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                 南京师范大学 200 —200 学年度第 学期                                                                                                                           ˆ
                                                                                                      1.5 One particle of mass m has position vector r  (4t  2t )i  (5t ) ˆ(m) . The velocity of
                                                                                                          the paticle at time t is_____________, the linear momentum is______________, the
                                                                                                          angular momentum of the particle is ____________________. The net torque on the particle
  物科院                      专业 《工程物理与电磁场》课程期末试卷                                                            is__________.

    班级 电自院中英班                                任课教师                  刘红                                 2. Mark the answer in front of the correct one( 30 pts. total, 5 pt each)
                                                                                                      2.1 The net torque on the wheel, as shown in the figure, about the axle through O is
    学号                                       姓  名
                                                                                                      A. r1 F1  r2 ( F2  F3 )k ; B. r1 F1  r2 ( F2  F3 )k ;
                                                                                                                                 ˆ                              ˆ
   题号           一          二          三          四          五          总分                                                                                                 F1
                                                                                                      C.  r1 F1  r2 ( F2  F3 )k ; D. r1 F1  r2 ( F2  F3 )k
                                                                                                                                   ˆ                              ˆ
1. Fill in the blankets with the correct anwsers(30 pts total)
1.1 One particle is having a circular motion with radius R . The angular speed is
     (t )  2t 2 rad / s . At time t  0 , the angle   0 . The angular acceleration                2.2 For the potential energy curve shown in the figure, the
      ____________. The tangential acceleration is____________. The angle                at t      unstable stable equilibrium points are
    is______________.                                                                                                                              U
1.2 The net force acting on a 2.00 -kg particle is (2.0t )i  (1.0  2.0t ) ˆ ( N ) . After the net
                                                                            j                         A. a, e ; B. b, d ;
    force has acted for 2.00s , the impulse of the force during this time period is__________,        C. c, d ; D. c .
    the average force acting on the particle is____________.
1.3 A uniformly charged insulating rod of length is bent
    into the shape of a circle with radius R  20cm , as                           R
    shown in the figure. However, there is a small open                       O                                                                                       b                d
    segment of length dl  0.1cm in the circle. The rod
    has a total charge of  8.0C . The magnitude and
    direction of the electric field at O , the center of the
    circle is__________________.                                     y         dl  0.1cm                                                                                          c

                                                                                                      2.3 Two particles A , B with mass m A  5kg , mB  2kg are attracted by only an internal
                                                                                                      force. Initial both particles are at rest. At time t , particle A moves with velocity
                                                                             y  3.0m                       ˆ
                                                               4.0kg                                  v A  5i m / s , the velocity of particle B is (The net external force on the system is zero)
1.4 Rigid rods of negligible mass lying along the y
                                                                                                               ˆ                  ˆ
                                                                                                      A. 12 .5i m / s ; B. 25i m / s ;
    axis connect three small particles. If the system
    rotates about the x axis with an angular speed of                                                            ˆ                   ˆ
                                                                                                      C.  12 .5i m / s ; D. 10 .0i m / s
     2.00rad / s , the moment ofinertia about the x
    axis is___________ and the total rotational kinetic                                       x
    energy is_______________.                                                                         .
                                                                2.0kg       y  2.0m

                                                                3.0kg        y  4.0m

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2.4 A cube has each side of length L . The electric           z
                                         ˆ j
field is uniform and given by E  E0 (i  ˆ) . The                                                                                                                          
electric flux through each of the cube faces S 1 and                                                                                                                  m                                    M
 S 2 is respectively                                                                                                                                                                             R
                                                                                              S 1 (right side)
          2       2             2
A. E 0 L ,2 E 0 L ; B. 0, E 0 L ;
     E 0 L2 ,0 ;     D.  E 0 L ,0 .

                                                                                                                 3.2 (10 pts) A rod of length L lies along the x axis with its left end at the origin. It has a
                                                                           (bottom)                              nonuniform charge density   x , where  is a positive constant. a) What is the value of 
                                                                                                                 if the total charge of the rod is Q ? b) Calculate the electric potential at A .

                                           x                                                                                                                  y
2.5 The magnitude of the magnetic field at a point P located a distance x from the corner of an
 infinitely long wire bent at a right angle, as shown in the figure is: (The wire carries a steady current
  I .)                                                                                                  P
   0 I        0 I
A.       ; B.       ;
   2x         4x                                                                        x
   2 0 I       0 I
C.        ; D.
    x          5x                                                         I
                                                                                                                                                                                L                 d

2.6 Four long, parallel conductors carry equal currents of I shown in the figure. The curent
                                                                                                                 3.3 (10pts.) In the figure, the current in the long, straight wire is I 1  5.00 A and the wire lies in
direction is into the page at points A and B and out of the page at C and D . The magnitude
of magnetic field at point P is                                                                                  the plane of the rectangular loop, which carries 10.0 A . Find the magnitude and direction of the
                                                                                                                 net force exerted on the loop by the magnetic field created by the wire. The dimensions are
     0 I      2 0 I        2 0 I            2 0 I                                                             a  0.150m , l  0.450m , c  0.100m
A.        ; B.        ; C.          ; D.
     2L        L           L                2L


                                                                                                                                                                           I1                         I2
3. Calculations (40 pts. total)
3.1 (10 pts) A wad of sticky clay of mass m and velocity v i is fired at a solid cylinder of mass
 M and raius R . The cylinder is initially at rest and is mounted on a fixed horizontal axle that runs                                                                                    c                a
through the center of mass. (a)Find the angular speed of the system just after the caly strikes and
sticks to the surface of the cylinder. (b) Is mechanical energy conserved in this process? Explain your

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3.4 An infinite sheet of current lying in the yz plane carries a surface current of density j s . The
current is in the y direction, and j s represents the current per unit length measured along the z
axis. Find the magnetic field near the sheet.                                     z


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