出版社: McGrawHill Science/Engineering/Math
副标题: Berkeley Physics Course Vol.2
出版年: 19840801
页数: 484
定价: 205.2
装帧: Hardcover
丛书: Berkeley physics course
ISBN: 9780070049086
内容简介 · · · · · ·
The sequence of topics covered include: electrostatics; steady currents; magnetic field; electromagnetic induction; and electric and magnetic polarization in matter. Taking a nontraditional approach, students focus on fundamental questions from different frames of reference. Each chapter has figures and problems to apply concepts studied.
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Cynosure (作业大魔王副手)
高斯单位制(CGS)的意义： This MKS system is convenient in engineering. For a treatment of the fundamental physics of fields and matter, it has one basic defect. Thus the MKS system, as it has been constructed, tends to obscure either the fundamental electromagnetic symmetry of the vacuum, or the essential asymmetry of the sources. That was one of our reasons for preferring the Gaussian CGS sy...20161014 23:05
高斯单位制(CGS)的意义：This MKS system is convenient in engineering. For a treatment of thefundamental physics of fields and matter, it has one basic defect.Thus the MKS system, as it has been constructed,tends to obscure either the fundamental electromagnetic symmetry of thevacuum, or the essential asymmetry of the sources. That was one of ourreasons for preferring the Gaussian CGS system in this book.Ch 1We try to treat carefully a question that is some times avoided and sometimes beclouded in introductory texts, the meaning o f the macroscopic fields E and B inside a material.。”电荷不变“源自经验，目前为止无实验违反之。the total electric charge o f an isolated system is a relativistically invariant number.。On present ideas, the electron and the proton are about as unlikeas two elementary particles can be. N o one yet understands whytheir charges should have to be equal to such a fantastically precisedegree. Evidently the quantization o f charge is a deep and universallaw o f nature. The fact of charge quantization lies outside the scope o f classicalelectromagnetism , o f course. Still, it is worth remembering that classicaltheory cannot be expected to explain the structure o f the elementaryparticles. (It is not certain that present quantum theory can either!)W hat holds the electron together is as mysterious as what fixes theprecise value o f its charge. Something m ore than electrical forcesmust be involved, for the electrostatic forces between different partso f the electron would be repulsive.。Coulomb’s law：10^13 cm to many kilometers。保守力做功与路径无关，因为保守力是central force。electrical potential energy of this paticular system： U=∑_{i!=j} qiqj/rij = 1/2∑_{i=1>N} (∑_{j!=i} qiqj/rij )。E=lim_{q0>0} F/q0, 批评E的这种定义，因为现实中q0不可能小于e。。Gauss’s law and Coulomb’s law are not two independent physicallaws, but the same law expressed in different ways。Gauss law is applicable to any inversesquare field in physics,。P33 problem 1.20 很有趣。CH 2potential function φ=∫_{P1>P2}E>*dspotential energy Ufield function is in the derivative of the potential function φ: E> =  ∇φsingle point charge: E> = q/r。φ(x, y,z) = ∫_{all sources} ρ(x', y', z') dx'dy'dz' / r, r=sqrt((xx')^2+(yy')^2+(zz')^2)。As we should expect, at a considerable distance from the disk (relative to its diameter), it doesn’t matter much how the charge is shaped;only the total charge matters, in first approximation.。圆盘边沿的电势：we see that, as we should expect, the potential, falls off from the centerto the edge of the disk. The electric field, therefore, must have anoutward component in the plane of the disk. T hat is why we remarked earlier that the charge, if free to move, would redistributeitself toward the rim. To put it another way, our uniformly chargeddisk is not a surface o f constant potential, which any conductingsurface must be unless charge is moving.As y approaches zero from the positive side, Ey approaches 2πσ.On the negative y side o f the disk, which we shall call the back, Epoints in the other direction and its y component Ey is 2πσ. Thisis the same as the field o f an infinite sheet o f charge o f density a,derived in Sec. 1.10. It ought to be, for at points close to the centerof the disk, the presence or absence of charge out beyond the rimcan’t make much difference. 【In other words, any sheet looks infiniteif viewed from close up】. Indeed, Ey has the value 2πσ not only at thecenter but all over the disk.。2.8 Energy Associated w ith an Electric FieldU = 1/(8π)∫_{entire space} E^2 dvOur accounting comes out right if we think o f it as stored in space with a density o fE^2/(8π) in ergs/cm 3. There is no harm in this, but in fact we have noway of identifying, quite independently o f anything else, the energystored in a particular cubic centimeter o f space.。potential energy U v.s. electric potential φ: The potential energy U of a stationary system of charges is the work required to assemble it out of its parts, energy which we may think of as stored in the assembled system. It is a single scalar quantity and a property of the system as a whole. The electric potential φ is a function of position in space, for a given distribution of electric charges. It is expressed in units o f ergs per esu, or statvolts. The difference between the values o f φ at two points in space is the work per unit charge required to transport charge from one place to the other. U = 1/(8π)∫_{entire space} ∇φ^2 dv 也可以这样解释U： U=1/2∑_{i=1>N} qj(∑_{j!=i} qi/rij )。其中(∑_{j!=i} qi/rij )≡ φ j表示the potential at qj due to all other charges。所以，U = ½ ∫ρ(x,y,z)φ(x,y,z)dv, 其中φ(x,y,z) is the electric potential for the whole system.。divF> ≡ lim_{Vi>0}1/Vi ∫_{Si}F>*dai>div F is the flux out of Vi, per unit of volume, in the limit of infinitesimal Vi.。Gauss’s theorem (or the Divergence Theorem):∫_S F> da> = ∫_V divF> dv (is meaningful on a macroscopic scale only(P63))。div E = 4πρ (Gauss’s law in differential form) （(P63)前提是the inversesquare law成立, 而the inversesquare law是Coulumb做实验总结出来的“经验定律”）。F>≡(Fx, Fy, Fz), divF>= ∂Fx/∂x +∂Fy/∂y +∂Fz/∂zIf divF> has a positive value at some point, we find—thinking of Fas a velocity field—a net “outflow” in th at neighborhood.。The divergence is a quantity that expresses only one aspect o f the spatial variation o f a vector field.。divE> =  div grad φ = 。Poisson’s equation: Δφ = 4πρ (is meaningful on a macroscopic scale only(P63))Laplace’s Equation: Δφ =0, (解φ被称为harmonic function)。harmonic function的性质之一：If φ(x,y,z) satisfies Laplace’s equation, then the average value o f cp over the surface o f any sphere (not necessarily a small sphere) is equal to the value o f cp at the center o f the sphere.。Stokes’ Theorem: ∫_C F>*ds> = ∫_S curlF>*da>。in the electrostatic field, curl E> around any closed path is zero(因为是保守场)。P76， Problem 2.15, 对 ∇*(∇xF) = 0的直观理解。。∇*(f∇f) = (∇f)^2 + f ΔfCH 3Δφ =0的解的唯一性源自Δ算子的特性Δ表示的是周围点的均值。导体内部电场为零，源自导体外边界是等势面。。the conservation of charge:div J = 0 (timeindependent charge distribution) steady currentdiv J =  ∂ρ/∂t (timedependent charge distribution)。J> = σE> (经验公式)CH 5 这一章非常赞！大开眼界But how do we know that Gauss’s law holds when charges are moving? Fortunately it does. We can take that as an experimental fact.。There is conclusive experimental evidence that the total charge ina system is not changed by the motion o f the charge carriers.(粗糙的反证见P153 5.4)。The experiments we have described, and many others, show thatthe value o f our Gauss’s law surface integral ∫_S E> da> depends only onthe number and variety o f charged particles inside S, and not on how they are moving.According to the postulate o f relativity, such a statement must be true for any inertial frame o f reference if it is true for one.。charge conservation：div J> =  ∂ρ/∂tthe relativistic invariance of charge: ∫_S(t) E> da> = ∫_S'(t') E'> da'>。P156Energy is conserved, but energy is not a relativistic invariant.Charge is conserved and charge is a relativistic invariant.In the language o f relativity theory, energy is one component o f a fourvector, while charge is a scalar, an invariant number, with respect to the Lorentz transformation. This is an observed fact with farreaching implications. It completely determines the nature of the field of moving charges.。relativity postulates + the relativistic invariance of charge ==>运动的电场产生波，该波的传播速度为光速。(P167）。If charge is to be invariant under a Lorentz transformation, the electric field E has to transform in a particular way.。If the electric field E at a point in spacetime is to have a unique meaning, then the way E appears in other frames of reference cannot depend on the nature of the sources. In other words, the observer in F, having measured the field in his neighborhood at some time, ought to be able to predict from these measurements alone what observers in other frames of reference would measure at the same spacetime point. Were this not true, field would be a useless concept. The evidence that it is true is the eventual agreement of our field theory with experiment.。the force acting on a charged particle in motion through F is q times the electric field E inthat frame, strictly independent o f the velocity o f the particle. F=qE，在任意惯性系下 电荷在电场中的受力F与电荷的运动速度无关(这是电荷不变的结果) 推导过程在Section 5.8。It is a remarkable fact that the force on the moving test chargedoes not depend separately on the velocity or density o f the chargecarriers in the wire, but only on the combination that determines thenet charge transport.。If we had to analyze every system of moving charges by transforming back and forth among various coordinate systems, our task would grow both tedious and confusing. There is a better way. The overall effect of one current on another, or o f a current on a moving charge,can be described completely and concisely by introducing a new field, the magnetic field.。CH 6Inother words, if two quite different systems o f moving charges happento produce the same E and B at a particular point, the behavior o fany test particle at the point w ould be exactly the same in the twosystems. It is for this reason only that the concept o f field, as an interm ediary in the interaction o f particles, is useful. And it is for thisreason that we think o f the field as an independent entityIs the field more, or less, real than the particles whose interaction,as seen from our present point of view, it was invented to describe?T hat is a deep question which we would do well to set aside for a longtime. People to whom the electric and magnetic fields were vividlyreal—Faraday and Maxwell, to name two—were led thereby to newinsights and great discoveries. Let’s view the magnetic field as concretely as they did and learn some of its properties.electromagnetic field: (Ex, Ey, Ez, Bx, By, Bz) tensorCH 7It is a remarkable fact that for any two circuits mutual inductance, M12=M21 (证明见P249，本质上是由双重积分导致的)electromotive force: Ƹ = 1/c * dΦ/dtƸ21 = M21 * dI1/dt (M21: mutual inductance)Ƹ11 = L1 * dI1/dt (L1: selfinductance)Maxwell's Equations:div B> = 0div E> = 4πρcurl B> = 4π/c J> + 1/c * ∂E>/∂t (div J> =  ∂ρ/∂t)curl E> =  1/c * ∂B>/∂tMaxwell’s Equations in empty space(ρ=0 and J>=0):div B> = 0div E> = 0curl B> = 1/c * ∂E>/∂t curl E> =  1/c * ∂B>/∂tDisplacement Current J>_d ≡ 1/(4π) * ∂E>/∂t (比如圆盘电容充放电时两极的E，会形成divE>!=0)>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>给定函数f(x)=0之后，利用求导法则可以得出新的关系式f'(x) = 0。同样，施加div，curl算子后能得到更多的关系式：div(f) = 0; curl(f)=0; div(curl(f))≡0;这应该算是向量分析里的一个技巧吧。<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<In em pty space, the term s with ρ and J arezero, and Maxwell’s equations become：E ^2B^2 and E>*B> remain invariant in a transformation to another inertial frameIn this case, since E = Bat any point, the invariant quantity E^2B^2 has the value zero. Also,because E is perpendicular to B, the other invariant E>*B> is zero. Itfollows that in any other frame the transform ed fields E' and B' mustbe equal to each other in magnitude and perpendicular in direction.A light wave looks like a light wave in any frame of reference.Ch 8In fact, we have now reduced the ac network problem to the dc network problem , with only this difference: the numbers we deal with are complex numbers.CH 9dipole moment> = charge * displacement>the moments o f the charge distribution：K0: the net charge, the monopole moment, or monopole strengthK1:dipole moment>.zK2: quadrupole moment of the distributionThe advantage to us o f describing a charge distribution by thishierarchy o f m om ents is that it singles out just those features o f thecharge distribution which determ ine the field at a great distance. Ifwe were concerned only w ith the field in the im m ediate neighborhoodo f the distribution, it w ould be a fruitless exercise. F o r our m ain task,understanding w hat goes on in a dielectric, it turns out th at only them onopole strength (the net charge) and the dipole strength o f them olecular building blocks m atter. We can ignore all other m om ents.CH 10 The world around us appears totally asymmetrical in the sense that we find no magneticcharges at all.There has been seriousspeculation, however, that pairs o f poles, like pairs of elementaryparticles, might be created and fly apart in very energetic nuclearevents. Several recent searches for such particles, termed magnetic monopoles, have detected none. Whether they cannot exist, and if so why not, remains an open question.We are forced to conclude that the only sources of the magneticfield are electric currents. This takes us back to the hypothesis ofAmpere, his idea that magnetism in matter is to be accounted for bya multitude o f tiny rings o f electric current distributed through thesubstance.the magnetic dipole moment: m> = I a>/cthe field o f a magnetic dipole: A> = m> cross r>/r^2It turns out that the lines o f H inside them agnet look ju st like the lines o f E inside the polarized cylinder o fFig. 10.21a. T hat is as it should be, for if magnetic poles really werethe source o f the m agnetization, rather than electric currents, them acroscopic m agnetic field inside the m aterial would be H , not B,and the sim ilarity o f m agnetic polarization to electric polarizationwould be complete.Auxiliary field H v.s. Magnetic field B¹²³⁴⁵⁶⁷⁸⁹ ᵃᵇᵈᵉᶠᵍʰⁱʲᵏˡᵐⁿᵒᵖ ʳˢᵗᵘᵛʷˣʸᶻ ᵅᵝᵞᵟᵠ ₀₁₂₃₄₅₆₇₈₉ ₐ ₑ ₕᵢⱼₖₗₘₙₒₚ ᵣₛₜᵤᵥ ₓ ᵦº¹²³⁴ⁿ₁₂₃₄·∶αβγδεζηθ ικ λ μ νξοπρστυφχψω ∽ ⊥ ∠ ⊙ ⊕ ⊗∈∩∪∑∫∞≡≠±≈＄㏒㎡㎥㎎㎏㎜ΑΒΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣΤΥΦΧΨΩ∈⊂∂Δ∇∀∃e̅Ζ͏͏͏͏͏͏ Z̅▹◃ ∧†┘˩⌋⎦┙┚┛回应 20161014 23:05

Cynosure (作业大魔王副手)
高斯单位制(CGS)的意义： This MKS system is convenient in engineering. For a treatment of the fundamental physics of fields and matter, it has one basic defect. Thus the MKS system, as it has been constructed, tends to obscure either the fundamental electromagnetic symmetry of the vacuum, or the essential asymmetry of the sources. That was one of our reasons for preferring the Gaussian CGS sy...20161014 23:05
高斯单位制(CGS)的意义：This MKS system is convenient in engineering. For a treatment of thefundamental physics of fields and matter, it has one basic defect.Thus the MKS system, as it has been constructed,tends to obscure either the fundamental electromagnetic symmetry of thevacuum, or the essential asymmetry of the sources. That was one of ourreasons for preferring the Gaussian CGS system in this book.Ch 1We try to treat carefully a question that is some times avoided and sometimes beclouded in introductory texts, the meaning o f the macroscopic fields E and B inside a material.。”电荷不变“源自经验，目前为止无实验违反之。the total electric charge o f an isolated system is a relativistically invariant number.。On present ideas, the electron and the proton are about as unlikeas two elementary particles can be. N o one yet understands whytheir charges should have to be equal to such a fantastically precisedegree. Evidently the quantization o f charge is a deep and universallaw o f nature. The fact of charge quantization lies outside the scope o f classicalelectromagnetism , o f course. Still, it is worth remembering that classicaltheory cannot be expected to explain the structure o f the elementaryparticles. (It is not certain that present quantum theory can either!)W hat holds the electron together is as mysterious as what fixes theprecise value o f its charge. Something m ore than electrical forcesmust be involved, for the electrostatic forces between different partso f the electron would be repulsive.。Coulomb’s law：10^13 cm to many kilometers。保守力做功与路径无关，因为保守力是central force。electrical potential energy of this paticular system： U=∑_{i!=j} qiqj/rij = 1/2∑_{i=1>N} (∑_{j!=i} qiqj/rij )。E=lim_{q0>0} F/q0, 批评E的这种定义，因为现实中q0不可能小于e。。Gauss’s law and Coulomb’s law are not two independent physicallaws, but the same law expressed in different ways。Gauss law is applicable to any inversesquare field in physics,。P33 problem 1.20 很有趣。CH 2potential function φ=∫_{P1>P2}E>*dspotential energy Ufield function is in the derivative of the potential function φ: E> =  ∇φsingle point charge: E> = q/r。φ(x, y,z) = ∫_{all sources} ρ(x', y', z') dx'dy'dz' / r, r=sqrt((xx')^2+(yy')^2+(zz')^2)。As we should expect, at a considerable distance from the disk (relative to its diameter), it doesn’t matter much how the charge is shaped;only the total charge matters, in first approximation.。圆盘边沿的电势：we see that, as we should expect, the potential, falls off from the centerto the edge of the disk. The electric field, therefore, must have anoutward component in the plane of the disk. T hat is why we remarked earlier that the charge, if free to move, would redistributeitself toward the rim. To put it another way, our uniformly chargeddisk is not a surface o f constant potential, which any conductingsurface must be unless charge is moving.As y approaches zero from the positive side, Ey approaches 2πσ.On the negative y side o f the disk, which we shall call the back, Epoints in the other direction and its y component Ey is 2πσ. Thisis the same as the field o f an infinite sheet o f charge o f density a,derived in Sec. 1.10. It ought to be, for at points close to the centerof the disk, the presence or absence of charge out beyond the rimcan’t make much difference. 【In other words, any sheet looks infiniteif viewed from close up】. Indeed, Ey has the value 2πσ not only at thecenter but all over the disk.。2.8 Energy Associated w ith an Electric FieldU = 1/(8π)∫_{entire space} E^2 dvOur accounting comes out right if we think o f it as stored in space with a density o fE^2/(8π) in ergs/cm 3. There is no harm in this, but in fact we have noway of identifying, quite independently o f anything else, the energystored in a particular cubic centimeter o f space.。potential energy U v.s. electric potential φ: The potential energy U of a stationary system of charges is the work required to assemble it out of its parts, energy which we may think of as stored in the assembled system. It is a single scalar quantity and a property of the system as a whole. The electric potential φ is a function of position in space, for a given distribution of electric charges. It is expressed in units o f ergs per esu, or statvolts. The difference between the values o f φ at two points in space is the work per unit charge required to transport charge from one place to the other. U = 1/(8π)∫_{entire space} ∇φ^2 dv 也可以这样解释U： U=1/2∑_{i=1>N} qj(∑_{j!=i} qi/rij )。其中(∑_{j!=i} qi/rij )≡ φ j表示the potential at qj due to all other charges。所以，U = ½ ∫ρ(x,y,z)φ(x,y,z)dv, 其中φ(x,y,z) is the electric potential for the whole system.。divF> ≡ lim_{Vi>0}1/Vi ∫_{Si}F>*dai>div F is the flux out of Vi, per unit of volume, in the limit of infinitesimal Vi.。Gauss’s theorem (or the Divergence Theorem):∫_S F> da> = ∫_V divF> dv (is meaningful on a macroscopic scale only(P63))。div E = 4πρ (Gauss’s law in differential form) （(P63)前提是the inversesquare law成立, 而the inversesquare law是Coulumb做实验总结出来的“经验定律”）。F>≡(Fx, Fy, Fz), divF>= ∂Fx/∂x +∂Fy/∂y +∂Fz/∂zIf divF> has a positive value at some point, we find—thinking of Fas a velocity field—a net “outflow” in th at neighborhood.。The divergence is a quantity that expresses only one aspect o f the spatial variation o f a vector field.。divE> =  div grad φ = 。Poisson’s equation: Δφ = 4πρ (is meaningful on a macroscopic scale only(P63))Laplace’s Equation: Δφ =0, (解φ被称为harmonic function)。harmonic function的性质之一：If φ(x,y,z) satisfies Laplace’s equation, then the average value o f cp over the surface o f any sphere (not necessarily a small sphere) is equal to the value o f cp at the center o f the sphere.。Stokes’ Theorem: ∫_C F>*ds> = ∫_S curlF>*da>。in the electrostatic field, curl E> around any closed path is zero(因为是保守场)。P76， Problem 2.15, 对 ∇*(∇xF) = 0的直观理解。。∇*(f∇f) = (∇f)^2 + f ΔfCH 3Δφ =0的解的唯一性源自Δ算子的特性Δ表示的是周围点的均值。导体内部电场为零，源自导体外边界是等势面。。the conservation of charge:div J = 0 (timeindependent charge distribution) steady currentdiv J =  ∂ρ/∂t (timedependent charge distribution)。J> = σE> (经验公式)CH 5 这一章非常赞！大开眼界But how do we know that Gauss’s law holds when charges are moving? Fortunately it does. We can take that as an experimental fact.。There is conclusive experimental evidence that the total charge ina system is not changed by the motion o f the charge carriers.(粗糙的反证见P153 5.4)。The experiments we have described, and many others, show thatthe value o f our Gauss’s law surface integral ∫_S E> da> depends only onthe number and variety o f charged particles inside S, and not on how they are moving.According to the postulate o f relativity, such a statement must be true for any inertial frame o f reference if it is true for one.。charge conservation：div J> =  ∂ρ/∂tthe relativistic invariance of charge: ∫_S(t) E> da> = ∫_S'(t') E'> da'>。P156Energy is conserved, but energy is not a relativistic invariant.Charge is conserved and charge is a relativistic invariant.In the language o f relativity theory, energy is one component o f a fourvector, while charge is a scalar, an invariant number, with respect to the Lorentz transformation. This is an observed fact with farreaching implications. It completely determines the nature of the field of moving charges.。relativity postulates + the relativistic invariance of charge ==>运动的电场产生波，该波的传播速度为光速。(P167）。If charge is to be invariant under a Lorentz transformation, the electric field E has to transform in a particular way.。If the electric field E at a point in spacetime is to have a unique meaning, then the way E appears in other frames of reference cannot depend on the nature of the sources. In other words, the observer in F, having measured the field in his neighborhood at some time, ought to be able to predict from these measurements alone what observers in other frames of reference would measure at the same spacetime point. Were this not true, field would be a useless concept. The evidence that it is true is the eventual agreement of our field theory with experiment.。the force acting on a charged particle in motion through F is q times the electric field E inthat frame, strictly independent o f the velocity o f the particle. F=qE，在任意惯性系下 电荷在电场中的受力F与电荷的运动速度无关(这是电荷不变的结果) 推导过程在Section 5.8。It is a remarkable fact that the force on the moving test chargedoes not depend separately on the velocity or density o f the chargecarriers in the wire, but only on the combination that determines thenet charge transport.。If we had to analyze every system of moving charges by transforming back and forth among various coordinate systems, our task would grow both tedious and confusing. There is a better way. The overall effect of one current on another, or o f a current on a moving charge,can be described completely and concisely by introducing a new field, the magnetic field.。CH 6Inother words, if two quite different systems o f moving charges happento produce the same E and B at a particular point, the behavior o fany test particle at the point w ould be exactly the same in the twosystems. It is for this reason only that the concept o f field, as an interm ediary in the interaction o f particles, is useful. And it is for thisreason that we think o f the field as an independent entityIs the field more, or less, real than the particles whose interaction,as seen from our present point of view, it was invented to describe?T hat is a deep question which we would do well to set aside for a longtime. People to whom the electric and magnetic fields were vividlyreal—Faraday and Maxwell, to name two—were led thereby to newinsights and great discoveries. Let’s view the magnetic field as concretely as they did and learn some of its properties.electromagnetic field: (Ex, Ey, Ez, Bx, By, Bz) tensorCH 7It is a remarkable fact that for any two circuits mutual inductance, M12=M21 (证明见P249，本质上是由双重积分导致的)electromotive force: Ƹ = 1/c * dΦ/dtƸ21 = M21 * dI1/dt (M21: mutual inductance)Ƹ11 = L1 * dI1/dt (L1: selfinductance)Maxwell's Equations:div B> = 0div E> = 4πρcurl B> = 4π/c J> + 1/c * ∂E>/∂t (div J> =  ∂ρ/∂t)curl E> =  1/c * ∂B>/∂tMaxwell’s Equations in empty space(ρ=0 and J>=0):div B> = 0div E> = 0curl B> = 1/c * ∂E>/∂t curl E> =  1/c * ∂B>/∂tDisplacement Current J>_d ≡ 1/(4π) * ∂E>/∂t (比如圆盘电容充放电时两极的E，会形成divE>!=0)>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>给定函数f(x)=0之后，利用求导法则可以得出新的关系式f'(x) = 0。同样，施加div，curl算子后能得到更多的关系式：div(f) = 0; curl(f)=0; div(curl(f))≡0;这应该算是向量分析里的一个技巧吧。<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<In em pty space, the term s with ρ and J arezero, and Maxwell’s equations become：E ^2B^2 and E>*B> remain invariant in a transformation to another inertial frameIn this case, since E = Bat any point, the invariant quantity E^2B^2 has the value zero. Also,because E is perpendicular to B, the other invariant E>*B> is zero. Itfollows that in any other frame the transform ed fields E' and B' mustbe equal to each other in magnitude and perpendicular in direction.A light wave looks like a light wave in any frame of reference.Ch 8In fact, we have now reduced the ac network problem to the dc network problem , with only this difference: the numbers we deal with are complex numbers.CH 9dipole moment> = charge * displacement>the moments o f the charge distribution：K0: the net charge, the monopole moment, or monopole strengthK1:dipole moment>.zK2: quadrupole moment of the distributionThe advantage to us o f describing a charge distribution by thishierarchy o f m om ents is that it singles out just those features o f thecharge distribution which determ ine the field at a great distance. Ifwe were concerned only w ith the field in the im m ediate neighborhoodo f the distribution, it w ould be a fruitless exercise. F o r our m ain task,understanding w hat goes on in a dielectric, it turns out th at only them onopole strength (the net charge) and the dipole strength o f them olecular building blocks m atter. We can ignore all other m om ents.CH 10 The world around us appears totally asymmetrical in the sense that we find no magneticcharges at all.There has been seriousspeculation, however, that pairs o f poles, like pairs of elementaryparticles, might be created and fly apart in very energetic nuclearevents. Several recent searches for such particles, termed magnetic monopoles, have detected none. Whether they cannot exist, and if so why not, remains an open question.We are forced to conclude that the only sources of the magneticfield are electric currents. This takes us back to the hypothesis ofAmpere, his idea that magnetism in matter is to be accounted for bya multitude o f tiny rings o f electric current distributed through thesubstance.the magnetic dipole moment: m> = I a>/cthe field o f a magnetic dipole: A> = m> cross r>/r^2It turns out that the lines o f H inside them agnet look ju st like the lines o f E inside the polarized cylinder o fFig. 10.21a. T hat is as it should be, for if magnetic poles really werethe source o f the m agnetization, rather than electric currents, them acroscopic m agnetic field inside the m aterial would be H , not B,and the sim ilarity o f m agnetic polarization to electric polarizationwould be complete.Auxiliary field H v.s. Magnetic field B¹²³⁴⁵⁶⁷⁸⁹ ᵃᵇᵈᵉᶠᵍʰⁱʲᵏˡᵐⁿᵒᵖ ʳˢᵗᵘᵛʷˣʸᶻ ᵅᵝᵞᵟᵠ ₀₁₂₃₄₅₆₇₈₉ ₐ ₑ ₕᵢⱼₖₗₘₙₒₚ ᵣₛₜᵤᵥ ₓ ᵦº¹²³⁴ⁿ₁₂₃₄·∶αβγδεζηθ ικ λ μ νξοπρστυφχψω ∽ ⊥ ∠ ⊙ ⊕ ⊗∈∩∪∑∫∞≡≠±≈＄㏒㎡㎥㎎㎏㎜ΑΒΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣΤΥΦΧΨΩ∈⊂∂Δ∇∀∃e̅Ζ͏͏͏͏͏͏ Z̅▹◃ ∧†┘˩⌋⎦┙┚┛回应 20161014 23:05

Cynosure (作业大魔王副手)
高斯单位制(CGS)的意义： This MKS system is convenient in engineering. For a treatment of the fundamental physics of fields and matter, it has one basic defect. Thus the MKS system, as it has been constructed, tends to obscure either the fundamental electromagnetic symmetry of the vacuum, or the essential asymmetry of the sources. That was one of our reasons for preferring the Gaussian CGS sy...20161014 23:05
高斯单位制(CGS)的意义：This MKS system is convenient in engineering. For a treatment of thefundamental physics of fields and matter, it has one basic defect.Thus the MKS system, as it has been constructed,tends to obscure either the fundamental electromagnetic symmetry of thevacuum, or the essential asymmetry of the sources. That was one of ourreasons for preferring the Gaussian CGS system in this book.Ch 1We try to treat carefully a question that is some times avoided and sometimes beclouded in introductory texts, the meaning o f the macroscopic fields E and B inside a material.。”电荷不变“源自经验，目前为止无实验违反之。the total electric charge o f an isolated system is a relativistically invariant number.。On present ideas, the electron and the proton are about as unlikeas two elementary particles can be. N o one yet understands whytheir charges should have to be equal to such a fantastically precisedegree. Evidently the quantization o f charge is a deep and universallaw o f nature. The fact of charge quantization lies outside the scope o f classicalelectromagnetism , o f course. Still, it is worth remembering that classicaltheory cannot be expected to explain the structure o f the elementaryparticles. (It is not certain that present quantum theory can either!)W hat holds the electron together is as mysterious as what fixes theprecise value o f its charge. Something m ore than electrical forcesmust be involved, for the electrostatic forces between different partso f the electron would be repulsive.。Coulomb’s law：10^13 cm to many kilometers。保守力做功与路径无关，因为保守力是central force。electrical potential energy of this paticular system： U=∑_{i!=j} qiqj/rij = 1/2∑_{i=1>N} (∑_{j!=i} qiqj/rij )。E=lim_{q0>0} F/q0, 批评E的这种定义，因为现实中q0不可能小于e。。Gauss’s law and Coulomb’s law are not two independent physicallaws, but the same law expressed in different ways。Gauss law is applicable to any inversesquare field in physics,。P33 problem 1.20 很有趣。CH 2potential function φ=∫_{P1>P2}E>*dspotential energy Ufield function is in the derivative of the potential function φ: E> =  ∇φsingle point charge: E> = q/r。φ(x, y,z) = ∫_{all sources} ρ(x', y', z') dx'dy'dz' / r, r=sqrt((xx')^2+(yy')^2+(zz')^2)。As we should expect, at a considerable distance from the disk (relative to its diameter), it doesn’t matter much how the charge is shaped;only the total charge matters, in first approximation.。圆盘边沿的电势：we see that, as we should expect, the potential, falls off from the centerto the edge of the disk. The electric field, therefore, must have anoutward component in the plane of the disk. T hat is why we remarked earlier that the charge, if free to move, would redistributeitself toward the rim. To put it another way, our uniformly chargeddisk is not a surface o f constant potential, which any conductingsurface must be unless charge is moving.As y approaches zero from the positive side, Ey approaches 2πσ.On the negative y side o f the disk, which we shall call the back, Epoints in the other direction and its y component Ey is 2πσ. Thisis the same as the field o f an infinite sheet o f charge o f density a,derived in Sec. 1.10. It ought to be, for at points close to the centerof the disk, the presence or absence of charge out beyond the rimcan’t make much difference. 【In other words, any sheet looks infiniteif viewed from close up】. Indeed, Ey has the value 2πσ not only at thecenter but all over the disk.。2.8 Energy Associated w ith an Electric FieldU = 1/(8π)∫_{entire space} E^2 dvOur accounting comes out right if we think o f it as stored in space with a density o fE^2/(8π) in ergs/cm 3. There is no harm in this, but in fact we have noway of identifying, quite independently o f anything else, the energystored in a particular cubic centimeter o f space.。potential energy U v.s. electric potential φ: The potential energy U of a stationary system of charges is the work required to assemble it out of its parts, energy which we may think of as stored in the assembled system. It is a single scalar quantity and a property of the system as a whole. The electric potential φ is a function of position in space, for a given distribution of electric charges. It is expressed in units o f ergs per esu, or statvolts. The difference between the values o f φ at two points in space is the work per unit charge required to transport charge from one place to the other. U = 1/(8π)∫_{entire space} ∇φ^2 dv 也可以这样解释U： U=1/2∑_{i=1>N} qj(∑_{j!=i} qi/rij )。其中(∑_{j!=i} qi/rij )≡ φ j表示the potential at qj due to all other charges。所以，U = ½ ∫ρ(x,y,z)φ(x,y,z)dv, 其中φ(x,y,z) is the electric potential for the whole system.。divF> ≡ lim_{Vi>0}1/Vi ∫_{Si}F>*dai>div F is the flux out of Vi, per unit of volume, in the limit of infinitesimal Vi.。Gauss’s theorem (or the Divergence Theorem):∫_S F> da> = ∫_V divF> dv (is meaningful on a macroscopic scale only(P63))。div E = 4πρ (Gauss’s law in differential form) （(P63)前提是the inversesquare law成立, 而the inversesquare law是Coulumb做实验总结出来的“经验定律”）。F>≡(Fx, Fy, Fz), divF>= ∂Fx/∂x +∂Fy/∂y +∂Fz/∂zIf divF> has a positive value at some point, we find—thinking of Fas a velocity field—a net “outflow” in th at neighborhood.。The divergence is a quantity that expresses only one aspect o f the spatial variation o f a vector field.。divE> =  div grad φ = 。Poisson’s equation: Δφ = 4πρ (is meaningful on a macroscopic scale only(P63))Laplace’s Equation: Δφ =0, (解φ被称为harmonic function)。harmonic function的性质之一：If φ(x,y,z) satisfies Laplace’s equation, then the average value o f cp over the surface o f any sphere (not necessarily a small sphere) is equal to the value o f cp at the center o f the sphere.。Stokes’ Theorem: ∫_C F>*ds> = ∫_S curlF>*da>。in the electrostatic field, curl E> around any closed path is zero(因为是保守场)。P76， Problem 2.15, 对 ∇*(∇xF) = 0的直观理解。。∇*(f∇f) = (∇f)^2 + f ΔfCH 3Δφ =0的解的唯一性源自Δ算子的特性Δ表示的是周围点的均值。导体内部电场为零，源自导体外边界是等势面。。the conservation of charge:div J = 0 (timeindependent charge distribution) steady currentdiv J =  ∂ρ/∂t (timedependent charge distribution)。J> = σE> (经验公式)CH 5 这一章非常赞！大开眼界But how do we know that Gauss’s law holds when charges are moving? Fortunately it does. We can take that as an experimental fact.。There is conclusive experimental evidence that the total charge ina system is not changed by the motion o f the charge carriers.(粗糙的反证见P153 5.4)。The experiments we have described, and many others, show thatthe value o f our Gauss’s law surface integral ∫_S E> da> depends only onthe number and variety o f charged particles inside S, and not on how they are moving.According to the postulate o f relativity, such a statement must be true for any inertial frame o f reference if it is true for one.。charge conservation：div J> =  ∂ρ/∂tthe relativistic invariance of charge: ∫_S(t) E> da> = ∫_S'(t') E'> da'>。P156Energy is conserved, but energy is not a relativistic invariant.Charge is conserved and charge is a relativistic invariant.In the language o f relativity theory, energy is one component o f a fourvector, while charge is a scalar, an invariant number, with respect to the Lorentz transformation. This is an observed fact with farreaching implications. It completely determines the nature of the field of moving charges.。relativity postulates + the relativistic invariance of charge ==>运动的电场产生波，该波的传播速度为光速。(P167）。If charge is to be invariant under a Lorentz transformation, the electric field E has to transform in a particular way.。If the electric field E at a point in spacetime is to have a unique meaning, then the way E appears in other frames of reference cannot depend on the nature of the sources. In other words, the observer in F, having measured the field in his neighborhood at some time, ought to be able to predict from these measurements alone what observers in other frames of reference would measure at the same spacetime point. Were this not true, field would be a useless concept. The evidence that it is true is the eventual agreement of our field theory with experiment.。the force acting on a charged particle in motion through F is q times the electric field E inthat frame, strictly independent o f the velocity o f the particle. F=qE，在任意惯性系下 电荷在电场中的受力F与电荷的运动速度无关(这是电荷不变的结果) 推导过程在Section 5.8。It is a remarkable fact that the force on the moving test chargedoes not depend separately on the velocity or density o f the chargecarriers in the wire, but only on the combination that determines thenet charge transport.。If we had to analyze every system of moving charges by transforming back and forth among various coordinate systems, our task would grow both tedious and confusing. There is a better way. The overall effect of one current on another, or o f a current on a moving charge,can be described completely and concisely by introducing a new field, the magnetic field.。CH 6Inother words, if two quite different systems o f moving charges happento produce the same E and B at a particular point, the behavior o fany test particle at the point w ould be exactly the same in the twosystems. It is for this reason only that the concept o f field, as an interm ediary in the interaction o f particles, is useful. And it is for thisreason that we think o f the field as an independent entityIs the field more, or less, real than the particles whose interaction,as seen from our present point of view, it was invented to describe?T hat is a deep question which we would do well to set aside for a longtime. People to whom the electric and magnetic fields were vividlyreal—Faraday and Maxwell, to name two—were led thereby to newinsights and great discoveries. Let’s view the magnetic field as concretely as they did and learn some of its properties.electromagnetic field: (Ex, Ey, Ez, Bx, By, Bz) tensorCH 7It is a remarkable fact that for any two circuits mutual inductance, M12=M21 (证明见P249，本质上是由双重积分导致的)electromotive force: Ƹ = 1/c * dΦ/dtƸ21 = M21 * dI1/dt (M21: mutual inductance)Ƹ11 = L1 * dI1/dt (L1: selfinductance)Maxwell's Equations:div B> = 0div E> = 4πρcurl B> = 4π/c J> + 1/c * ∂E>/∂t (div J> =  ∂ρ/∂t)curl E> =  1/c * ∂B>/∂tMaxwell’s Equations in empty space(ρ=0 and J>=0):div B> = 0div E> = 0curl B> = 1/c * ∂E>/∂t curl E> =  1/c * ∂B>/∂tDisplacement Current J>_d ≡ 1/(4π) * ∂E>/∂t (比如圆盘电容充放电时两极的E，会形成divE>!=0)>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>给定函数f(x)=0之后，利用求导法则可以得出新的关系式f'(x) = 0。同样，施加div，curl算子后能得到更多的关系式：div(f) = 0; curl(f)=0; div(curl(f))≡0;这应该算是向量分析里的一个技巧吧。<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<In em pty space, the term s with ρ and J arezero, and Maxwell’s equations become：E ^2B^2 and E>*B> remain invariant in a transformation to another inertial frameIn this case, since E = Bat any point, the invariant quantity E^2B^2 has the value zero. Also,because E is perpendicular to B, the other invariant E>*B> is zero. Itfollows that in any other frame the transform ed fields E' and B' mustbe equal to each other in magnitude and perpendicular in direction.A light wave looks like a light wave in any frame of reference.Ch 8In fact, we have now reduced the ac network problem to the dc network problem , with only this difference: the numbers we deal with are complex numbers.CH 9dipole moment> = charge * displacement>the moments o f the charge distribution：K0: the net charge, the monopole moment, or monopole strengthK1:dipole moment>.zK2: quadrupole moment of the distributionThe advantage to us o f describing a charge distribution by thishierarchy o f m om ents is that it singles out just those features o f thecharge distribution which determ ine the field at a great distance. Ifwe were concerned only w ith the field in the im m ediate neighborhoodo f the distribution, it w ould be a fruitless exercise. F o r our m ain task,understanding w hat goes on in a dielectric, it turns out th at only them onopole strength (the net charge) and the dipole strength o f them olecular building blocks m atter. We can ignore all other m om ents.CH 10 The world around us appears totally asymmetrical in the sense that we find no magneticcharges at all.There has been seriousspeculation, however, that pairs o f poles, like pairs of elementaryparticles, might be created and fly apart in very energetic nuclearevents. Several recent searches for such particles, termed magnetic monopoles, have detected none. Whether they cannot exist, and if so why not, remains an open question.We are forced to conclude that the only sources of the magneticfield are electric currents. This takes us back to the hypothesis ofAmpere, his idea that magnetism in matter is to be accounted for bya multitude o f tiny rings o f electric current distributed through thesubstance.the magnetic dipole moment: m> = I a>/cthe field o f a magnetic dipole: A> = m> cross r>/r^2It turns out that the lines o f H inside them agnet look ju st like the lines o f E inside the polarized cylinder o fFig. 10.21a. T hat is as it should be, for if magnetic poles really werethe source o f the m agnetization, rather than electric currents, them acroscopic m agnetic field inside the m aterial would be H , not B,and the sim ilarity o f m agnetic polarization to electric polarizationwould be complete.Auxiliary field H v.s. Magnetic field B¹²³⁴⁵⁶⁷⁸⁹ ᵃᵇᵈᵉᶠᵍʰⁱʲᵏˡᵐⁿᵒᵖ ʳˢᵗᵘᵛʷˣʸᶻ ᵅᵝᵞᵟᵠ ₀₁₂₃₄₅₆₇₈₉ ₐ ₑ ₕᵢⱼₖₗₘₙₒₚ ᵣₛₜᵤᵥ ₓ ᵦº¹²³⁴ⁿ₁₂₃₄·∶αβγδεζηθ ικ λ μ νξοπρστυφχψω ∽ ⊥ ∠ ⊙ ⊕ ⊗∈∩∪∑∫∞≡≠±≈＄㏒㎡㎥㎎㎏㎜ΑΒΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣΤΥΦΧΨΩ∈⊂∂Δ∇∀∃e̅Ζ͏͏͏͏͏͏ Z̅▹◃ ∧†┘˩⌋⎦┙┚┛回应 20161014 23:05
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0 有用 Stephen 20070812
电磁学
0 有用 吞噬黑洞 20161027
伯克利物理讲义系列其实不太适合做标准教材，作为辅导倒是非常不错。本书最棒的地方在于论证磁现象是电现象的相对论效应，不足是对介质的讨论浅了些。
0 有用 Nefiya 20141220
in CGS. very good classical EM textbook though.
1 有用 不科学的小明 20151113
伯克利的书都是很经典的~不过这本书好像我的确是读完了
0 有用 andrew 20130626
miscellaneous with simple maths.
0 有用 吞噬黑洞 20161027
伯克利物理讲义系列其实不太适合做标准教材，作为辅导倒是非常不错。本书最棒的地方在于论证磁现象是电现象的相对论效应，不足是对介质的讨论浅了些。
0 有用 令狐折口 20160106
内容和Griffith 的电动力学导论前7章差不多。是普通力学不可多得的好教材。向量微积分也介绍的很不错。
0 有用 Nefiya 20141220
in CGS. very good classical EM textbook though.
1 有用 不科学的小明 20151113
伯克利的书都是很经典的~不过这本书好像我的确是读完了
0 有用 andrew 20130626
miscellaneous with simple maths.