电磁场与电磁波(双语)样卷

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 11 2 12 3 13 4 14 5 15 6 16 7 17 8 18 9 19 10 20 Total Scores Scores Question Number Scores --------------------------------------------------------------------------------------------------------------------

Formula of operations on scalar and vector fields in cylindrical coordinates and spherical coordinates

ffa1ffafzazfr2ar1fr1rr22a1frsin12a

f1122f21()1f222fz2(r2fr)rsin(sin)f22rsinA1(A)a1AazzBzAzz1(rAr)r2rrarB1rsin(Asin)Arsin

aar12rsinarsinBB1BBrrsinr

B--------------------------------------------------------------------------------------------------------------------

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)

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-------------------------Terminal Examination Paper A, Electromagnetic Field and Waves-------------------------

[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)

q4πr2ar

(B)

q4πεar

0r2ar (C)

q4πε0εrr2You select ( ). Solution:

2. The polarization vector P can be expressed as (A)q4πε2(εr1)ar (B)

q0r4πεr1)ar

rr2(ε(C)

q4πε(εr1)ar

(D)

qrr24πε2(εr1)ar

0rYou select ( ). Solution:

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(D)

q4πε0ε2ar

rr -------------------------Terminal Examination Paper A, Electromagnetic Field and Waves-------------------------

3. Determine the total bound charge Qsb, which is on the surface of the dielectric next to the point charge q. (A)

q(εr-1)/εr

(B)

q/εr (C)

q(εr1)

(D) q

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

EExaxEyayEzaz.

Determine the Electric field intensity on the other side of the interface. (A) (C)

ExaxEyayEzaz (B) (D)

Ex/εraxEyayEzazExaxEyayEz/εraz

ExaxEy/εrayEzazYou select ( ). Solution:

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-------------------------Terminal Examination Paper A, Electromagnetic Field and Waves-------------------------

[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)

4πε0abba (B)

4πε0εrabba (C)

4πε0εrabba (D)

4πε0abba

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)

kb4πε0(hb)kb223/21πba2hayz2 1πba2hayz2

(B)

(D)

kb4πε0(hb)kb4πε0(hb)223/2223/21πba2hayz2 1πba2hayz2

(C)

2πε0(hb)223/2You select ( ). Solution:

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-------------------------Terminal Examination Paper A, Electromagnetic Field and Waves-------------------------

[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.

v2εa(a)0E2vaa(a)2ε0v4εa(a)0E2vaa(a)4ε0E(A) (B)

Ev2ε0(C)

a(D)

va24ε0a

You select ( ). Solution: 8. Take

 as the zero electric potential point. Compute the electric

potential at all points inside the cylinder. (A)(C)

va202lnv402a22 (B)

va202ln

v20v40a2 (D)

va202lna22

You select ( ). Solution:

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-------------------------Terminal Examination Paper A, Electromagnetic Field and Waves-------------------------

[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)

la40az22(B)

la20az22(C)

lz40az22(D)

lz20az22

You select ( ). Solution:

10. The electric field intensity at point P (0, 0, z) on the axis of the ring is (A)(C)

223/220(az)lazaz  (B) (D)

223/220(az)laaaz

223/220(az)lazaz 223/240(az)lazazYou select ( ). Solution:

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-------------------------Terminal Examination Paper A, Electromagnetic Field and Waves-------------------------

[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)

qdcos4πε0r2 (B)

qdcos2πε0r2 (C)

qdcos4πε0r (D)

qdsin4πε0r2

You select ( ). Solution:

12. Calculate the electric field intensity at point P. (A)(C)

Eqd4πε0rqd4πε0r22

[ar2cosasin]

(B)(D)

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Eqd4πε0rqd2πε0r33[ar2cosasin]

E[arcosa2sin]

E[ar2cosasin]

You select ( ).

-------------------------Terminal Examination Paper A, Electromagnetic Field and Waves-------------------------

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), h13. If the shell is not grounded, determine its electric potential. (A)

q40b(B)

q40a(C)

q40(ah)(D)

q40(b-a)

You select ( ). Solution:

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-------------------------Terminal Examination Paper A, Electromagnetic Field and Waves-------------------------

14. If the shell is not grounded and has an electric potential V0, find the electric potential at the center of the shell. (A)(B)(C) (D)

V0

V0q4πε0hq(1(11a1b)

V04πε0hq(1)

)V04πε0h2ba

You select ( ). Solution:

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-------------------------Terminal Examination Paper A, Electromagnetic Field and Waves-------------------------

15. If the shell is not grounded, determine the electric force which the point charge +q experienced. (A)(C)

ayq22a/h24πε0(a/hh)q22(B) (D)

ayq22h/a24πε0(a/hh)q22

ayb/h24πε0(b/hh)ayh/b24πε0(b/hh)You select ( ). Solution:

16. Now suppose another point +Q is located at point D (0, d, 0), d>b. If the shell is grounded, determine the electric potential at a point P (x, y, z) outside the metalized shell. (A)(B)

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4πε014πε01Qx(yd)zQx(yd)z2222 222x(yb/d)zQb/d222x(ya/d)zQa/d

-------------------------Terminal Examination Paper A, Electromagnetic Field and Waves-------------------------

(C)(D)

4πε014πε01Qx(yd)zQx(yd)z2222Qb/dx(yb/d)zQb/d22222x(yh)zqq

x(yb/d)z222x(yh)z22222x(ya/h)zqa/hYou 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)(C)(D)

Vp14πε014πε02qbQ/dxyzq222(B)Vp

Vpx(yh)z22

 222x(yd)zQ4πε01qx(yh)z222  You select ( ). Solution:

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-------------------------Terminal Examination Paper A, Electromagnetic Field and Waves-------------------------

18. At problem 16, when the shell is grounded, determine total induced charge on the outer surface of the shell. (A) q (B)

Qb/d (C)Qa/d(D)

qQb/d

You select ( ). Solution:

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-------------------------Terminal Examination Paper A, Electromagnetic Field and Waves-------------------------

19. At problem 16, when the shell is not grounded, determine total induced charge on the outer surface of the shell. (A) q (B)

Qb/d (C)Qa/d(D)

qQb/d

You select ( ). Solution:

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-------------------------Terminal Examination Paper A, Electromagnetic Field and Waves-------------------------

20. At problem 16, when the shell is not grounded, calculate the electric force which the point charge +Q experienced. (A)(B)(C) (D)

2qQQb/d ay2224πε0d(db/d)12(qQb/d)QQb/d ay2224πε0d(db/d)12qQQb/day 2224πε0(dh)(db/d)1ay1qQ24πε0d

You select ( ). Solution:

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