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1、-Terminal Examination Paper A, Electromagnetic Field and Waves- 1 -Beijing Jiaotong University Terminal Examination (Paper A)(the second term, 2011-2012 academic year)Course Name: electromagnetic fields and waves Teacher: Wei YanClass_Student ID_Name_Question Number1 2 3 4 5 6 7 8 9 10ScoresTotalSco
2、resQuestion Number11 12 13 14 15 16 17 18 19 20Scores-Formula of operations on scalar and vector fields in cylindrical coordinates and spherical coordinates11sinzrffffffr aaaa2 22 222 211()()(sin)i sinfff fff zr r2 )11sinizrA AA 2sinsinzrzrBBB aaa-There are 4 choices marked A, B, C, and D in every q
3、uestion 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. (520=100 marks)-Terminal Examination Paper A, Electromagnetic Field and Waves- 2 -1-3 A
4、point charge q is enclosed in a linear, isotropic, and homogeneous dielectric medium of infinite extent. The medium has a relative permittivity r. 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) (B) (C) (D)
5、 24rqa204rqa20r4qa20r4qaYou select ( ).Solution:2. The polarization vector P can be expressed as(A) (B) r20(1)4qar2r(1)4qa(C) (D) r2r() r20()You select ( ).Solution:-Terminal Examination Paper A, Electromagnetic Field and Waves- 3 -3. Determine the total bound charge Qsb, which is on the surface of
6、the dielectric next to the point charge q.(A) (B) (C) (D) rr(-1)/qr/qr(1)qqYou select ( ).Solution:4. The plane z=0 marks the boundary between free space and a dielectric medium with a relative permittivity of r . The Electric field intensity next to the interface in free space is . xyzEaDetermine t
7、he Electric field intensity on the other side of the interface.(A) (B) xyzEaa/xryzEa(C) (D) /rzE/zraYou select ( ).Solution:-Terminal Examination Paper A, Electromagnetic Field and Waves- 4 -5. A spherical capacitor is formed by two concentric metallic spheres with inner radius a and outer radius b,
8、 b a. The region between the two concentric spherical shells is filled with a dielectric medium with a relative permittivity of r. Find the capacitance of the capacitor.(A) (B) (C) (D) 04ab04ab0r4ba04abYou select ( ).Solution:6. A charged semicircular ring of radius b extending from =0 to = lies in
9、the x-y plane and is centered at origin. If the charge distribution is ksin(), compute the electric field intensity at P(0,0,h).(A) (B)23/20124()yzkbbhha23/2014()yzkbhha(C) (D) 23/20()yz 23/202()yzbYou select ( ).Solution:-Terminal Examination Paper A, Electromagnetic Field and Waves- 5 -7-8. Charge
10、 is uniformly distributed inside an infinite long cylinder of radius a. The volume charge density is v. 7. Calculate the electric field intensity at all points inside and outside the cylinder.(A)(B)020()vvaE020()4vvaE(C) (D)02va204vaYou select ( ).Solution:8. Take as the zero electric potential poin
11、t. Compute the electric potential at all points inside the cylinder. (A)(B)2200ln4vvaa20lnva(C)(D)20v 2200lvvaYou select ( ).Solution:-Terminal Examination Paper A, Electromagnetic Field and Waves- 6 -9-10 A charged ring of radius a carries a uniform charge distribution. The linear charge density is
12、 l.9. The electric potential at point P (0, 0, z) on the axis of the ring is(A) (B)(C)(D)204laz20laz204la20lzaYou select ( ).Solution:10. The electric field intensity at point P (0, 0, z) on the axis of the ring is(A)(B)23/20()l zaa23/20()l zaa(C)(D)23/20()l z23/204()l zYou select ( ).Solution:-Term
13、inal Examination Paper A, Electromagnetic Field and Waves- 7 -11-12 We define an electric dipole as a pair of equal charges of opposite signs that are very close together. Assume that the magnitude of each charge is q and the separation between them is d. If the charges are symmetrically placed along the z axis, and the point of observation P (r, , ) is quite far away so that rd, as illustrated in Figure P11.Figure P
