Beijing Jiaotong University Terminal Examination (Paper A)
(the second term, 2011-2012 academic year)
Course Name: electromagnetic fields and waves Teacher: Wei Yan
Class__________________Student ID____________Name___________
Question Number
1
2
3
4
5
6
7
8
9
10
Total
Scores
Scores
Question Number
11
12
13
14
15
16
17
18
19
20
Scores
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Formula of operations on scalar and vector fields in cylindrical coordinates and spherical coordinates
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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) (B) (C) (D)
You select ( ).
Solution:
2. The polarization vector P can be expressed as
(A) (B)
(C) (D)
You select ( ).
Solution:
3. Determine the total bound charge Qsb, which is on the surface of the dielectric next to the point charge q.
(A) (B) (C) (D)
You select ( ).
Solution:
[4]. The plane z=0 marks the boundary between free space and a dielectric medium with a relative permittivity of εr . The Electric field intensity next to the interface in free space is. Determine the Electric field intensity on the other side of the interface.
(A) (B)
(C) (D)
You select ( ).
Solution:
[5]. A spherical capacitor is formed by two concentric metallic spheres with inner radius a and outer radius b, b > a. The region between the two concentric spherical shells is filled with a dielectric medium with a relative permittivity of εr. Find the capacitance of the capacitor.
(A) (B) (C) (D)
You select ( ).
Solution:
[6]. A charged semicircular ring of radius b extending from φ=0 to φ=π lies in the x-y plane and is centered at origin. If the charge distribution is ksin(φ), compute the electric field intensity at P(0,0,h).
(A) (B)
(C) (D)
You select ( ).
Solution:
[7-8]. Charge is uniformly distributed inside an infinite long cylinder of radius a. The volume charge density is ρv.
7. Calculate the electric field intensity at all points inside and outside the cylinder.
(A) (B)
(C) (D)
You select ( ).
Solution:
8. Take as the zero electric potential point. Compute the electric potential at all points inside the cylinder.
(A) (B)
(C) (D)
You select ( ).
Solution:
[9-10] A charged ring of radius a carries a uniform charge distribution. The linear charge density is ρl.
9. The electric potential at point P (0, 0, z) on the axis of the ring is
(A) (B) (C) (D)
You select ( ).
Solution:
10. The electric field intensity at point P (0, 0, z) on the axis of the ring is
(A) (B)
(C) (D)
You select ( ).
Solution:
[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, θ, φ) is quite far away so that r>>d, as illustrated in Figure P11.
Figure P11
11. The electric potential at point P can be written as
(A) (B) (C) (D)
You select ( ).
Solution:
12. Calculate the electric field intensity at point P.
(A) (B)
(C) (D)
You select ( ).
Solution:
[13-20] A metallic spherical shell with inner radius a and outer radius b is shown in Figure P13. The center of the spherical shell is located at the origin of the coordinate system. There is a point charge +q at point C (0, h, 0), h
b. If the shell is grounded, determine the electric potential at a point P (x, y, z) outside the metalized shell.
(A)
(B)
(C)
(D)
You select ( ).
Solution:
17. At problem 16, when the shell is grounded, suppose the electric potential at point P (x, y, z) outside the metalized shell is Vp. Now Assume the shell is not grounded, find the electric potential at point P.
(A) (B)
(C)
(D)
You select ( ).
Solution:
18. At problem 16, when the shell is grounded, determine total induced charge on the outer surface of the shell.
(A) q (B) (C) (D)
You select ( ).
Solution:
19. At problem 16, when the shell is not grounded, determine total induced charge on the outer surface of the shell.
(A) q (B) (C) (D)
You select ( ).
Solution:
20. At problem 16, when the shell is not grounded, calculate the electric force which the point charge +Q experienced.
(A)
(B)
(C)
(D)
You select ( ).
Solution: