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《费恩曼物理学讲义》(第2卷)讲述当时美国大学物理教学改革试图解决的一个主要问题是基础物理教学应尽可能反映近代物理的巨大成就。《费恩曼物理学讲义》在基础物理的水平上对20世纪物理学的两大重要成就——相对论和量子力学——作了系统的介绍，对于量子力学，费恩曼教授还特地准备了一套适合大学二年级水平的讲法。教学改革试图解决的另一个问题是按照当前物理学工作者在各个前沿研究领域所使用的方式来介绍物理学的内容。在《费恩曼物理学讲义》一书中对一些问题的分析和处理方法反映了费恩曼自己以及其他在前沿研究领域工作的物理学家所通常采用的分析和处理方法。全书对基本概念、定理和定律的讲解不仅生动清晰，通俗易懂，而且特别注重从物理上作出深刻的叙述。为了扩大学生的知识面，全书还列举了许多基本物理原理在各个方面(诸如天体物理、地球物理、生物物理等)的应用，以及物理学的一些最新成就。由于全书是根据课堂讲授的录音整理编辑的，它在一定程度保留了费恩曼讲课的生动活泼、引人入胜的独特风格。《费恩曼物理学讲义》从普通物理水平出发，注重物理分析，深入浅出，避免运用高深烦琐的数学方程，因此具有高中以上物理水平和初等微积分知识的读者阅读起来不会感到十分困难。至于大学物理系的师生物理工作者更能从此书中获得教益。1989年，为纪念费恩曼逝世一周年，原书编者重新出版本书，并增加了介绍费恩曼生平的短文和新的序言。我们按照新版的原本进行了翻译。

chapter 1. electromagnetism .

1-1 electrical forces 1-1

1-2 electric and magnetic felds 1-3

1-3 characteristics of vector fields 1-4

1-4 the laws of electromagnetism i-5

i-5 what are the fields? 1-9

1-6 electromagnetism in science and technology 1-10

chapter 2. differential calculus of vector fields

2-1 understanding physics 2-1

2-2 scalar and vector fields—t and h 2-2

2-3 derivatives of fields—the gradient 2-4

2-4 the operator v 2-6

2-5 operations with v 2-7

2-6 the differential equation of heat flow 2-8

2-7 second derivatives of vector fields 2-9

2-8 pitfalls 2-11

chapter 3. vector integral calculus

3-1 vector integrals; the line integral of v,it 3-1

3-2 the flux of a vector field 3-2

3-3 the flux from a cube; gauss' theorem 3-4

.3-4 heat conduction; the diffusion equation 3-6

3-5 the circulation of a vector field 3-8

3-6 the circulation around a square;

stokes' theorem 3-9

3-7 curl-free and divergence-free fields 3-10

3-8 summary 3-11

chapter 4. electrostatics

4-1 statics 4—1

4-2 coulomb's law; superposition 4-2

4-3 electric potential 4-4

4-4 e=- φ 4-6

4-5 the flux of e 4-7

4-6 gauss' law; divergence of e 4-9

4-7 field of a sphere of charge 4-10

4-8 field lines; equipotential surfaces 4-1l

chapter 5. application of gauss' law

5-1 electrostatics is gauss's law plus . . . 5-1

5-2 equilibrium in an electrostatic field 5-1

5-3 equilibrium with conductors 5-2

5-4 stability of atoms 5-3

5-5 the field of a line charge 5-3

5-6 a sheet of charge; two sheets 5-4

5-7 a sphere of charge; a spherical shell 5-4

5-8 is the field of a point charge exactly 1/r2？ 5-5

5-9 the fields of a conductor 5-7

5-10 the field in a cavity of a conductor 5-8

chapter 6. the electric field in various

circumstances

6-1 equations of the electrostatic potential 6-1

6-2 the electric dipole 6-2

6-3 remarks on vector equations 6-4

6-4 the dipole potential as a gradient 6-4

6-5 the dipole approximation for an arbitrary

distribution 6-6

6-6 the fields of charged conductors 6-8

6-7 the method of images 6-8

6-8 a point charge near a conducting plane 6-9

6-9 a point charge near a conducting sphere 6-10

6-10 condensers; parallel plates 6-11

6-11 high-voltage breakdown 6-13

6-12 the field-emission microscope 6-14

chapter 7. the electric field in various

circumstances (continued)

7-1 methods for finding the electrostatic field 7-1

7-2 two-dimensional fields; functions of the complex

variable 7-2

7-3 plasma oscillations 7-5

7—4 colloidal particles in an electrolyte 7-8

7-5 the electrostatic field of a grid 7-10

chapter 8. electrostatic energy

8-1 the electrostatic energy of charges. a uniform

sphere 8-t

8-2 the energy of a condenser. forces on charged

conductors 8-2

8-3 the electrostatic energy of an ionic crystal 8-4

8-4 electrostatic energy in nuclei 8-6

8-5 energy in the electrostatic field 8-9

8-6 the energy of a point charge 8-12

chapter 9. electricity in the atmosphere

9-1 the electric potential gradient of the

atmosphere 9-1

9-2 electric currents in the atmosphere 9-2

9-3 origin of the atmospheric currents 9-4

9-4 thunderstorms 9-5

9-5 the mechanism of charge separation 9-7

9-6 lightning 9-10

chapter 10. dielectrics

10-1 the dielectric constant 10-1

10—2 the polarization vector p 10-2

10-3 polarization charges 10-3

10-4 the electrostatic equations with dielectrics 10-6

10-5 fields and forces with dielectrics 10-7

chapter 11. inside dielectrics

11-1 molecular dipoles 11-1

11-2 electronic polarization 11-1

11-3 polar molecules; orientation polarization 11-3

11-4 electric fields in cavities of a dielectric 11-5

11-5 the dielectric constant of liquids; the clausius-

mossotti equation 11-6

11-6 solid dielectrics 11-8

11-7 ferroelectricity; batioa 11-8

chapter 12. electrostatic analogs

12-1 the same equations have the same solutions 12-1

12-2 the flow of heat; a point source near an infinite

plane boundary 12-2

12-3 the stretched membrane 12-5

12-4 the diffusion of neutrons; a uniform spherical

source in a homogeneous medium 12-6

12-5 irrotational fluid flow; the flow past a sphere 12-8

12-6 illumination; the uniform lighting of a plane 12-10

12-7 the "underlying unity" of nature 12-12

chapter 13. magnetostatics

13-1 the magnetic field 13-1

13-2 electric current; the conservation of charge 13-1

13-3 the magnetic force on a current 13-2

13-4 the magnetic field of steady currents;

ampere's law 13-3

13-5 the magnetic field of a straight wire and of a

solenoid; atomic currents 13-5

13-6 the relativity of magnetic and electric fields 13-6

13-7 the transformation of currents and charges 13-11

13-8 superposition; the right-hand rule 13-11

chapter 14. the magnetic field in various

situations

14-1 the vector potential 14-1

14-2 the vector potential of known currents 14-3

14-3 a straight wire 14-4

14-4 a long solenoid 14-5

14-5 the field of a small loop; the magnetic dipole 14-7

14-6 the vector potential of a circuit 14-8

14-7 the law of blot and savart 14-9

chapter 15. the vector potential

15-1 the forces on a current loop; energy of

a dipole 15-1

15-2 mechanical and electrical energies 15-3

15-3 the energy of steady currents 15-6

15-4 b versus a 15-7

15-5 the vector potential and quantum mechanics 15-8

15-6 what is true for statics is false for dynamics 15-14

chapter 16. induced currents

16-1 motors and generators 16-1

16-2 transformers and inductances 16-4

16-3 forces on induced currents 16-5

16-4 electrical technology 16-8

chapter 17. the laws of induction

17-1 the physics of induction 17-1

17-2 exceptions to the "flux rule" 17-2

17-3 particle acceleration by an induced electric field;

the betatron 17-3

17-4 a paradox 17-5

17-5 alternating-current generator 17-6

17-6 mutual inductance 17-9

17-7 self-inductance 17-11

17-8 inductance and magnetic energy 17-12

chapter 18. the maxwell equations

18-1 maxwell's equations 18-1

18-2 how the new term works 18-3

18-3 all of classical physics 18-5

18-4 a travelling field 18-5

18-5 the speed of light 18-8

18-6 solving maxwell's equations; the potentials and the

wave equation 18-9

chapter 19. the principle of least action

a special lecture—almost verbatim 19-1

a note added after the lecture 19-14

chapter 20. solutions of maxwell's equations

in free space

20-1 waves in free space; plane waves 20-1

20-2 three-dimensional waves 20-8

20-3 scientific imagination 20-9

20-4 spherical waves 20—12

chapter 21. solutions of maxwell's equations ..

with currents and charges

21-1 light and electromagnetic waves 21-1

21-2 spherical waves from a point source 21-2

21-3 the general solution of maxwell's equations 21-4

21-4 the fields of an oscillating dipole 21-5

21-5 the potentials of a moving charge; the general

solution of lienard and wiechert 21-9

21-6 the potentials for a charge moving with constant

velocity; the lorentz formula 21-12

chapter 22. ac circuits

22-1 impedances 22-1

22-2 generators 22-5

22-3 networks of ideal elements; kirchhoff's rules 22-7

22-4 equivalent circuits 22-10

22-5 energy 22-11

22-6 a ladder network 22-12

22-7 filters 22-14

22-8 other circuit elements 22-16

chapter 23. cavity resonators

23-1 real circuit elements 23-1

23-2 a capacitor at high frequencies 23-2

23-3 a resonant cavity 23-6

23-4 cavity modes 23-9

23-5 cavities and resonant circuits 23-10

chapter 24. waveguides

24-1 the transmission line 24-1

24-2 the rectangular waveguide 24-4

24-3 the cutoff frequency 24-6

24-4 the speed of the guided waves 24-7

24-5 observing guided waves 24-7

24-6 waveguide plumbing 24-8

24-7 waveguide modes 24-10

24-8 another way of looking at the guided waves 24-10

chapter 25. electrodynamics in relativistic

notation

25-1 four-vectors 25-1

25-2 the scalar product 25-3

25-3 the four-dimensional gradient 25-6

25-4 electrodynamics in four-dimensional notation 25-8

25-5 the four-potential of a moving charge 25-9

25-6 the invariance of the equations of

electrodynamics 25-10

chapter 26. lorentz transformations of the fields

26-1 the four-potential of a moving charge 26-1

26-2 the fields of a point charge with a constant

velocity 26-2

26-3 relativistic transformation of the fields 26-5

26-4 the equations of motion in relativistic

notation 26-11

chapter 27. field energy and field momentum

27-1 local conservation 27-1

27-2 energy conservation and electromagnetism 27-2

27-3 energy density and energy flow in the

electromagnetic field 27-3

27-4 the ambiguity of the field energy 27-6

27-5 examples of energy flow 27-6

27-6 field momentum 27-9

chapter 28. electromagnetic mass

28-1 the field energy of a point charge 28-1

28-2 the field momentum of a moving charge 28-2

28-3 electromagnetic moss 28-3

28-4 the force of an electron on itself 28-4

28-5 attempts to modify the maxwell theory 28-6

28-6 the nuclear force field 28-12

chapter 29. the motion of charges in electric

and magnetic fields

29-1 motion in a uniform electric or magnetic field 29-1

29-2 momentum analysis 29-1

29-3 an electrostatic lens 29-2

29-4 a magnetic lens 29-3

29-5 the electron microscope 29-3

29-6 accelerator guide fields 29-4

29-7 alternating-gradient focusing 29-6

29-8 motion in crossed electric and magnetic fields 29-8

chapter 30. the internal geometry of crystals

30-1 the internal geometry of crystals 30-1

30-2 chemical bonds in crystals 30-2

30-3 the growth of crystals 30-3

30-4 crystal lattices 30-3

30-5 symmetries in two dimensions 30-4

30-6 symmetries in three dimensions 30-7

30-7 the strength of metals 30-8

30-8 dislocations and crystal growth 30-9

30-9 the bragg-nye crystal model 30-10

chapter 31. tensors

31-1 the tensor of polarizability 31-1

31-2 transforming the tensor components 31-3

31-3 the energy ellipsoid 3 i-3

31-4 other tensors; the tensor of inertia 31-6

31-5 the cross product 31-8

31-6 the tensor of stress 31-9

31-7 tensors of higher rank 31-11

31-8 the four-tensor of electromagnetic

momentum 31-12

chapter 32. refractive index of dense materials

32-1 polarization of matter 32-1

32-2 maxwell's equations in a dielectric 32-3

32-3 waves in a dielectric 32-5

32-4 the complex index of refraction 32-8

32-5 the index of a mixture 32-8

32-6 waves in metals 32-10

32-7 low-frequency and high-frequency approximations;

the skin depth and the plasma frequency 32-11

chapter 33. reflection from surfaces

33-1 reflection and refraction of light 33-1

33-2 waves in dense materials 33-2

33-3 the boundary conditions 33-4

33-4 the reflected and transmitted waves 33-7

33-5 reflection from metals 33-11

33-6 total internal reflection 33-12

chapter 34. the magnetism of matter

34-1 diamagnetism and paramagnetism 34-1

34-2 magnetic moments and angular momentum 34-3

34-3 the precession of atomic magnets 34-4

34-4 diamagnetism 34-5

34-5 larmor's theorem 34-6

34-6 classical physics gives neither diamagnetism nor

paramagnetism 34-8

34-7 angular momentum in quantum mechanics 34-8

34-8 the magnetic energy of atoms 34-11

chapter 35. paramagnetism and magnetic resonance

35-1 quantized magnetic states 35-1

35-2 the stern-gerlach experiment 35-3

35-3 the rabi molecular-beam method 35-4

35-4 the paramagnetism of bulk materials 35-6

35-5 cooling by adiabatic demagnetization 35-9

35-6 nuclear magnetic resonance 35-10

chapter 36. ferromagnetism

36-1 magnetization currents 36-1

36-2 the field h'36-5

36-3 the magnetization curve 36-6

36-4 iron-core inductances 36-8

36-5 electromagnets 36-9

36-6 spontaneous magnetization 36-11

chapter 37. magnetic materials

37-1 understanding ferromagnetism 37-1

37-2 thermodynamic properties 37-4

37-3 the hysteresis curve 37-5

37-4 ferromagnetic materials 37-10

37-5 extraordinary magnetic materials 37-11

chapter 38. elasticity

38-1 hooke's law 38-1

38-2 uniform strains 38-2

38-3 the torsion bar; shear waves 38-5

38-4 the bent beam 38-9

38-5 buckling 38-i1

chapter 39. elastic materials

39-1 the tensor of strain 39-1

39-2 the tensor of elasticity 39-4

39-3 the motions in an elastic body 39-6

39-4 nonelastic behavior 39-8

39-5 calculating the elastic constants 39-10

chapter 40. the flow of dry water

40-1 hydrostatics 40-1

40-2 the equations of motion 40-2

40-3 steady fiow—bernoulli's theorem 40-6

40-4 circulation 40-9

40-5 vortex lines 40-10

chapter 41. the flow of wet water

41-1 viscosity 41-1

41-2 viscous flow 41-4

41-3 the reynolds number 41-5

4l-4 flow past a circular cylinder 41-7

41-5 the limit of zero viscosity 41-9

41-6 couette flow 41-10

chapter 42. curven space

42-1 curved spaces with two dimensions 42-1

42-2 curvature in three-dimensional space 42-5

42-3 our space is curved 42-6

42-4 geometry in space-time 42-7

42-5 gravity and the principle of equivalence 42-8

42-6 the speed of clocks in a gravitational field 42-9

42-7 the curvature of space-time 42-11

42-8 motion in curved space-time 42-12

42-9 einstein's theory of gravitation 42-13

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显然久已明白，高耸的东西常受雷击。波斯王薛西斯的顾问阿塔班尼斯曾有一句名言，那是当薛西斯企图把整个已知世界都归由波斯人管辖而出征时，他给予他的主子关于对希腊的一次预谋攻击的忠告。阿塔班尼斯说：“看上帝怎样利用他的闪电来毁灭那些大的野兽，他不能容忍它们逐渐变傲慢，而那些小动物却从未惹怒过他。同样，他又如何使他的闪电总是落在高屋和大树上。”然后，他才解释理由：“因此，十分明白，他喜欢把灾难降落在那些自高自大的东西身上。”

你是否会认为——现在你已经懂得了闪电总要打在高大树木的真正原因——比2300年前的阿塔班尼斯对国王有关军事上的忠告更加明智？不要自高自大，你做起来只会比他更缺乏诗意。

我们将仅仅关心表面张力τ在整张膜中为常数的那一种情况。于是可以将式（12.17）写成

▽²u=-f/τ （12.18）

这样就有另一个与静电学相同的方程了——只是这回限制在二维上。位移u对应Φ，而f/τ对应于ρ/ε_0。所以无论是对于无限大的平面带电板、或两平行长导线、或带电的圆筒形导体，我们所做过的一切工作，均可直接应用到一张绷紧的薄膜上。

假设我们在膜的某些点上将膜推到一定高度——也就是说，在某些点上把u值固定下来，这就是在电的情况下，在各对应地方有一个特定势的一种模拟。因此，比如我们可以用一个与筒形导体对应的截面形状的物体把膜推上去，因而形成一个正“势”。例如，若我们用一根圆棒把膜推上去，该表面便将如图12-6所示的形状。高度与一带电圆棒的静电势Φ相同。它是按ln（1/r）下降的（其斜率，对应于电场E，将按1下降）。

一张绷紧的橡胶薄层，往往用来作为一种从实验上解决复杂的电学问题的途径。这里，模拟是倒过来用了！各种不同的棒和杆被用来把膜推至对应于一组电极的势的高度。此后，对高度的测量就能给出在电情况下的电势。这一种模拟甚至被发展得更远。如果将一些小球放在膜上面，它们的运动会近似地对应于电子在相应电场中的运动。人们能够实际上观看到“电子”在其轨道上运动。这一方法曾被用来对许多光电倍增管（诸如那些用在闪烁计数器上的，以及那些用于控制卡迪拉克牌汽车的车前灯光的）的复杂几何图形进行设计。这一方法目前仍被采用，但其准确度却是有限的。对于最准确的工作，更好的是通过数值计算法，即利用大型电子计算机把场求出来。

书籍介绍

《费恩曼物理学讲义》(第2卷)讲述当时美国大学物理教学改革试图解决的一个主要问题是基础物理教学应尽可能反映近代物理的巨大成就。《费恩曼物理学讲义》在基础物理的水平上对20世纪物理学的两大重要成就——相对论和量子力学——作了系统的介绍，对于量子力学，费恩曼教授还特地准备了一套适合大学二年级水平的讲法。教学改革试图解决的另一个问题是按照当前物理学工作者在各个前沿研究领域所使用的方式来介绍物理学的内容。在《费恩曼物理学讲义》一书中对一些问题的分析和处理方法反映了费恩曼自己以及其他在前沿研究领域工作的物理学家所通常采用的分析和处理方法。全书对基本概念、定理和定律的讲解不仅生动清晰，通俗易懂，而且特别注重从物理上作出深刻的叙述。为了扩大学生的知识面，全书还列举了许多基本物理原理在各个方面(诸如天体物理、地球物理、生物物理等)的应用，以及物理学的一些最新成就。由于全书是根据课堂讲授的录音整理编辑的，它在一定程度保留了费恩曼讲课的生动活泼、引人入胜的独特风格。《费恩曼物理学讲义》从普通物理水平出发，注重物理分析，深入浅出，避免运用高深烦琐的数学方程，因此具有高中以上物理水平和初等微积分知识的读者阅读起来不会感到十分困难。至于大学物理系的师生物理工作者更能从此书中获得教益。1989年，为纪念费恩曼逝世一周年，原书编者重新出版本书，并增加了介绍费恩曼生平的短文和新的序言。我们按照新版的原本进行了翻译。