic field H. (10%)
5. An infinite plane sheet lying in the z = 0 plane in free space carries a
surface current of density J_s = J_s(t) a_y where J_s(t) is as shown in
Fig. 5. Find and sketch
http://ppt.cc/JDAb
(1) E (t) for z = 300 m plane. (5%)
(2) E (z) for t =2 μs. (5%)
(3) Hx(z) for t = 4 μs. (5%)