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Terminal-examination

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Page 1 Beijing JIAO TONG UNIVERSITY Terminal-examination of University Physics (II) January 10, 2007 Class:_____________Student No.:_________ Name:__________ University Physics Exercises & Problems (I) Choose one correct answer among following choices: (3 points of each) ..

     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?dsq/B?ds0(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 B0.001ti

    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 ]

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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

     C) x-rays

     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

     B) energy

     C) probability

    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_______

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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: ____________________________

    E=(r/2)(dB/dT)=(0.03/4)(0.6)=0.0045V/m__________________________.

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:

    _____________0.93c___________________

    318. (4 points) The work that must be done to increase the speed of an electron (m = 9.11 × 10

    112kg) from 0.98c to 0.99c is: _W = K K= mc( - )= (511keV)()fi fi221(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

    24520.0009xdx(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:

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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 I3I003B (2 marks) ?QCMM 4N I 2R8R

    II100B (2 marks) ?MN22R4R

     (1 marks) B0PQ

    ;I310 (1 marks) |B|(;)o4R2

    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 ).

Solution:

    IIIRR:::;00012(1) 2 marks B?;?444RRRR1212

     Direction: into the page. 1 marks

    IA

    22):RR;;12?;I(2) 2 marks ?,22,?

    I22?;()RR122

     Direction: into the page. 1 marks

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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).

    Solution:

    (a) Choose a circular loop of radius r.

     BdsBdsBrNI????(2);:0??LL

    NI0 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 marks

    2NhNb):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,?22NIh1b):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)

    1240124071.24?10(nm)1021061/210[(1.0?10);2(1.0?10)?0.511?10]1.0?10

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    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.

    ho~(a)(1cos)2.43(1cos180)4.86pmmce

    hchc11(b)E(1240)()(1240)(67.295100)41keV 3'0.010.01;4.86?10

    (c)Fromconservationofenergy,K-E41keV

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.

    1~dIIndlI(N/R)Rd2

    22ydIyI2N00~dBRd 方向?右手定则 223/2223/222R;;(xy)(xy)

    2/2NI/2NINIy2000Bdsind~~~??223/200R4R;(xy)

    22rdINIr22200or,dBdx(xrR);223/2223/222R(xr)(xr);;

    22NINIRRx00Bdx?302R2RR

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