电磁场与电磁波(双语)样卷
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Beijing Jiaotong University T erminal Examination (Paper A)
(the second term, 2011-2012 academic year)
Course Name: electromagnetic fields and waves Teacher: Wei Y an Class__________________Student ID____________Name___________
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Formula of operations on scalar and vector fields in cylindrical coordinates and spherical coordinates
111sin z r f f
f f f f
f z
r
r r ρφθφ
ρρφθθφ
∂∂∂∂∂∂∇=
+
+
=
+
+
∂∂∂∂∂∂a a a a a a
2
2
22
2
2
2
2
2
2
2
2
2
1111
1
()()(sin )sin sin f f
f f f f
f r
z
r r
r
r r ρθρρ
ρ
ρ
φ
θθ
θθφ
∂
∂∂∂∂∂∂
∂∂∇=
+
+
=+
+
∂∂∂∂∂∂∂∂∂22
()
(sin )
()11111
sin sin z r A A A A A r A z
r
r
r r ρφ
φ
θρθρρ
ρφ
θ
θ
θφ
∂∂∂∂∂∂∇∙=
+
+
=
+
+
∂∂∂∂∂∂A
2
sin 11
sin sin z r
z
r
r r z r r
B B B B rB r B ρ
φθφ
ρ
φ
θ
φ
θρρφ
θθφρθ∂∂∂∂∂∂∇⨯=
=
∂∂∂∂∂∂a a a a a a B
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There are 4 choices marked A, B, C, and D in every question and only one choice is correct. Please write the symbol of the choice which one you think is right in the blank in each question. In the same time, you must write down the process to obtain the solution . (5×20=100 marks)
[1-3] A point charge q is enclosed in a linear, isotropic, and homogeneous dielectric medium of infinite extent. The medium has a relative permittivity εr . Suppose the point charge is located at the origin of the spherical coordinate system.
1. The electric field intensity E can be expressed as (A)
2
4πr q r
a
(B)
2
04πεr
q r
a (C)
2
0r 4πεεr q r
a
(D)
2
0r 4πεεr
q r
-
a
Y ou select ( ). Solution:
2. The polarization vector P can be expressed as (A)r 2
0(ε1)4πεr
q r -a (B)
r 2
r (ε1)4πεr q r -a
(C)
r 2
r (ε1)4πεr q r
-
-a
(D)
r 2
0(ε1)4πεr q r
-
-a
Y ou select ( ). Solution: