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武汉大学2007-2008学年下学期《大学物理》期末考试(A卷)

武汉大学2007-2008学年下学期《大学物理》期末考试(A卷)
武汉大学2007-2008学年下学期《大学物理》期末考试(A卷)

武汉大学2007-2008学年下学期《大学物理》期末考试(A 卷)

一、填空题(共27分) 1(本题3分)(5125)

一根无限长直导线通有电流I ,在P 点处被弯成了一个半径为R 的圆,且P 点处无交叉和接触,则圆心O 处的磁感强度 大小为_______________________________________,方向为 ______________________________. 2. (本题3分)(5134)

图示为三种不同的磁介质的B ~H 关系曲线,其中虚线表示的是B = μ0H 的关系.说明a 、b 、c 各代表哪一类磁介质的B ~H 关系曲线:

a 代表______________________________的B ~H 关系曲线.

b 代表______________________________的B ~H 关

系曲线.

c 代表______________________________的B ~H 关系曲线. 3. (本题3分)(2624)

一个中空的螺绕环上每厘米绕有20匝导线,当通以电流I =3 A 时,环中磁 场能量密度w =_____________ .(μ 0 =4π×10-7 N/A 2) 4. (本题3分)(5161)

一平行板空气电容器的两极板都是半径为R 的圆形导体片,在充电时,板间电场强度的变化率为d E /d t .若略去边缘效应,则两板间的位移电流为 ________________________. 5. (本题4分)(3177)

如图,在双缝干涉实验中,若把一厚度为e 、折射率 为n 的薄云母片覆盖在S 1缝上,中央明条纹将向__________移动;覆盖云母片后,两束相干光至原中央明纹O 处的光程差为__________________. 6. (本题3分)(4611)

某一波长的X 光经物质散射后,其散射光中包含波长________和波长 __________的两种成分,其中___________的散射成分称为康普顿散射. 7. (本题5分)(4203)

设描述微观粒子运动的波函数为),(t r

ψ,则*ψψ表示____________________________________________________________________; ),(t r

ψ须满足的条件是______________________________________;其归一化条 件是__________________________________________. 8. (本题3分)(4787)

在主量子数n =2,自旋磁量子数2

1

=s m 的量子态中,能够填充的最大电子

S

数是_________________.

二、选择题(共27分) 9 (本题3分) (2717)

距一根载有电流为3×104 A 的电线1 m 处的磁感强度的大小为 (A) 3×10-5 T . (B) 6×10-3 T . (C) 1.9×10-2T . (D) 0.6 T .

(已知真空的磁导率μ0 =4π×10-7 T ·m/A) [ ] 10. (本题3分)(2391)

一电子以速度v 垂直地进入磁感强度为B 的均匀磁场中,此电子在磁场中运动轨道所围的面积内的磁通量将

(A) 正比于B ,反比于v 2. (B) 反比于B ,正比于v 2.

(C)

正比于B ,反比于v . (D) 反比于B ,反比于v .

[ ] 11 (本题3分)(2594)

有一矩形线圈AOCD ,通以如图示方向的电流I ,将它置于均匀磁场B 中,B 的方向与x 轴正方向一致,线圈平面与x 轴之间的夹角为α,α < 90°.若AO 边在y 轴上,且线圈可绕y 轴自由转动,则线圈将

(A) 转动使α 角减小.

(B) 转动使α角增大. (C) 不会发生转动.

(D) 如何转动尚不能判定. [ ] 12. (本题3分)(2314)

如图所示,M 、N 为水平面内两根平行金属导轨,ab 与cd 为垂直于导轨并可在其上自由滑动的两根直裸导线.外磁场垂直水平面向上.当外力使

ab 向右平移时,cd (A) 不动. (B) 转动. (C) 向左移动. (D) 向右移动.[ ]

13 (本题3分)(2125)

如图,长度为l 的直导线ab 在均匀磁场B

中以速度v

移动,直导线ab 中的电动势为

(A) Bl v . (B) Bl v sin α. (C) Bl v cos α. (D) 0. [ ] 14. (本题3分)(2421)

已知一螺绕环的自感系数为L .若将该螺绕环锯成两个半环式的螺线管,则两个半环螺线管的自感系数

c a b

d N

M

B

(A) 都等于

L 21. (B) 有一个大于L 21,另一个小于L 21

. (C) 都大于L 21. (D) 都小于L 2

1

. [ ]

15 (本题3分)(3174)

在双缝干涉实验中,屏幕E 上的P 点处是明条纹.若将缝S 2盖住,并在S 1 S 2连线的垂直平分面处放一高折射率介质反射面M ,如图所示,则此时 (A) P 点处仍为明条纹.

(B) P 点处为暗条纹.

(C) 不能确定P 点处是明条纹还是暗条纹.

(D) 无干涉条纹. [ ]

16(本题3分)(3718)

在单缝夫琅禾费衍射实验中,若增大缝宽,其他条件不变,则中央明条纹 (A) 宽度变小. (B) 宽度变大. (C) 宽度不变,且中心强度也不变. (D) 宽度不变,但中心强度增大. [ ] 17 (本题3分)(3215)

若用衍射光栅准确测定一单色可见光的波长,在下列各种光栅常数的光栅中选用哪一种最好?

(A) 5.0×10-1 mm . (B) 1.0×10-1 mm . (C) 1.0×10-2 mm . (D) 1.0×10-3 mm . [ ] 18. (本题3分)(4223)

下述说法中,正确的是 (A) 本征半导体是电子与空穴两种载流子同时参予导电,而杂质半导体(n 型或p 型)只有一种载流子(电子或空穴)参予导电,所以本征半导体导电性能比杂质半导体好.

(B) n 型半导体的导电性能优于p 型半导体,因为n 型半导体是负电子导电,p 型半导体是正离子导电.

(C) n 型半导体中杂质原子所形成的局部能级靠近空带(导带)的底部,使局部能级中多余的电子容易被激发跃迁到空带中去,大大提高了半导体导电性能. (D) p 型半导体的导电机构完全决定于满带中空穴的运动. [ ] 三、计算题(共33分) 19. (本题10分)(2567)

AA '和CC '为两个正交地放置的圆形线圈,其圆心相重合.AA '线圈半径为20.0 cm ,共10匝,通有电流10.0 A ;而CC '线圈的半径为10.0 cm ,共20匝,通有电流 5.0 A .求两线圈公共中心O 点的磁感强度的大小和方向.

(μ0 =4π×10-7 N ·A -2)

20. (本题8分)(3628)

用白光垂直照射置于空气中的厚度为0.50 μm 的玻璃片.玻璃片的折射率为1.50.在可见光范围内(400 nm ~ 760 nm)哪些波长的反射光有最大限度的增强? (1 nm=10-9 m)

21. (本题5分)(3768)

强度为I 0的一束光,垂直入射到两个叠在一起的偏振片上,这两个偏振片的偏振化方向之间的夹角为60°.若这束入射光是强度相等的线偏振光和自然光混合而成的,且线偏振光的光矢量振动方向与此二偏振片的偏振化方向皆成30°角,求透过每个偏振片后的光束强度. 22. (本题5分)(4393)

以波长λ = 410 nm (1 nm = 10-9 m)的单色光照射某一金属,产生的光电子的最大动能E K = 1.0 eV ,求能使该金属产生光电效应的单色光的最大波长是多少? (普朗克常量h =6.63×10-34 J ·s) 23. (本题5分)(4547)

已知电子在垂直于均匀磁场B

的平面内运动,设电子的运动满足玻尔量子化条件,求电子轨道的半径r n =? 四、理论推导与证明题(共5分) 24. (本题5分)(4550)

一束具有动量p

的电子,垂直地射入宽度为a 的狭缝,若在狭缝后远处与狭缝相距为R 的地方放置一块荧光屏,试证明屏幕上衍射图样中央最大强度的宽度)/(2ap Rh d =,式中h 为普朗克常量. 五、回答问题(共5分) 25. (本题5分)(4781)

粒子(a)、(b)的波函数分别如图所示,若用位置和动量描述它们的运动状态,两者中哪一粒子位置的不确定量较大?哪一粒子的动量的不确定量较大?为什么?

参考答案:

一、选择题(共27分) 1. (本题3分) (2717) B 2. (本题3分)(2391) B 3. (本题3分)(2594) B 4. (本题3分)(2314)D 5. (本题3分)(2125)D 6. (本题3分)(2421)D 7. (本题3分

)(3174)B

x (a)

x

(b)

8. (本题3分)(3718)A

9. (本题3分)(3215)D 10. (本题3分)(4223)C 二、填空题(共27分) 11 (本题3分)(5125)

)1

1(20π

-R I μ 2分

垂直纸面向里. 1分 12. (本题3分)(5134)

铁磁质 1分 顺磁质 1分

抗磁质 1分 13. (本题3分)(2624)

22.6 J ·m -3 3分 14. (本题3分)(5161)

t E R d /d 20πε 3分 15. (本题4分)(3177)

上 2分 (n -1)e 2分 16. (本题3分)(4611)

不变 1分 变长 1分 波长变长 1分 17. (本题5分)(4203)

粒子在t 时刻在(x ,y ,z )处出现的概率密度 2分 单值、有限、连续 1分

1d d d 2

=???z y x ψ 2分

18. (本题3分)(4787)

4 2分

三、计算题(共33分)

19. (本题10分)(2567)

解:AA '线圈在O 点所产生的磁感强度

02502μμ==A

A A A r I N

B (方向垂直AA '平面) 3分 C

C '线圈在O 点所产生的磁感强度 005002μμ==C

C C C r I

N B (方向垂直CC '平面) 3分 O 点的合磁感强度 4

2/1221002.7)(-?=+=C A B B B T 2分

A

B 的方向在和AA '、C

C '都垂直的平面内,和CC '平面的夹角

?==-4.63tg 1A

C B B

θ 2分

20. (本题8分)(3628)

解:加强, 2ne+21

λ = k λ, 2分

123000

1242

12-=

-=-

=k k ne k ne λ nm 2分 k = 1, λ1 = 3000 nm , k = 2, λ2 = 1000 nm ,

k = 3, λ3 = 600 nm , k = 4, λ4 = 428.6 nm ,

k = 5, λ5 = 333.3 nm .

2分 ∴ 在可见光范围内,干涉加强的光的波长是

λ=600 nm 和λ=428.6 nm . 2分 21. (本题5分)(3768)

解:透过第一个偏振片后的光强为

2001c o s 212121??

?

??+??? ??=I I I 30° 2分

=5I 0 / 8 1分 透过第二个偏振片后的光强I 2=( 5I 0 / 8 )cos 260°

1分

=5I 0 / 32 1分

22. (本题5分)(4393)

解:设能使该金属产生光电效应的单色光最大波长为λ0. 由 00=-A h ν

可得 0)/(0=-A hc λ A hc /0=λ 2分 又按题意: K E A hc =-)/(λ ∴ K E hc A -=)/(λ

得 λλ

λλK K E hc hc E hc hc -=

-=)/(0= 612 nm 3分 23. (本题5分)(4547)

解:设轨道半径为r n ,电子运动速度为v .则由

n r m B e /2v v = 2分 n r m L n ==v 2分 得 n eB r n ?=2/1)/( ( n = 1,2,3……) 1分 四、理论推导与证明题(共5分) 24. (本题5分)(4550)

证:单缝夫朗禾费衍射各级极小的条件为: λφk a ±=s i n ( k = 1,2……) 令 k = 1, 得 λφ=s i n a 1分 可见,衍射图形第一级极小离中心点距离 a f f R x /s i n tg 1λφφ?=≈= 1分 又电子德布罗意波的波长 p h /=λ 2分 所以中央最大强度宽度 )/(221ap Rh x d == 1分 五、回答问题(共5分) 25. (本题5分)(4781)

答:由图可知,(a)粒子位置的不确定量较大. 2分 又据不确定关系式 x

p x ??≥π

2h

可知,由于(b)粒子位置的不确定量较小,故(b)粒子动量的不确定量较大. 3分

x

(a)

x (b)

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