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大学物理双语(下)试题补考

大学物理双语(下)试题补考

2009─2010年 第 二 学期 《 大学物理》双语补考试卷

注意:1、本试卷共 6 页; 2、考试时间: 120 分钟 3、姓名、学号必须写在指定地方 4、可以携带计算器

大学物理双语(下)试题补考

Ⅰ. Filling the Blanks

大学物理双语(下)试题补考

(每小题 2 分,共 20 分)

1.一空气平行板容器,两板相距为d ,与一电池连接时两板之间相互

作用力的大小为F ,在与电池保持连接的情况下,将两板距离拉开到4d ,则两板之间的相互作用力的大小是

2. There is a point charge of electric quantity 3Q at the center of a cube, the electric flux through one surface of cube is

大学物理双语(下)试题补考

3.如图1所示,真空中有两个点电荷,带电量分别为2Q 和-Q ,相距2R 。若以负电荷所在处O 点为中心, 以R 为半径作高斯球面S ,则高斯面上a 、b 两点的电场强度大小分别为 、________________

4. As shown in the figure 2, in the vacuum let the metal sphere with radius R be grounded, place a point charge Q with a distance r (r>R) away from the center O of the sphere, the total induced charge on the surface of the metal sphere is

大学物理双语(下)试题补考

a Figure 1

5. 如图3所示,AOC 为一折成∠形的金属导线(AO =

OC = L ),位于xoy 平面上. 磁感应强度为B 的匀强磁场垂直于xoy 平面. 当AOC 以速度v 沿x 轴正向运动时,导线上A 、C 两点间的电势差U AC = ,当以速度v 沿y 轴正向运动时A 、C

两点中 点电势高.

大学物理双语(下)试题补考

6.有一由N 匝细导线绕成的平面正三角形线圈,

边长为a, 通有电流I ,置于均匀外磁场B 中,当线圈平面的法向与外磁场方向夹角为300时,该

线圈所受的磁力矩M m 为________________

7. The period of a pendulum(单摆) is measured to be 3.0s in the reference frame of the pendulum. The period when measured by an observer moving at a speed of 0.95c relative to the pendulum is

大学物理双语(下)试题补考

8.把一个静止质量为0m 的粒子,由静止加速到0.6v c =(c 为真空中的光速)需做功为 Ⅱ.Choose the Correct Answer

(每小题 3 分,共 30 分)

1. 如图4所示,在真空中半径分别为R 和2R 的两个同心球面,其上分别均匀地带有电量+2q 和-

2q ,今将一电量为+Q 的带电粒子从内球面处由静止释放,则该粒子到达外球面时的动能为: ( )

(A)

02Qq R πε. (B)

大学物理双语(下)试题补考

04Qq R

πε.

(C) 08Qq R

πε. (D)

038Qq

R

πε.

2.In following statements which one is correct ( )

2q

Figure 4

Figure 3

大学物理双语(下)试题补考

(A) The electric potential is definitely zero at the point where the electric field is zero.

(B) The electric potential is non-zero at the point where the electric field is not zero.

(C) The electric field is definitely zero at the point where the electric potential is zero.

(D) The electric field is definitely zero in this area where the electric potential is constant

3.有两个长直密绕螺线管,长度及线圈匝数均相同,半径分别为r 1和r 2.管内充满均匀介质,其磁导率分别为μ1和μ2.设r 1∶r 2=1∶2,

μ1∶μ2=4∶1,当将两只螺线管串联在电路中通电稳定后,其自感系

数之比L 1∶L 2与磁能之比Wm 1∶Wm 2分别为: ( )

(A) L 1∶L 2=1∶1,Wm 1∶Wm 2 =1∶1

(B) L 1∶L 2=1∶2,Wm 1∶Wm 2 =1∶1 (C) L 1∶L 2=1∶2,Wm 1∶Wm 2 =1∶2 (D) L 1∶L 2=2∶1,

Wm 1∶Wm 2 =2∶1

大学物理双语(下)试题补考

4. One circular wire loop carries a clockwise current I in a uniform magnetic field B directed to the right as in the figure

5. If B increases, what will happen to the net magnetic force and the torque on the current loop, respectively? ( ) (A) increase, increase (B) both keep the same (C) keep the same, decrease (D) keep the same, increase

5. 尺寸相同的铁环与铜环所包围的面积中,通以相同变化率的磁通量,则环中: ( ) (A) 感应电动势相同,感应电流相同 (B) 感应电动势不同,感应电流不同 (C) 感应电动势相同,感应电流不同

Figure 5

(D) 感应电动势不同,感应电流相同

6. The segment of wire in Figure 6 carries a current of I, where the radius of the circular arc is R, the magnitude

大学物理双语(下)试题补考

of the magnetic field at the origin O is ( )

(A) R I 80μ (B) R I 40μ (C) R

I πμ80 (D) R I

πμ20

7. 半径分别为4R 和R 的两个金属球,相距很远. 用

一根长导线将两球连接,并使它们带电.在忽略导线影响的情况下,两球表面的电荷面密度之比为: ( )

(A) 1/2 (B) 4 (C) 1/4 (D) 2

8. Which of the following statements is NOT true: ( ) (A) No two electric field lines can cross each other

(B) The electric field vector is tangent to the electric field line at each point. (C) Magnetic field lines are always closed curves

(D) The magnetic fields can be produced by current, so magnetic fields have sources

9. 在某地发生两件事,静止位于该地的甲测得时间间隔为3s ,若相对甲以4c/5(c 表示真空中光速)的速率作匀速直线运动的乙测得时间间隔为:(A) 2.4s (B) 4s (C) 3.6s (D) 5s ( )

10. A spaceship is measured to be 120.0 m long and 20.0 m in diameter while at rest relative to an observer. If this spaceship now flies by the observer with a speed of 0.99c, the diameter does the observer measure is ( ) (A) 17m (B) 19m (C) 15m (D) 20m

大学物理双语(下)试题补考

Ⅲ.如图7所示,两个同心的均匀带电球面,内球面半径为R 1,带电量Q 1,外球面半径为R 2,带电

Figure 6

大学物理双语(下)试题补考

量为Q 2.设无穷远处为电势零点, 求(1)空间各处电场强度的分布;(2)在内球面内,距中心为r 处的P 点的电势。 (15分)

大学物理双语(下)试题补考

Ⅳ.A rectangular loop of width a and length b is

大学物理双语(下)试题补考

located near a long wire carrying a current I (Fig. 8). The distance between the wire and the closest

side of the loop is c. The wire is parallel to the long side of the loop. Find the total magnetic flux through the loop due to the current in the wire.

(10分)

大学物理双语(下)试题补考

Figure 7

大学物理双语(下)试题补考

ⅤA conducting rod of length l moves with velocity v parallel to a long wire carrying a steady current I . The

axis of the rod is maintained perpendicular to the wire with the near end a distance r away, as shown in Figure 9. Find the magnitude of the emf induced in the rod. (10分)

大学物理双语(下)试题补考

Ⅵ. 地面观测者测得地面上甲、乙两地相聚

大学物理双语(下)试题补考

68.010m ?,设测得作匀速直线运动的火车,由甲地

到乙地历时2.0s 。在一列与列车同方向相对地面运行速率0.6u c =的宇宙飞船中观测,试求改列车由甲地到乙地相对地面运行的路程、时间、和速度。

(15分)

Figure 9

2009─2010学年 第二学期《大学物理》(双语)

课程补考试卷参考答案及评分标准

一、 Fill in the Blanks. (2 ?10=20 marks)

1. 16

F 2.

2Q ε 3. 0217Q/(36R )πε, 023Q/(4R )πε

4. R Q r

-

5. sin blv α, A 点

6.

2IB

8

大学物理双语(下)试题补考

7. 9.6s

8. 204

m c

二、Choose the Correct Answer. (3?10=30 marks)

大学物理双语(下)试题补考

三.(15 marks )

1解:

(1)依据高斯定律有=??S E d S

204r E Q πε= ( 2分)

r

R 1

r> R 2 Q= Q 1 +Q 2 E 3= (Q 1+Q 2 )/(4πε0r 2) ( 5分)

方向均沿径向向外。

(2)由电势定义式:12

1

12

d d d R R r

r

R V ∞=?=+

???E r E r E r ?∞

+2

d 3

R r E ( 3分)

111

2

02

010

2

1201

02

044444Q Q Q Q

R R R Q Q R R πεπεπεπεπε+=-

+

+=

+

( 5分)

四.(10marks )

Solution: We know that the magnitude of the magnetic field created by the

wire at a distance r from the wire is

02I

B r

μπ= ( 2分)

The figure shows that the field is directed into the page. Because B is parallel to dA at any point within the loop, the magnetic flux through an area element dA is

02B I

BdA dA r

μπΦ==?? ( 3分)

To integrate, we first express the area element as dA bdr =. Because r is now the

only variable in the integral, we have 00ln()22a c B c Ib Ib dr a c

r c

μμππ++Φ=

=? ( 5分)

五.(10 marks )

Solution: We know that the magnitude of the magnetic field created by the

wire at a distance r from the wire is

02I

B r

μπ= ( 2分)

The expression for the flux through a rectangular area “swept out ” by the bar in time interval t is

02B I

BdA dA r μπΦ==

?

? ( 2分)

The area element is dA vtdx =, substituting in the above equation, yielding

00ln 22r l

B r Ivt Ivt r l

BdA dr r r

μμππ++Φ==

=?? ( 4分) The magnitude of the emf induced in the rod is

0ln 2B Iv d r l

dt r

μεπΦ+=

= ( 2分)

六.(15 marks )

解:取地面参考系为S 系,飞船为S ’系,飞船对地面运行的方向为x 轴

和x ’轴的正方向,由题意可得

621218.010, 2.0x x x m t t t s ?=-=??=-= ( 2分) 列车相对地面的速度为

64.010/x v m s t

??==?? ( 3分)

在飞船系中观测,两件事件的空间间隔和时间间隔为

68'

84.4010x m ?=

=

=-? ( 5分)

大学物理双语(下)试题补考

大学物理双语(下)试题补考

6

28

大学物理双语(下)试题补考

大学物理双语(下)试题补考

068102.0 2.48u .Δt Δx Δt's ??--=== ( 5分) 所以列车的速度为

8

'

8' 4.4010 1.7710/' 2.48

x v m s t ?-?===-?? ( 5分)