Beijing JIAO TONG UNIVERSITY
Terminal-examination of University Physics (II)
January 10, 2007
Class:_____________Student No.:_________ Name:__________
(I) (II) (III) Total Score
University Physics Exercises & Problems
(I) Choose one correct answer among following choices: (3 points of each)
1. Which of the following equations can be used to show that magnetic field lines form
closed loops? ;;;; A) B) E?ds？q/，B?ds？0(i0??SS;;;;
C) = –d，/dt D) = ：i + ：5d，/dt E?dlB?dlB000E??LL
[ B ]
;2ˆ2. The magnetic field in a region of space is given by for ；2s ? t ? +2s (in SI B？0.001ti
unit). What is the direction of the induced electric field when t = 0s?
A). Parallel to the x axis. B). Parallel to the y axis.
C). The electric field is in the circles centered on the x axis.
D). There is no induced electric field when t = 0s.
[ D ] 3.
;;What is the value of for the path shown in the B?ds?
figure? ；7A. ；8；?10 T?m ；7 B. ；4；?10 T?m ；7 C. +8；?10 T?m ；7 D. +32；?10 T?m
[ A ]
4. Magnetization ;磁化强度；is:
A) the current density in an object
B) the charge density of moving charges in an object
C) the magnetic dipole moment (磁偶极矩) of an object
D) the magnetic dipole moment per unit volume of an object
[ D ]
5 . A consequence ;结果；of Einstein's theory of relativity is:
A) everything is relative
B) moving rods are longer than when they are at rest
C) moving clocks run more slowly than when they are at rest
D) the laws of physics must appear the same to all observers moving with
uniform velocity relative to each other
[ C ]
6. Two events occur simultaneously at separated points on the y axis of reference frame S.
According to an observer moving in the positive x direction:
A) the events are simultaneous
B) the event with the greater y coordinate occurs first
C) the event with the greater y coordinate occurs last
D) either event might occur first, depending on the observer's speed
[ A ]
7. The proper time (原时)between two events is measured by clocks at rest in a reference frame
in which the two events:
A) occur at the same time
B) occur at the same location (position)
C) are separated by the distance a light signal can travel during the time interval
D) satisfy none of the above
[ B ]
8. Which of the following electromagnetic radiations has photons with the greatest energy?
A) radio waves
B) blue light
D) yellow light
[ C ] 9. The Compton effect demonstrates ;表明；
A) light acts as photons
B) relativistic formulation works well
C) consistent;一致的；explanations of scattered photon shift in wavelength
D) all of the above
[ D ]
2 10. The significance ;意义；of ??? is:
A) probability density
D) energy density
[ A ]
II) Fill in the blank with correct answer:
(dE1. (3 points) Displacement current (位移电流) is:____________________________ ，0dt
2. (3 points) As the figure shown, uniform electric current flows i i . into and then out from a circular ring. The magnetic field at the o
center of the ring should be:______0_______
3. (4 points) A rod with resistance R lies across frictionless conducting rails ;轨道；in a
constant uniform magnetic field B, as shown. Assume the rails have negligible resistance.
The force that must be applied by a person to pull the rod to the right at constant speed v
22is:____ _______BLv/R __________ _____ _____________.
4. (4 points) A cylindrical (圆柱的) region of radius R = 3.0 cm contains a uniform magnetic
field parallel to its axis. If the field is changing at the rate 0.60 T/s, the electric field
induced at a point R/2 from the cylinder axis is: ____________________________
5. (4 points) The circular wire loop of radius R in the figure
carries a clockwise current I. There is a uniform magnetic field
B directed to the right. We conclude that (the direction of) the
net force on the current loop is zero (into, out of, up,
down the page, or zero). And (the direction of) the torque on the current loop is down the
page _____ (into, out of, up, down the page, or zero).
6. (4 points) A meter stick ;米尺；moves at 0.95c in the direction of its length through a
laboratory. According to measurements taken in the laboratory, its length is:____0.31m __
7. (4 points) Quasar ;类星体；Q1 is moving away from us at a speed of 0.8c. Quasar Q2 is
moving away from us in the opposite direction at a speed of 0.5c. The speed of Q1 as
measured by an observer on Q2 ;Q2观察到Q1的速度；is:
–318. (4 points) The work that must be done to increase the speed of an electron (m = 9.11 × 10
112；kg) from 0.98c to 0.99c is: _W = K – K= mc(； -； )= (511keV)()fi fi22；；1(0.99)1(0.98)
= 1055 keV_
29. If the wave function of a particle is ?(x) = 0.030x in a region, then the probability of finding
2452？0.0009xdx？(0.0009/5)x|this particle in the region of x = 1 to x = 2 is __=0.0056___. 1?1
10. For n = 4 and l = 2, the possible values of mandm are m= -2, -1, 0, 1, 2_____ l s _____l _
______ and _______ m= -1/2, 1/ 2____ ________ respectively.s
(III) Calculate Following Problems:
1. (7 points) A long conducting wire PQCMN is bent into the shape as shown in below figure.
(All parts are in the same plane of the paper and part QCM is three quarters of a circular arc of ;
radius R) . Calculate magnetic field at the point of O. B
I Q P R O C Solution: R I3I：：003B (2 marks) ？?？QCMM 4N I 2R8R
：：II100B (2 marks) ？?？MN22；R4；R
(1 marks) B？0PQ
;：I310 (1 marks) ！|B|？(;)o；4R2
Direction of magnetic field at point P is out of the paper. (1 marks)
2. (6 marks) A wire is formed into the shape of two half circles connected by equal-length
straight sections as shown in below figure (current I is clockwise). (a) What are the ;magnitude and direction of magnetic fieldB at the center C ? (b) Find the magnetic dipole
moment ： (磁矩或磁偶极矩) of the circuit. (give both the magnitude and the direction of ：).
IIIRR：：：;00012(1) 2 marks B？;？444RRRR1212
Direction: into the page. 1 marks
22)：RR；；12？;I(2) 2 marks ?，22，?
Direction: into the page. 1 marks
3. (8 marks) A toroid consists of N turns and has a rectangular cross-section (inner and
outer radii a and b, and thickness h), with air inside. (a) Find the self-inductance of this
toroid. (b) If the wire around the toroid carries a current I, find the magnetic field energy
density (磁能密度)as a function of the radial distance r from its center u(r), and (c) the total
energy stored in the magnetic field of the toroid (U).
(a) Choose a circular loop of radius r.
NI：0 B a<r<b 1 marks ？2r；
The magnetic flux through the cross-section is The cross-section of the toroid b：：NINIhb)：00 ()ln，？?？？BdAhdrB?，???a22ra；；，?
2：NhN，b)：B0 1 marks lnL？？?，2Ia；，?
(b) The magnetic energy density at the point a distance r from the center is
2222：：NINIB1)：00 2 marks u？？？B?，222228rr：：；；，?00
22b)：：NI0(2)UudVrhdr？？；?，BB22????a8r；，?(c ) 2 marks 22NIhb)：：0ln？?，4a，?；22：NIh1b)：20or ULI？？lnB?，24a；，?
4. (5 points) (a) A photon has energy of 10.00 keV, (b) an electron has a kinetic energy of -3110.00 GeV. What are their wavelengths? (The mass of electron: m= 9.1?10kg and e -34the Planck constant h = 6.63?10 Js).
hc1240a) ; (2 marks) ，？？？0.124(nm)pho3E10?10
hchc(b)？？，ele22pcK;2Kmce (3 marks)
5. (6 points) X rays of wavelength 0.010 nm are directed onto a target containing free oelectrons. For Compton scattering (散射)from one of those electrons, at an angle of 180, what are (a) the Compton shift, (b) the corresponding change in photon energy, (c) the kinetic
energy of the recoiling ;反冲；electron.
IV. Additional Problem:
(5 points)A coil of N turns is closely wound along the surface of a half ball (radius R). Each turn carries a current I. All coils cover the whole semi-circle parallel ;单层线圈均匀平行缠绕盖住半个球面；as the figure shown. Find the magnetic field at the center O of the ball.
22：：ydIyI2N00~？？dBRd 方向？右手定则 223/2223/2；22R;;(xy)(xy)