Calculation of the Casimir Force between Similar and Dissimilar Metal Plates at Finite Temp

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海底两万里中物理学的句子

海底两万里中物理学的句子英文回答：Physics plays a significant role in Jules Verne's novel "Twenty Thousand Leagues Under the Sea." As the story follows the adventures of Professor Aronnax, Ned Land, and Conseil aboard the Nautilus, many instances highlight the application of physics principles.One example is the concept of buoyancy. The Nautilus, being a submarine, must maintain neutral buoyancy to navigate underwater. This is achieved by adjusting the amount of water in the ballast tanks. By controlling the density of the Nautilus, Captain Nemo ensures that the upward force exerted by the water equals the downward force of the submarine, allowing it to float at a desired depth. This demonstrates Archimedes' principle, which states that an object immersed in a fluid experiences an upward buoyant force equal to the weight of the fluid it displaces.Another physics concept explored in the novel is pressure. As the Nautilus dives deeper into the ocean, the pressure increases significantly. The characters experience this firsthand when they descend to great depths and feel the pressure on their bodies. This aligns with Pascal's principle, which states that pressure is transmitted uniformly in all directions in a fluid. The immense pressure at great depths is a result of the weight of the water above pressing down on the submarine.Furthermore, the novel touches upon the principles of electricity and magnetism. The Nautilus is powered by electricity, and Verne describes the use of electric motors to propel the submarine through the water. The concept of electromagnetism is also evident in the use of magnetic fields to navigate and detect underwater objects. These applications of physics showcase the integration of scientific knowledge into the fictional world of the Nautilus.中文回答：物理学在朱尔·凡尔纳的小说《海底两万里》中起着重要的作用。

碳墨移动比值英语

碳墨移动比值英语The Ratio of Carbon Ink MovementThe world of printing and writing has undergone a remarkable transformation in recent years, driven by the rapid advancements in technology. One of the most significant developments in this field is the emergence of carbon ink, a versatile and innovative material that has revolutionized the way we approach the printed word. In this essay, we will delve into the intriguing concept of the ratio of carbon ink movement, exploring its implications and the factors that influence this crucial aspect of modern printing and writing.At the heart of the carbon ink movement lies the fundamental principle of efficient ink transfer and distribution. The ratio of carbon ink movement refers to the precise balance between the amount of ink deposited on a surface and the distance it travels across that surface. This ratio is of paramount importance in ensuring consistent and high-quality output, whether it be in the realm of commercial printing, artistic expression, or personal writing.The ratio of carbon ink movement is influenced by a multitude of factors, each playing a crucial role in the overall performance and effectiveness of the printing or writing process. One of the primary determinants is the composition of the carbon ink itself. The precise blend of carbon-based pigments, binders, and solvents can significantly impact the ink's viscosity, surface tension, and drying characteristics, all of which directly affect the way it moves and interacts with the substrate.Another key factor is the surface characteristics of the material being printed or written upon. The porosity, smoothness, and absorbency of the paper, fabric, or other media can greatly influence the way the carbon ink behaves, affecting its ability to spread, penetrate, and adhere to the surface. The interplay between the ink and the substrate is a delicate balance that requires careful consideration and optimization.The ratio of carbon ink movement is also influenced by the printing or writing technology employed. In the realm of commercial printing, advanced digital presses and offset printing machines utilize sophisticated ink delivery systems that precisely control the amount and distribution of carbon ink on the printed page. In the case of handwriting and artistic applications, the choice of writing instrument, the angle and pressure of the pen or brush, and the technique of the user all contribute to the final ratio of inkmovement.Achieving the optimal ratio of carbon ink movement is essential for a variety of reasons. In commercial printing, a well-calibrated ratio ensures consistent color reproduction, sharp text, and vibrant imagery, ultimately enhancing the visual impact and quality of the final product. In the realm of artistic expression, the ratio of carbon ink movement can be manipulated to create unique textures, gradients, and expressive qualities, allowing artists to push the boundaries of their craft.Furthermore, the ratio of carbon ink movement plays a crucial role in the longevity and preservation of printed materials. A well-balanced ratio can help prevent issues such as smearing, bleeding, and fading, ensuring that the printed content remains legible and visually appealing over time. This is particularly important in the preservation of historical documents, archival materials, and fine art prints, where the long-term integrity of the work is of paramount concern.The ongoing research and development in the field of carbon ink technology have led to significant advancements in our understanding of the ratio of carbon ink movement. Scientists and engineers are constantly exploring new formulations, materials, and printing techniques to optimize this crucial aspect of the printing and writing process. From the development of specialized inks withenhanced flow properties to the design of innovative printing mechanisms, the quest for the perfect ratio of carbon ink movement continues to drive innovation in the industry.As we look to the future, the significance of the ratio of carbon ink movement will only continue to grow. With the increasing demand for high-quality, sustainable, and personalized printed materials, the ability to precisely control the movement and distribution of carbon ink will be essential. Furthermore, the integration of digital technologies, such as 3D printing and augmented reality, may introduce new challenges and opportunities in the management of carbon ink ratios, requiring even greater precision and adaptability.In conclusion, the ratio of carbon ink movement is a fundamental concept that underpins the world of printing and writing. By understanding and optimizing this crucial aspect, we can unlock new possibilities in the realm of commercial printing, artistic expression, and personal communication. As technology continues to evolve, the importance of the ratio of carbon ink movement will only become more pronounced, driving further advancements and innovations in this dynamic and ever-changing field.。

库仑法容量法英文

库仑法容量法英文Coulomb's Law and Capacitance: Understanding the Fundamentals of ElectricityElectricity is a fundamental aspect of our modern world, powering our devices, lighting our homes, and enabling the vast interconnected systems that support our daily lives. At the heart of this electrical realm lies the understanding of two crucial concepts: Coulomb's law and capacitance. These principles, rooted in the pioneering work of scientists and physicists, provide the foundation for our comprehension of the behavior and interactions of electric charges.Coulomb's law, named after the French physicist Charles-Augustin de Coulomb, is a fundamental principle that describes the force of interaction between two stationary electric charges. This law states that the force between two point charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them. Mathematically, this relationship can be expressed as F = k(q1 * q2) / r^2, where F is the force, q1 and q2 are the magnitudes of the charges, r is the distance between them, and k is a constant known as the Coulomb constant.This law has far-reaching implications in the world of electricity and electronics. It governs the behavior of charged particles, such as electrons and protons, and helps us understand the interactions between charged objects. For instance, Coulomb's law explains the attraction and repulsion between charged particles, which is crucial in understanding the behavior of electric fields and the movement of electric current.Capacitance, on the other hand, is a measure of the ability of a system to store electric charge. It is a fundamental property of electrical circuits and devices, and it plays a crucial role in the storage and manipulation of electrical energy. Capacitance is typically measured in units of farads (F), and it is determined by the physical characteristics of the capacitor, such as the area of the plates, the distance between them, and the dielectric material used.Capacitors are essential components in many electronic circuits, serving a variety of functions. They can be used to filter and smooth electrical signals, to store energy for later use, and to control the flow of electric current in various applications. Capacitors are found in a wide range of electronic devices, from simple household appliances to complex communication systems and advanced computing technologies.The concept of capacitance is closely tied to Coulomb's law. When a capacitor is charged, the electric field between the plates creates a potential difference, or voltage, across the capacitor. The amount of charge that can be stored in a capacitor is directly proportional to the voltage applied across it, and this relationship is described by the formula Q = C * V, where Q is the charge, C is the capacitance, and V is the voltage.Understanding the interplay between Coulomb's law and capacitance is crucial for the design and analysis of electrical circuits and systems. Engineers and scientists use these principles to predict the behavior of electrical components, to design efficient power supplies and energy storage systems, and to develop advanced technologies that rely on the manipulation of electric charges.In the field of electronics, Coulomb's law and capacitance are fundamental concepts that underpin the operation of a wide range of devices, from simple switches and transistors to complex integrated circuits and microprocessors. These principles are also essential in the study of electromagnetism, which encompasses the behavior of electric and magnetic fields and their interactions.As our reliance on electricity and electronic technology continues to grow, the understanding of Coulomb's law and capacitance will become increasingly important. Researchers and engineers willcontinue to explore new applications and innovations that leverage these fundamental principles, driving the development of ever-more sophisticated and efficient electrical systems that power our modern world.。

关于阿基米德发现浮力定律的英语作文

关于阿基米德发现浮力定律的英语作文Title: Archimedes and the Discovery of the Buoyancy PrincipleIntroduction:One of the most significant discoveries in the field of physics is the buoyancy principle, which was first documented by the ancient Greek mathematician and inventor, Archimedes. This principle, also known as Archimedes' Principle, explains why objects float or sink in a fluid. It has numerous applications in various fields, including engineering, shipbuilding, and submarine design. This essay aims to explore Archimedes' contributions and elaborate on his discovery of the buoyancy principle.The Life and Contributions of Archimedes:Archimedes was born in Syracuse, a Greek colony in Sicily, around 287 BC. He made groundbreaking contributions to mathematics, physics, engineering, and many other fields. His notable works include the invention of the Archimedes' screw, development of hydrostatics, and pioneering studies in the science of levers.The Discovery of Buoyancy Principle:The story behind Archimedes' discovery of the buoyancy principle is widely known. According to historical records, the King of Syracuse ordered a golden crown to be made for himself. However, he had doubts about the purity of the gold and sought Archimedes' assistance to determine whether the crown was made of pure gold or if other metals had been mixed in.Archimedes pondered over this problem for some time but was unable to find a direct solution. It was during one of his visits to the public bathhouse that he observed an interesting phenomenon - the water level rose as he entered the tub. This observation sparked an idea in Archimedes' mind, leading him to the discovery of the buoyancy principle.The Buoyancy Principle Explained:Archimedes realized that the upward force exerted on an object submerged in a fluid is equal to the weight of the fluid displaced by the object. This meant that an object submerged in a fluid experiences an upward buoyant force equal to the weight of the displaced fluid. If this upward force is equal to or greater than the object's weight, it floats. If the weight of the object exceeds the upward force, it sinks.Significance and Applications:Archimedes' discovery of the buoyancy principle had a profound impact on various fields. In shipbuilding, understanding buoyancy is crucial for designing vessels that can stay afloat in water. This principle also plays a vital role in naval architecture and submarine design. Furthermore, engineers rely on the buoyancy principle when designing structures that will be partially or entirely submerged, such as dams and underwater support systems.Conclusion:Archimedes' discovery of the buoyancy principle remains one of his greatest contributions to science and engineering. His remarkable observation and subsequent understanding of this principle have had a lasting impact, revolutionizing several fields. The buoyancy principle is still studied and applied today, demonstrating the enduring significance of Archimedes' work.。

Calculation of Electric Unit charge

Calculation of Electric Unit chargeIl-Tong CheonDepartment of Physics,Yonsei University,Seoul120-749,KoreaAbstractConsidering the stresses due to the vacuumﬂuctuation and the electric chargeloaded over the surface of a spherical cavity,we estimate the maximum valueof the charge.Since this value is independent of the cavity size and parameterfree,it is regarded as the electric unit charge.Our result is Q=1.55×10−19Coulomb which implies the relevantﬁne structure constantα=1/145.90.PACS numbers:01.90.+g,03.65.-w,03.65.BzThe most fundamental constants in physics are the speed of light c,the Planck constant h and the electric unit charge e.Their numerical values,c=2.997924562(11)×108m/sec, h=6.6260755(40)×10−34J.sec and e=1.60217733(49)×10−19Coulomb,were determined ex-perimentally.However,physicists should sometime explain where those values could come from.If they could be derived on the purely theoretical basis,it would be nice and help us to have deeper understanding of nature.Let us consider a cavity,and suppose that some amount of electric charge is loaded over its surface.Then,the charge exerts an outward stress so that the cavity will explode. on the other hand,it is well known that the vacuumﬂuctuation in the cavity yields the Casimir force[1].If this force is inward,the cavity may stay in equilibrium on the balance between these two forces.Previous calculation[2,3]derived an outward force due to vacuum ﬂuctuation for a spherical cavity.However,for the case of two parallel plates,the Casimir force is deﬁnitely inward[1,4].1Although the Casimir force is dependent of the cavity shape,it is hard to believe such a drastic change in its sign.There might be a pitfall in the calculation of the Casimir force for a spherical cavity.Notice that the Casimir force for a cube turns out to be inward in calculation based on the Casimir’s semi-classical treatment[1,4].In this situation,it is important to estimate again very carefully the Casimir force for a spherical cavity by a rigorous method extended in this letter.If the Casimir force could turn out to be inward,one would be allowed to ask how much charge should be loaded on the cavity surface to save it from collapse.This amount of charge might be related to the electric unit charge.First of all,we shall investigate precautiously a spherical cavity in contex of works on various phenomena occuring between two parellel plates[1,4-21].The zero-point energy in a free space is given byE=2¯h c2a2π3k21+k22+k23dk x dk y dk z(1)where a is the size of normalization box.Forﬁnite space,the wave number becomes discrete,i.e.k x=πa n1,k y=πan2and k z=πan3where n i are integers.Then,the Casimir energyin a spherical cavity of diameter a or a cubic cavity of a×a×a can be deduced from the zero-point energy of electromagnetic vacuumﬁeld expressed as[1]E=2¯h c218∞n1,n2,n3=−∞πan12+πan22+πan32 1=¯h c8πa∞n1,n2,n3=−∞[n21+n22+n23]12.(2)This expression is obtained simply by introducing the discrete photon momentum which implies the discrete photon propagator.Although this procedure does not give a complete answer,it provides a good approximation.For the case ofﬁnite space restricted by two parallel plates,Bordag et al.[22]derived the photon propagator which satisﬁes the boundary condition on the plate surfaces.And it was shown[13]that the discrete photon propagator corresponds to the lowest order of theﬁeld theoretical propagator proposed by Bordag et2al.[22].Therefore,eq.(2)may be regarded as the lowest order of the zero-point energy derived based on theﬁeld theory.The summation is actually divergent,but if the value in the free space is substracted from it,the rest value will remainﬁnite and this quantity gives the Casimir energy.To evaluate the summation,we apply the Poisson’s summation formula on Fourier Trans-form[23],∞ n=−∞f(n)=∞s=−∞∞−∞f(x)e iξs x dx,(3)withξs=2πs.This formula suggests that the sum of f(n)can be converted into the sum of its Fourier transformed function.Validity of eq.(3)can be seen with f(n)=exp(−πn2) for which the integral on the right-hand side yields exp(−πs2).Another example is f(n)= 1(β2+n2)withβ>0.The integral in eq.(3)is easily evaluated and,then,we have∞ n=−∞1β2+n2=∞s=−∞πβe−2πβ|s|.(4)Both sides give identical answer,π(eπβ+e−πβ)/(eπβ−e−πβ)[24].For a three componentfunction,the formula(3)is expressed as∞ n1,n2,n3 =−∞f(n1,n2,n3)=∞λ1,λ2,λ3=−∞∞−∞f(p1,p2,p3)exp[i(ξ1p1+ξ2p2+ξ3p3)]dp1dp2dp3,(5)withξi=2πλi.Thus,the summation in eq.(2)can be expressed as∞ n1,n2,n3 =−∞n21+n22+n23=∞λ1,λ2,λ3=−∞p21+p22+p23exp[i(ξ1p1+ξ2p2+ξ3p3)]dp1dp2dp3.(6)In the spherical coordinates,n1=n sinθcosφ,n2=n sinθsinφ,n3=n cosθ,sim-ilarly p1=p sinθcosφ,p2=p sinθsinφ,p3=p cosθandξ1=ξsinθ cosφ ,ξ2=ξsinθ sinφ ,ξ3=ξcosθ .Then we haveiξi p i=pξ(sinθcosφsinθ cosφ +sinθsinφsinθ sinφ +cosθcosθ )=pξ[sinθsinθ cos(φ−φ )+cosθcosθ ]=pξcosω,(7)3whereωis the angle between p andξ.Accordingly,eq.(6)becomesleft-hand side=∞n=−∞(n sinθcosφ)2+(n sinθsinφ)2+(n cosθ)2=∞n=−∞√n·n,(8.a)right-hand side=∞λ=−∞√p·p e iξp cosωp2dp sinθdθdφ,(8.b)withξ=2πλ.The integral in eq.(8b)is indeﬁnite,i.e.ultraviolet divergence.However, for wavelengths shorter than the atomic size,it is unrealistic to use a model of cavity. Therefore,we take the well known regularization procedure such as introducing a smooth cut-oﬀfunction,e−εp,and making a limitε→0.As a result,the zero-point energy is found in the spherical coordinates asE=¯h c8πa∞λ=−∞limε→0∞dp|p|p2e−εp2πdφπdθsinθe iξp cosω.(9)Forλ=0,we haveE0=¯h c8πalimε→0|p|e−εp p2dp sinθdθdφ=¯h ca2π3|k|d k,(10)where k i=πp i is used.This value is exactly identical to the zero-point energy in a freespace with a normalization volume a3.The Casimir energy is,then,obtained forλ=0by expanding the exponential in eq.(9)with the spherical hamonics asE c=¯h c8 πa∞λ=−∞,(λ=0)limε→04πl,mi l∞p3e−εp j l(ξp)dpY∗lm(θ ,φ )Y lm(θ,φ)sinθdθdφ=¯h c8πa∞λ=−∞,(λ=0)limε→04π∞p3e−εp j0(ξp)dp=¯h c8πa∞λ=−∞,(λ=0)limε→08π(3ε2−ξ2)(ε2+ξ2)3=−¯h c8πa1π3∞λ=11λ4,(11)where the summation is just the Riemann’s zeta function,ζ(4)=π4/90.Thus,forλ=0, weﬁndE c=−¯h c8π2aζ(4).(12)4This is the Casimir energy of a spherical cavity with diameter a.Notice the negative sign!At this stage,we explore why the previous calculation yielded the Casimir energy with a positive sign.After rewriting the integral in eq.(1)as|k|d k=4π ∞|k|k2dk=2π∞−∞|k|k2dk→2π πa4∞n=−∞|n|n2,(13)we apply the formular,(3),to obtain2π πa4∞n=−∞|n|n2=2ππa4∞s=−∞∞−∞|p|p2e iξs p dp,(14)whereξs=2πs.For s=0,weﬁnd the right-hand side as2π πa4 ∞−∞|p|p2dp=πa44π∞|p|p2dp=πa4|p|d p=|k|d k.(15)This is exactly identical to the quantity in a free space.For s=0,eq.(14)is evaluated as2π πa4∞s=−∞,(s=0)∞−∞|p|p2e iξs p dp=4ππa4∞s=1∞−∞|p|p2cos(ξs p)dp=8ππa4∞s=1limε→0∞p3e−εp cos(ξs p)dp=8ππa4∞s=1limε→06(ε4−6ε2ξ2s+ξ4s)(ε2+ξ2s)4=48ππa4∞s=11ξ4=πa43π3ζ(4).(16)Thus,weﬁndE c=¯h c8 πa3π3ζ(4)=3¯h c8π2aζ(4)=π2¯h c240a.(17)This result has,indeed,a positive sign and is consistent with other previous calcula-tions[2,3].However,it is controversial because of one-dimensional calculation in principle.5It should be calculated three-dimensionally as was presented through eqs.(6)-(12).The fac-tor,exp(iξp cosω),in eq.(9)is actually a key point to obtain a negative sign.Although one dimensional calculation is run with the factor,exp(iξs p)which is independent of angles, three dimensional calculation contains the angleωin the factor which is eﬀective to the integrals overθandφ.However,after integration over anglesθandφ,the result does not have any dependence of anglesθ andφ at all,because of Y00(θ ,φ )=1√4π.As a result, cos(ξs p)in the integral over p appearing in eq.(16)is replaced by j0(ξp)as seen in eq.(11). Thus,the negative sign is realized.Finally,the stress due to the vacuumﬂuctuation is obtained by diﬀerentiating eq.(12) with respect to a asP c=14π(a/2)2−∂E c∂a=−¯h c8π3a4ζ(4)=−π¯h c720a4.(18)If there were only this inward force acting on the cavity surface,it would collapse.How much electric charge do we have to load over the cavity surface to stabilize it?Supposing that the electric charge of Q is loaded and applying the Gauss’s law to the sphere,we obtain the electricﬁeld in the normal direction to the surface,E n=4πQ4π(a/2)2=4Qa2.(19)Then,the stress due to charge Q can be found as[25]P e=E 2n 8π=2Q2πa4.(20)From the stability condition,P c+P e=0,we obtainQ=π2¯h c14401=1.55×10−19Coulomb.(21)It is surprising that the electric charge is completely independent of the cavity size.This result might be retained even in the limit,a→0.Therefore,it may be regarded as the electric unit charge.Accordingly,the value associated with theﬁne structure constant is6α=1145.90.(22)The experimental value of theﬁne structure constant is[26]αexp=1137.035987(29).(23)Discrepancy betweenαandαexp is only6%.This discrepancy is not much important here. The essential point is that theαvalue has beenﬁrstly calculated based on purely theoritical analysis.If we start with the fullyﬁeld theoretical photon spectrum,the result may be improved. It will be explored on another occasion.ACKNOWLEDGMENTSThis work was supported by the Korean Ministry of Education(Project no.BSRI-95-2425).The author thanks Dr.Su Houng Lee for valuable discussion.7REFERENCES[1]H.B.G.Casimir,Proc.Ned.Akad.Wet.,51,793(1949).[2]T.H.Boyer,Ann.Phys.56,474(1970).[3]R.Balian and B.Duplantier,Ann.Phys.112,165(1978).[4]H.B.G.Casimir,Physica19,846(1953).[5]Il-T.Cheon,Abstracts of the Proc.X Int.Conf.on Atomic Physics,Tokyo1986,p.49.[6]Il-T.Cheon,Solid State Comm.59,887(1986).[7]G.Barton,Proc.Roy.Soc.London A410,141(1987).[8]Il-T.Cheon,Phys.Rev.A37,2785(1988).[9]Il-T.Cheon and S.D.Oh,J.phys.Soc.Japan58,1581(1989).[10]D.Meshede,et al.,Phys.Rev.A41,1587(1990).[11]Il-T.Cheon,Proc.4th Asia Paciﬁc Phys.Conf.(Seoul),World Scientiﬁc,p.1176(1990).[12]Il-T.Cheon,J.Phys.Soc.Japan60,833(1991).[13]Il-T.Cheon,J.Phys.Soc.Japan61,1535(1992).[14]Il-T.Cheon,J.Phys.Soc.Japan61,2257(1992).[15]Il-T.Cheon,Hyperﬁne interactions78,231(1993).[16]Il-T.Cheon,J.Phys.Soc.Japan62,4240(1993).[17]Il-T.Cheon,J.Phys.Soc.Japan63,47(1994).[18]Il-T.Cheon,J.Phys.Soc.Japan63,2453(1994).[19]Il-T.Cheon,Laser Physics(Moscow)4,579(1994).[20]Il-T.Cheon,JSPS-INS Int.Spring School(Tokyo),”New Frontiers in Nuclear Physics”,8World Scientiﬁc,p.241(1994).[21]Il-T.Cheon,Proc.Int.School-Seminar,”93-Hadrons and Nuclei from QCD”,Tsuruga-Vladivostok-Sapporo Aug.1993,World Scientiﬁc,p.280(1994).[22]M.Bordag,D.Robaschik and E.Wieczorek,Ann.Phys.165,192(1985).[23]”Encyclopedic Dictionary of Mathematics”,MIT Press1977,p.374I.[24]”Table of Integrals,Series and Products”,by I.S.Gradshteyn and I.W.Ryzhik,AcademicPress1980,p.23,Formula1.217(1).[25]J.A.Stratton,”Electromagnetic Theory”,McGraw Hill,1941,Sect.2.26,p.153.[26]B.N.Taylor et al.Rev.Mod.Phys.41No.2(1969).9。

2022年自考专业(英语)英语科技文选考试真题及答案27

2022年自考专业(英语)英语科技文选考试真题及答案一、阅读理解题Directions: Read through the following passages. Choose the best answer and put the letter in the bracket. (20%)1、(A) In the aftermath of a disaster like the massive typhoon Haiyan, which devastated the Philippines on 8 November, confusion often reigns and sketchy information abounds. This can leave responders unsure if their efforts are being put to the best effect. A coordinated army of smart software and aerial drones could change that. By gathering information from across an affected software agents — algorithms that can work with a degree of autonomy — will build a picture of the situation and give recommendations for how people should direct their resources to mitigate damage and save lives. The system, called Orchid, is being developed as part of a ￡10 million project of the same name funded by the UK government. Initial testing has shown promising results, and Rescue Global, a London-based disaster responder, is planning a field trial next year. Orchid’s software agents come in several flavours: theyinhabit flying drones with on-board cameras, and servers that sift data coming in from the disaster area, like pictures, tweets or even sensor readings. Each is programmed to watch for rapid changes to a situation. For example, if air quality sensors suggested that a chemical plant was leaking toxic gas, the sensors could send a signal to drones on a mapping project that could then fly to the scene, take further readings and shoot video from several different camera angles. The information is then communicated wirelessly to an agent called a planner that assesses it and makes a suggestion to the person coordinating the aid effort on how to proceed. “We are trying to fix the inefficiencies in deploying emergency responders that prevent proper prioritisation and scheduling of rescue tasks,” says Sarvapali Ramchum, a computer scientist at the University of Southampton in the UK, which leads a consortium of universities and companies working on the Orchid project. In the wake of the magnitude 7 quake that devastated Port-au-Prince, Haiti, in January 2022, such a a system could have been a huge help, says Ramchum. “Roads were completely blocked and buildings were down so they had to remap the city to find the accessible zones for relief operations,” he says. That was performed via crowdsourced reports to the Ushahidiwebsite and use of Open Street Map—but it took 48 hours to complete. The Orchid team say software agents in charge of swarms of airborne drones could do that far quicker. The agents are also designed to address a common problem in disasters: unreliable data. Distressed people in traumatic circumstances can supply inaccurate information. For instance, following the 2022 nuclear disaster at the Fukushima Daiichi power plant in Japan, people bought or built their own Geiger counters to track the spread of radiation. But many of the reported readings were implausibl y high. Orchid’s information-gathering agents weed out reports that appear erroneous, quashing outlying high or low numbers in a dataset. In simulations of radioactive plumes that the team has run, this has worked well.What is the passage primarily about?A.Drones inhabited with smart software to plot disaster relief.B.Orchid’s software.C.How to plot typhoon relief.D.Application of Orchid to plotting quake relief.2、It can be inferred from the passage that______.A.Orchid did a great deal in the relief operations at Port-au-PrinceB.Port-au-Prince suffered acutely from the earthquakeC.Orchid has some weaknesses in preventing prioritization of rescue tasksD.Orchid’s information-gathering agents have worked well in real situations3、In which of the aspects does the Orchid system need improving?A.Inefficiency.B.Addressing unreliable data.C.Proper prioritisation.D.Gathering information.4、The word “traumatic” in line 2, para. 9 is closest in meaning to______.A.powerfulB.terribleC.troublesomeD.emotionally disturbing5、Orchid’s software agents can perform all the following tasks EXCEPT_______,A.dealing with inaccurate dataB.examining sensor readingsC.removing incorrect reportsD.coordinating the aid effort6、(B) To a casual observer of the latest round of United Nations climate talks in Warsaw, Poland, last week, it was a battle between Polish coal miners determined to hang on to their jobs, and the people of the Philippines, who would rather not lose their lives to the tempests likely unleashed by climate change. In the corridors, the talks looked different: another stage in the agonizingly slow crawl towards a deal on carbon emission that diplomats hope to seal in 2022. Little progress was made on most issues, but the two-week negotiations did end with an outline agreement that could one day allow people like the Filipino victims of the super-typhoon Haiyan to use science to sue coal-mining firms and power companies for compensation. The deal was still being hammered out on Saturday—a day after the talks were due to close. After compromises from all sides, the negotiators agreed to set up an “international mechanism to provide roost vulnerable populations with better protection against loss and damage caused by extreme weather”. It was a tacit acceptance that the promises made by governments at the Earth Summit in Rio de Janiero in 1992 to prevent “dangerous climate change” have failed. Dangerous climate change is now happening. It is not yet clear how such an internationalmechanism will work. Rich nations remain deeply hostile to the idea to handing out compensation payments after disasters. But, with efforts to prevent escalating climate change making such slow progress, it could all end up in court with or without this mechanism in place. Lawyers say nations hit by extreme weather might already have a case at the UN International Court of Justice in The Hague, the Netherland, which resolves legal disputes between nations. For example, the court could attempt to charge rich nations with failing to honor their Earth Summit commitment.Such cases would depend on researchers’ increasing ability to attribute blame for specific disasters. Myles Allen and fellow climate modellers at the University of Oxford have shown that the European heatwave of 2022, which may have killed as many as 70,000 people, was made at least twice as likely by global warming. Researchers could well conclude that typhoon Haiyan has human fingerprints all over it. Especially since the most recent assessment of climate science from the Intergovernmental Panel on Climate Change (IPCC) found that warmer oceans are increasing the intensity of winds in tropical cyclones, while rising sea levels worsen storm surges. Allen says legal culpability should start 1990, the year governments signed off the first IPCC report about climate change. Afterthat date, polluters cannot claim they were ignorant of the consequences. Moreover, Allen says, by 2023, two-thirds of all the planet-warming emissions ever caused by humans will have happened since 1990.What is the passage mainly concerned with?A.Who should pay for climate change disasters.B.United Nations climate talks in Warsaw.C.Carbon emission.D.Dangerous climate change.7、Which of the following is NOT true about the latest round of United Nations climate conference in Warsaw?A.It was stormy.B.It was full of argument and conflict.C.It concluded with an agreement to set up an international mechanism.D.It was a battle between Polish coal miners and the people of the Philippines.8、Paying compensation after disasters may involve all of the following EXCEPT_______.A.pollutersB.victims’ suitC.the ability of the climate change researches to prove who was responsible for specific disastersD.rich countries’ commitment9、The word “fingerprints” in line 5, para. 7 refers to______.A.marksB.tracesC.factorsD.interference10、What does Allen imply when he mentions the first IPCC report about climate change?A.Winds in the tropical storm are becoming more and more intense.B.Polluters cannot claim they did not know the consequences.C.He is doubtful about the effectiveness of international agreements about climate changes.D.Polluters should be responsible for their wrong doings. 参考答案：【一、阅读理解题】1~5ABCDD6~10ADDC。

The Casimir force between metallic mirrors

a rX iv:q u a nt-p h/0105051v111M ay21THE CASIMIR FORCE BETWEEN METALLIC MIRRORS ASTRID LAMBRECHT,CYRIAQUE GENET AND SERGE REYNAUD Laboratoire Kastler Brossel ∗Universit´e Pierre et Marie Curie,Ecole Normale Sup´e rieure et CNRS Campus Jussieu,Case 74,75252Paris Cedex 05,France In order to compare recent experimental results with theoretical predictions we study the inﬂuence of ﬁnite conductivity of metals on the Casimir eﬀect.The correction to the Casimir force and energy due to imperfect reﬂection and ﬁnite temperature are evaluated for plane metallic plates where the dielectric functions of the metals are modeled by a plasma model.The results are compared with the common approximation where conductivity and thermal corrections are evaluated separately and simply multiplied.1Introduction After its prediction in 19481the Casimir force has been observed in a number of ‘historic’experiments 2,3,4,5but has only recently been remeasured with an im-proved experimental precision 6,7,8.An accurate comparison with the predictions of Quantum Field Theory should therefore now be possible,provided that theoretical predictions account for the diﬀerences between real experiments and the idealized Casimir situation.In particular,experiments are performed at room temperature between metallic mirrors while theoretical calculations are often performed at zero temperature and for perfect reﬂectors.As the experimental accuracy is claimed to be up to the order of 1%,theoretical expectations should also be computed with the same accuracy if the aim is to test agreement between theory and experiment.A high accuracy is also important in order to control the eﬀect of Casimir force when studying small short range forces 9,10,11.The inﬂuence of thermal ﬁeld ﬂuctuations on the Casimir force are known to become important for distances of the order of a typical length 12,13,14,15λT =2πc k B T (1)When evaluated at room temperature,λT amounts to approximately 7µm.In contrast,the ﬁnite conductivity of metals has an appreciable eﬀect for distances smaller than or of the order of the plasma wavelength λP determined by the plasma frequency ωP of the metal (see 16and references therein)λP =2πc∗mailto:lambrecht@spectro.jussieu.fr;http://www.spectro.jussieu.fr/Vacuumsame time.To characterize the whole correction,we will compute the factorηF describing the combined eﬀect of conductivity and temperatureηF=F240L4(3)F Cas is the ideal Casimir force corresponding to perfect mirrors in vacuum.L is the distance between the mirrors,A their surface and¯h and c respectively the Planck constant and the speed of light.We will also evaluate the factors associated with each eﬀect taken separately from each otherηP F=F PF Cas(4)F P is the Casimir force evaluated by accounting forﬁnite conductivity of the metals but assuming zero temperature and F T is the Casimir force evaluated at tempera-ture T for perfect reﬂectors.Now the question is to which level of accuracy the complete correction factor ηF can be approximated as the product of the factorsηP F andηT F?To answer this question we will evaluate the quantityδF=ηF2Casimir force and free energyWhen real mirrors are characterized by frequency dependent reﬂection coeﬃcients, the Casimir force is obtained as an integral over frequencies and wavevectors asso-ciated with vacuum and thermalﬂuctuations22.The Casimir force is a sum of two parts corresponding to the2ﬁeld polarizations with the two parts having the same form in terms of the corresponding reﬂection coeﬃcientsF=∞k=−∞ωT2π2 +∞ωe2κL−r2⊥(iω,iκ)+r2||(iω,iκ)c F[ω](7)The contribution of vacuumﬂuctuations,that is also the limit of a null temperature (ωT→0)in(6),corresponds to the contribution m=0in(7)F P= F(0)= ∞0dωF[ω](8)Hence,the whole force(7)is the sum of this vacuum contribution m=0and of thermal contributions m=0.We will consider metallic mirrors with the dielectric functionε(iω)for imaginary frequencies given by the plasma modelε(iω)=1+ω2PWe will also focus our attention on mirrors with a large optical thickness for which the reﬂection coeﬃcients r⊥(iω,iκ)and r||(iω,iκ)correspond to a simple vacuum-metal interface.Their expressions can be found in standard literature.The Casimir energy will be obtained from the force by integration over the mirrors relative distanceE= ∞L F(x)d x(10) As this procedure is performed at constant temperature,the energy thus obtained corresponds to the thermodynamical deﬁnition of a free energy.For simplicity we will often use the denomination of an energy.We will deﬁne a factorηE measuring the whole correction of energy due to conductivity and temperature eﬀects with respect to the ideal Casimir energyEηE=(11)720L3The positive value of the energy here means that the Casimir energy is a binding energy while the positive value of the force is associated with an attractive character.3Numerical evaluationsIn the following we present the numerical evaluation of the correction factors of the Casimir force and energy using equations written in the former section.The force correction factor was evaluated for the experimentally relevant dis-tance range of0.1-10µm with the help of equation(7),supposing explicitly a plasma model for the dielectric function,and the result was normalized by the ideal Casimir force.The energy correction factor was then calculated by numerically integrating the force and normalizing by the ideal Casimir energy.Integration was restricted to aﬁnite interval,the upper limit exceeding at least by a factor of104the distance at which the energy value was calculated.Extending the integration range by a factor of100changed the numerical result by less than10−7.The results of the numerical evaluation ofηF are shown as the solid lines in ﬁgures1for Al and for Cu-Au assuming a temperature of T=300K.They are compared with the force reduction factorηP F due toﬁnite conductivity(dashed lines)and the force enhancement factorηT F calculated for perfect mirrors at300K (dashed-dotted lines).Figure2shows similar results for the factorηE obtained through numerical evaluation of the Casimir free energy.The shape of the graphs is similar to the ones of the force.However,whileﬁnite conductivity corrections are more important for the force,thermal eﬀects have a larger inﬂuence on energy.For the force as well as for the energy,temperature corrections are negligible in the short distance limit while conductivity corrections may be ignored at large distances.The whole correction factorηbehaves roughly as the productηPηT of the2correction factors evaluated separately.However,both correction factors are appreciable in the distance range1−4µm in between the two limiting cases.0.1 1.010.0L[µm]0.50.60.70.80.91.02.03.0ηFηPηT ηAl 0.1 1.010.0L[µm]0.50.60.70.80.91.02.03.0ηFηPηT ηCu-Au Figure 1.Force correction factor for Al (upper ﬁgure)and Cu and Au (lower graph)as function of the mirrors distance at T =300K .Since this range is important for the comparison between experiments and theory,it is necessary to discuss more precisely how good is the often used approximation which identiﬁes ηto the product ηP ηT .In order to assess the quality of this approximation,we have plotted in ﬁgure 3the quantities δF and δE (cf.eq.(5)as a function of the distance for Al,Cu-Au and two additional plasma wavelengths.A value of δ=0would signify that the approximation gives an exact estimation of the whole correction.An important outcome of our calculation is that the errors δF and δE are of the order of 1%for Al and Cu-Au at a temperature of 300K .For estimations at the 5%level,the separate calculation of ηP and ηT and the evaluation of ηas the product ηP ηT can therefore be used.However,if a 1%level0.1 1.010.0L[µm]0.60.70.80.91.02.03.04.0ηE ηPηT ηAl 0.1 1.010.0L[µm]0.60.70.80.91.02.03.04.0ηE ηPηT ηCu-Au Figure 2.Energy correction factor for Al (upper ﬁgure)and Cu and Au (lower graph)as function of the mirrors distance at T =300K .or a better accuracy is aimed at,this approximation is not suﬃcient.It should be noticed furthermore that the error increases when the temperature or the plasma wavelength are increased.It becomes of the order of 4%for a plasma wavelength of 0.5µm at 300K.The sign obtained for δmeans that the approximation gives too small values of force and energy.4Scaling laws for the deviationsAn inspection of ﬁgure 3shows that the curves corresponding to diﬀerent plasma wavelengths λP have similar shapes with a maximum which is practically attained0.1 1.010.0L[µm]0.000.010.020.030.040.05δF AlCu-AuλP =0.3µmλP =0.5µm0.1 1.010.0L[µm]0.000.010.020.030.040.05δE AlCu-AuλP =0.3µmλP =0.5µmFigure 3.δF (upper graph)and δE (lower graph)as a function of the mirrors distance.The resultsare given for the three metals Al,Cu-Au and two larger plasma wavelengths.for the same distance between the mirrors.The amplitude of the deviations,which is larger for the energy than for the force,is found to vary linearly as a function of the plasma wavelength λP .This scaling property is conﬁrmed by ﬁgure 4where we have drawn the devia-tions after an appropriate rescaling∆=λTthe scaling law would not be obeyed so well otherwise.0.1 1.010.0L[µm]0.00.10.20.30.40.50.6∆F λP =0.1µm λP =0.3µm λP =0.5µm theory 0.1 1.010.0L[µm]0.00.10.20.30.40.50.6∆E λP =0.1µm λP =0.3µm λP =0.5µm theory Figure 4.The deviations are represented for the force (upper graph)and the free energy (lower graph)after the rescaling described by equation (12).Diﬀerent plasma wavelengths lead to nearly identical functions,drawn as dotted,dashed and dotted-dashed lines.These functions are hardly distinguishable from the solid lines which represent the analytical expressions derived in the next section.In other words,the deviations δF and δE are proportional to the factor λPλT ∆ (13)This method is less direct than the complete numerical integration of the forces which has been performed for obtaining the curves presented in the previous section. But it requires easier computations while nevertheless giving accurate estimations of the correction factors.Typically,the deviationδwith a magnitude of the order of the%may be estimated with a much better precision through the mere inspection ofﬁgure4.One may explain this scaling law by using a partial analytical integration of the whole correction factors and calculating analytical expressions for the functions∆F and∆E toﬁrst order inλP:∆F=8LηT F−1LφFπλTηTE+λTηTE(15)This function is plotted as the solid line onﬁgure4and it is found toﬁt well the results of the complete numerical integration presented before.The detailed calculations may be found in23.5SummaryWe have given an accurate evaluation of the Casimir force and Casimir free energy between2plane metallic mirrors,taking into account conductivity and tempera-ture corrections at the same time.The whole corrections with respect to the ideal Casimir formulas,corresponding to perfect mirrors in vacuum,have been charac-terized by factorsηF for the force andηE for the energy.These factors have been computed through a numerical evaluation of the integral formulas.They have also been given a simpliﬁed form as a product of3terms,namely the reduction fac-tor associated with conductivity at null temperature,the increase factor associated with temperature for perfect mirrors,and a further deviation factor measuring a kind of interplay between the two eﬀects.This last factor turns out to lie in the1% range for metals used in the recent experiments performed at ambient temperature. Hence the conductivity and temperature corrections may be treated independently from each other and simply multiplied for theoretical estimations above this accu-racy level.However,when accurate comparisons between experimental and theoretical val-ues of the Casimir force are aimed at,the deviation factor has to be taken into account in theoretical estimations.The deviation factor is appreciable for dis-tances greater than the plasma wavelengthλP but smaller or of the order of the thermal wavelengthλT.We have used this property to derive a scaling law of the deviation factor.This law allows one to obtain a simple but accurate estimation of the Casimir force and free energy through a mere inspection ofﬁgure4.Alterna-tively one can use analytical expressions which have been obtained through aﬁrst order expansion inλP of the thermal contributions to Casimir forces andﬁt well the results of complete numerical integration.We have represented the optical properties of metals by the plasma model.This model does not lead to reliable estimations of the forces at small distances but thisdeﬁciency may be corrected by using the real dielectric function of the metals.This does not aﬀect the discussion of the present paper,except for the fact that the pure conductivity eﬀect has to be computed through an integration of optical data for distances smaller than0.5µm.Finally surface roughness corrections,which have not been considered in the present paper,are expected to play a signiﬁcant role in theory-experiment comparisons in the short distance range.References1.H.B.G.Casimir,Proc.Kon.Nederl.Akad.Wet.51,793(1948)2.B.V.Deriagin and I.I.Abrikosova,Soviet Physics JETP3,819(1957)3.M.J.Sparnaay,Physica XXIV,751(1958);W.Black,J.G.V.De Jongh,J.Th.G.Overbeek and M.J.Sparnaay,Transactions of the Faraday Society 56,1597(1960)4.D.Tabor and R.H.S.Winterton,Nature219,1120(1968)5.E.S.Sabisky and C.H.Anderson,Phys.Rev.A7,790(1973)moreaux,Phys.Rev.Lett.78,5(1997);erratum in Phys.Rev.Lett.81,5475(1998)7.U.Mohideen and A.Roy,Phys.Rev.Lett.81,4549(1998)8.A.Roy,C.Lin and U.Mohideen,Phys.Rev.D60,111101(1999)9.E.Fischbach and C.Talmadge,in The Search for Non Newtonian Gravity(AIP Press/Springer Verlag,1998)and references therein;E.Fischbach andD.E.Krause,Phys.Rev.Lett.82,4753(1999)10.G.Carugno,Z.Fontana,R.Onofrio and C.Rizzo,Phys.Rev.D55,6591(1997)11.M.Bordag,B.Geyer,G.L.Klimchitskaya,and V.M.Mostepanenko,Phys.Rev.D60,055004(1999)12.E.M.Lifshitz,Sov.Phys.JETP273(1956);E.M.Lifshitz and L.P.Pitaevskii,Landau and Lifshitz Course of Theoretical Physics:Statistical Physics Part2 ch VIII(Butterworth-Heinemann,1980)13.J.Mehra,Physica57,147(1967)14.L.S.Brown and G.J.Maclay,Phys.Rev.184,1272(1969)15.J.Schwinger,L.L.de Raad Jr.,and ton,Annals of Physics115,1(1978)mbrecht and S.Reynaud,Eur.Phys.J.D8,309(2000)17.B.V.Deriagin,I.I.Abrikosova and E.M.Lifshitz,Quart.Rev.10,295(1968)18.J.Blocki,J.Randrup,W.J.Swiatecki and C.F.Tsang,Ann.Physics105,427(1977)19.V.M.Mostepanenko and N.N.Trunov Sov.J.Nucl.Phys.42,812(1985)20.V.B.Bezerra,G.L.Klimchitskaya and C.Romero,Mod.Phys.Lett.12,2613(1997)21.G.L.Klimchitskaya,A.Roy,U.Mohideen and V.M.Mostepanenko,Phys.Rev.A60,3487(1999)22.M.T.Jaekel and S.Reynaud,J.Physique I-1,1395(1991)23.C.Genet,mbrecht,and S.Reynaud,Phys.Rev.A62,012110(2000)。

越分练习题

一、选择题1. 下列哪个数是偶数？A. 3B. 5C. 8D. 102. 下列哪个图形是正方形？A. 正三角形B. 长方形C. 正五边形D. 梯形3. 下列哪个国家位于欧洲？A. 中国B. 美国C. 法国D. 日本4. 下列哪个季节是夏季？A. 春季B. 夏季C. 秋季D. 冬季5. 下列哪个单位是长度单位？A. 千克B. 米C. 秒D. 摄氏度二、填空题1. 2 + 3 = _______2. 5 × 4 = _______3. 7 2 = _______4. 8 ÷ 2 = _______5. 3 × 5 + 2 = _______三、判断题1. 2 × 2 = 4 （）2. 5 × 5 = 25 （）3. 8 ÷ 2 = 4 （）4. 7 3 = 4 （）5. 6 × 6 = 36 （）四、应用题1. 小明有10个苹果，他吃掉了3个，还剩下多少个苹果？2. 小红有20元，她买了5本书，每本书5元，她还剩下多少钱？3. 一辆汽车每小时行驶60千米，行驶2小时后，汽车行驶了多少千米？4. 一桶水有5升，小明喝掉了3升，还剩下多少升水？5. 小华有30个气球，他送给朋友10个，还剩下多少个气球？五、简答题1. 请简述圆的性质。

2. 请简述平行四边形的性质。

3. 请简述长方形的性质。

4. 请简述正方形的性质。

5. 请简述三角形的性质。

六、计算题1. 123 + 4562. 789 3213. 456 × 784. 321 ÷ 125. 12.5 ×6.3七、几何题1. 画一个直径为8厘米的圆。

2. 画一个边长为6厘米的正方形。

3. 画一个底边为4厘米，高为5厘米的三角形。

4. 画一个长为10厘米，宽为5厘米的长方形。

5. 画一个对角线相等的菱形。

八、代数题1. 解方程：2x + 3 = 112. 解方程：5x 2 = 183. 解方程：3x + 4 = 2x + 104. 解方程：4x 3 = 2(x + 1)5. 解方程：x^2 5x + 6 = 0九、应用题1. 一辆汽车以每小时80千米的速度行驶，行驶了4小时后，汽车行驶了多少千米？2. 一桶油重20千克，每次倒出5千克，倒出几次后，油桶里还剩多少千克？3. 一块长方形菜地，长为20米，宽为15米，这块菜地的面积是多少平方米？4. 一个班级有40名学生，其中有男生25名，女生多少名？5. 一辆火车以每小时100千米的速度行驶，行驶了5小时后，火车行驶了多少千米？十、英语题1. What is the capital of France?2. How many days are in a week?3. What is the opposite of "hot"?4. What is the plural form of "cat"?5. What is the past tense of "do"?十一、物理题1. What is the unit of force?2. What is the formula for calculating work?3. What is the speed of light in a vacuum?4. What is the law of conservation of energy?5. What is the difference between mass and weight?十二、历史题1. Who was the first president of the United States?2. What year did World War II begin?3. What was the main cause of the French Revolution?4. Who was the first woman to fly solo across the Atlantic Ocean?5. What was the significance of the Great Wall of China?十三、化学题1. What is the chemical symbol for oxygen?2. What is the formula for water?3. What is the process called when atoms gain or lose electrons?4. What is the pH scale used to measure?十四、生物题1. What is the function of the mitochondria in a cell?2. List the three domains of life.3. What is photosynthesis?4. What is the difference between a plant and an animal cell?5. What is the process of digestion?十五、地理题1. What is the largest continent on Earth?2. What is the deepest ocean on Earth?3. What is the capital city of Brazil?4. What is the significance of the Amazon Rainforest?5. What is the main cause of desertification?十六、数学题1. Solve for x: 3x 5 = 142. Simplify: (x^2 4) / (x + 2)3. Find the perimeter of a rectangle with a length of 12 units and a width of 5 units.4. Solve for y: 2y + 6 = 3y 25. Find the area of a circle with a radius of 7 units.十七、逻辑题1. If it is raining, then the ground is wet. The groundis wet. What can be concluded?2. All cats have fur. Some dogs have fur. Can we conclude that all dogs have fur?3. If a number is divisible 3, then it is also divisible 6. Is the number 18 divisible 3?4. If all birds can fly, and a penguin is a bird, then what can we conclude about penguins?5. If it is not morning, then it is either afternoon or evening. It is not morning. What time of day is it?十八、物理实验题1. Describe the steps to measure the speed of sound.2. What is the purpose of a calorimeter in an experiment?3. How would you set up an experiment to test the effect of gravity on falling objects?4. Describe the procedure for conducting an experiment to determine the density of a substance.5. What safety precautions should be taken when conducting a chemical experiment?十九、文学题1. Who wrote "To Kill a Mockingbird"?2. What is the theme of Shakespeare's "Romeo and Juliet"?3. Describe the setting of "The Great Gats" F. Scott Fitzgerald.4. What is the significance of the red rose in "Wuthering Heights" Emily Brontë?5. What is the main character's quest in "The Lord of the Rings" J.R.R. Tolkien?二十、艺术题1. What is the difference between an oil painting and an acrylic painting?2. Describe the technique of chiaroscuro in art.3. What is the role of the conductor in an orchestra?4. What are the four elements of music?5. What is the difference between a symphony and an opera?二十一、经济学题1. What is the difference between microeconomics and macroeconomics?2. Define the term "supply and demand."3. What is the role of central banks in an economy?4. Explain the concept of inflation.5. What are the three types of economic systems?二十二、心理学题1. Define the term "learning theory."2. What is the difference between cognitive and behavioral therapy?3. Explain the concept of the "fight or flight" response.4. What is the role of the prefrontal cortex in decisionmaking?5. Define the term "sensation" in psychology.二十三、社会学题1. What is the difference between social structure and social institutions?2. Define the term "social capital."3. What is the role of social norms in society?4. Explain the concept of social stratification.5. What is the difference between ethnicity and race?二十四、计算机科学题1. What is the difference between a binary tree and a binary search tree?2. Define the term "algorithm."4. Explain the concept of objectoriented programming.5. What is the difference between a stack and a queue?二十五、天文学题1. What is the difference between a planet and a star?2. Define the term "black hole."3. What is the speed of light in a vacuum?4. Explain the theory of relativity.5. What is the significance of the Hubble Space Telescope?二十六、哲学题1. Define the term "existentialism."2. What is the difference between metaphysics and epistemology?3. Explain the concept of "the self" in philosophy.4. What is the role of ethics in philosophy?5. Define the term "ontology."二十七、法律题1. What is the difference between a civil law and a criminal law?2. Define the term "due process."3. What is the role of the Supreme Court in the United States?4. Explain the concept of "precedent" in law.5. What is the difference between a tort and a contract?二十八、体育题1. What is the primary objective in basketball?2. Define the term "dribbling" in soccer.3. What is the difference between a forward pass and a lateral pass in American football?4. Explain the scoring system in tennis.答案一、选择题1. C2. B3. C4. B5. B二、填空题1. 52. 203. 54. 45. 23三、判断题1. √2. √3. √4. ×5. √四、应用题1. 7个苹果2. 5元3. 160千米4. 2升5. 20个气球五、简答题1. 圆的性质包括：所有点到圆心的距离相等，圆周角定理，圆内接四边形的对角互补等。

库仑定律

I NSTITUTE OF P HYSICS P UBLISHING M ETROLOGIA Metrologia 41 (2004) S159-S170 PII: S0026-1394(04)80313-XPhysical implications of Coulomb’s LawG Spavieri1, G T Gillies2 and M Rodriguez31Centro de Astrofisica Tecorica, Facultad de Ciencias, Universidad de Los Andes, Merida,5101 Venezuela2Department of Mechanical and Aerospace Engineering, University of Virginia,PO Box 400746, Charlottesville, VA 22904, USA3Departamento de Fisica, FACYT, Universidad de Carabobo, Valencia, 2001 Venezuela E-mail: spavieri@ula.ve andgtg@Received 3 March 2004 Published 16 September 2004 Online at /Met/41/S159doi:10.1088/0026-1394/41/5/S06AbstractWe examine the theoretical and experimental foundations of Coulomb’sLaw and review the various roles it plays not only in electromagnetismand electrodynamics，but also in quantum mechanics, cosmology, andthermodynamics. The many implications of Coulomb’s Law drawattention to its fundamental importance within virtually all branches ofphysics and make this elementary yet profound law one of the mostuseful of all scientific tools.1.Introductory historical outlookFew investigations in physics have enjoyed as sustained an interest as have tests of Coulomb’s Law. As has been the case with most of the fundamental laws of physics, it was discovered and elucidated through observations of basic phenomena. In his research, Coulomb was interested in the mutual interactions between electric charges, a topic that had been studied previously by Priestley [1], and in fact even earlier, in 1755, during the experimental work of Franklin [2].Franklin (1706-1790) was an American printer, writer, politician, diplomat, and scientist. He is credited with the invention of such practical everyday items as bifocal eyeglasses and a free-standing, wood-burning heater called the ‘Franklin stove’. His principal connection to electrical experimentation came via his investigations of the properties of Leyden Jars1. He is also commonly credited with giving the names ‘positive’ and ‘negative’ to the two opposite species of electrical charge, although his assignment convention was eventually reversed.Also living in America at the time was Priestley (1733-1804)2, an English chemist and amateur natural philosopher who had broad scientific interests in physics, electricity, magnetism, and optics, in addition to chemistry. He was a politically involved Unitarian preacher and a sympathizer with the French Revolution, and these aspects of1In 1752,he flew a kite attached to a silk string in a thunderstorm, and showed that a metal key tied to the thread would charge a Leyden jar. (Incidentally, the next two people who attempted the experiment were killed in the effort.) His experiments with Leydenjars showed that they discharged more easily if near a pointed surface. He thus suggested the use of lightning rods.2The objects of his chemical studies included ‘fixed air’ (carbon dioxide), ‘nitrous air’ (nitric oxide), ‘marine acid air’ (hydrogen chloride), ‘alkaline air’ his life forced him to move to America with his family in 1794. Priestley is credited with the discovery of oxygen in 1774, which he produced by focusing sunlight on mercuric oxide. Duri ng his studies of this ‘dephlogisticated air’, he noticed that it made him light-headed and that it had a similar effect on animals.The background studies underpinning Coulomb’s Law began when Franklin took a small sphere made of cork and placed it inside a charged metallic cup (see figure 1) and observed that it did not move, suggesting that there was no interaction between it and the cup. After Franklin communicated his finding to Priestley, the Englishman explained the phenomenon in 1767, providing a line of reasoning analogous to that used by Newton [3] to formulate and enunciate the law of universal gravitation.Underlying Newtonian gravity was the observation that the gravitational field inside a spherical shell of homogeneous material is null if the field is inversely proportional to the square of the distance r, i.e. if its intensity goes as r-2. By approximati ng Franklin’s cup as a spherical shell, Priestley deduced that the observed phenomenon should be physicallyon Different Kinds of Airs (1774-1777) and in the three-volume Experiments and Observations Relating to Various Branches of Natural Philosophie (1779-1786). By dissolving fixed air in water, he invented carbonated water. He also noticed that the explosion of inflammable air with common air produced dew. Lavoisier repeated this experiment and took credit for it. Priestley believed in the phlogiston theory, and was convinced that his discovery of oxygen proved it to be correct.0026-1394/04/050159+12$30.00 © 2004 BIPM and IOP Publishing Ltd Printed in theUKI NSTITUTE OF P HYSICS P UBLISHING M ETROLOGIAS159G Spavieri et alInsulatedmetallic cup^ -------- ^Figure 1. Franklin placed a small sphere made of cork inside a metallic cup, and when this was charged heobserved that the sphere did not move, suggesting that there was nointeraction between it and the cup. Priestley explained thephenomenon in 1767, providing a line of reasoning analogous to that used by Newton for the law of universal gravitation,implying that the field has an inverse square dependence on distance. In the subsequent tests, instead of the cork sphere inside a metallic cup, experimentalists considered a metallic shell enclosed within an outer charged shell or several concentric shells.analogous to the gravitational case and he thus concluded that the electric force, like the gravitational force, must depend on distance as r -2. The lack of an observed ponderable force on the cork sphere inside the charged spherical shell was thus evidence of an inverse square law behaviour in the electric force.Franklin’s work also served as inspiration for the efforts of Aepinus (1724-1802) [4], a German physicist 3. He made experimental and theoretical contributions to the study of electricity and in 1759 proposed in a theoretical essay, written in Latin, the existence of two types of electric charges (positive and negative) and a 1/r 2 behaviour of the electric force. His conjectures were made in analogy to what Newton had proposed in order to explain Kepler’s Law, the free fall of bodies near the Earth’s surface, and the outcome of Cavendish’s laboratory experiment that investigated the gravitational attraction between lead spheres [5].All of these early qualitative phenomenological and theoretical studies paved the way for the eventual quantitative verification of the basic law describing the electrical force. In fact, the essay of Aepinus was read by Robison (1739-1805) [6], an English physician who in 1769 carried out experimental tests of the inverse square law and used the results to surmise that it was indeed correct. His determination was made somewhat before that of Coulomb, but history has given the name of this interaction to the latter.2. Early experimental verifications of Coulomb’s Law Robison’s experiment was very straightforward. Hemeasured the repulsive force between two charged masses, equilibratedby the force of gravity acting on them. By knowing their weight, and by repeating the measurements at different distances, it was possible to calculate the size of the electrical force, evaluate its dependence on distance, and thus verify the exactness of the hypothesized 1/r 2 law.Fromhis observations, Robison deduced that the law must have the functional form3 He studied at Jena and Rostock and taught mathematics at Rostock from 1747 to 1755. After a brief stay in Berlin he went to St Petersburg as professor of physics and academician, remaining there until 1798 and rising to a high position as courtier to Catherine the Great.F a ⑴ where & represents a measure of the precision to which the 1/r 2 behaviour is verified. He found an upper limit of 0. 06 for & and thus could state that for masses in electrical repulsion to each other, the force went as r -2.06. However, for electrical attraction his limit was weaker, stated as r —c where c < 2, but still essentially confirming the expected r -2 dependence. Unfortunately, Robison did not publish his results until 1801, and by then Coulomb [7] had already presented his. The parameter & appearing in equation (1) and related to the precision of the 1/r 2 behaviour, is not very useful from a theoretical point of view but is retained here because of its common historical use. Subsequent theoretical developments and improved understanding of the foundations for high precision tests of Coulomb’s Law have led to the use of the quantity ^ = m y c/h =入—1 which, as consideredbelow, is well motivated theoretically and represents the inverse Compton wavelength of a photon of mass m y . Coulomb’s Law is violated if ^ = 0, i.e. if the photon mass is not zero. Before discussing Coulomb’s experiment, we note that Cavendish, in addition to his celebrated measurement of the mean density of the Earth, also carried out an early experiment on the physics of the electrical force. Inspired by the same idea that motivated his predecessors, he too considered a metallic spherical shell enclosed within an outer shell consisting of two hemispheres that could be opened or closed. In the closed position, the two hemispheres were connected electrically to an electrostatic machine and charged while in ohmic contact with the inner sphere. The hemispheres were then disconnected from the inner sphere and opened, and it was verified that they remained charged. At this point, an electrometer was used to check that the inner sphere was still uncharged, thus confirming the 1 /r 2 law but with an uncertainty that was smaller than that of Robison (less than 1/60 of the charge moved to the inner shell over the thin wire interconnecting the two spheres). With reference to equation (1), Cavendish obtained & 彡 0.03 . An improved version of the experiment was later performed by Maxwell [8], who increased the precision of the test and found that the exponent of r in Coulomb’s Law could differ from 2 by no more than e ^ 5 x 10—5. We now turn to the famous experiment of Coulomb of 1788. Charles Augustin de Coulomb (1736-1806) was a French physicist and a pioneer in electrical theory. He was born in Angouleme. He served as a military engineer for France in the West Indies, but retired to Blois at the time of the French Revolution to continue his research on magnetism, friction, and electricity. In 1777, he invented the torsion balance for the purpose of measuring the force of magnetic and electrical attractions. With this device, Coulomb was able to formulate the principle, now known as Coulomb’s Law, governing the interaction between electric charges. InPhysical implications of Coulomb’s Law V(r) — V(a) ~V(a)~ — 1 (6) :sM(a, r), (7) 1 M(a, r) (8)⑵where the value of the constant of proportionality, k , will be considered in section 7.The reasons why Coulomb achieved greater success and recognition than did his predecessors are essentially two. First, he performed his tests with combinations of both negative and positive charges. Cavendish used only charges of the same sign, but Coulomb sought to measure both attractive and repulsive forces. Second, he published his results immediately, while Robison did not make his findings available until 1801, thirteen years after Coulomb. Cavendish too delayed the dissemination of his work, and it thus garnered no attention until nearly a century later when a citation to it was given by Maxwell in his famous essay [8]. Coulomb’s prompt f(a + r) — f(a — r)'fO) , a r To first order in s, equation (6) yields V(r) — V(a) ~V(a)~ where a (a + r' ( 4a 2 、一 ln ( ---- ) — ln ( ^ ----- 2 r a r a 2 r 2 2 Since M(a, r) turns out to be of order unity, & is essentially the quotient [V (r) — V(a)]/V(a) of the measured potential difference, V(r) — V (a), and the applied voltage, V(a).Light sourceFigure 2. The Coulomb torsion balance was similar in principle to the torsion balance used by Cavendish for measurement of thegravitational attraction between masses. The interaction between the charged spheres produces a measurable twist in the torsion fibre, which lets the apparatus rotate until equilibrium is reached. By accurately measuring the torsion angle, Coulomb confirmed the 1/r 2 law with a precision surpassing that of the previous experiments of Robison and Cavendish.QdV (3) J (r 2 + a 2 — 2ar cos 0')(1+s)/2 f +1 dcos 0! J —1 (r 2 + a 2 — 2ar cos 0')(1+s)/2 +a) — — a) 2ar In the case & = 0 and V (r) = 2np j ■ const, 1779, Coulomb published the treatise Theorie des machines simples (Theory of Simple Machines), an analysis of friction in machinery. After the war Coulomb came out of retirement and assisted the new government in devising a metric system of weights and measures. The unit of quantity used to measure electrical charges, the coulomb, was named for him.His torsion balance, shown in figure 2, was similar in principle to that used by Cavendish for the measurement of the mean density of the Earth (now interpreted as a seminal laboratory test of Newtonian gravitation). The interaction between the charged spheres produces a torque that acts on the torsion fibre, with the apparatus then rotating until equilibrium is reached. By accurately measuring the torsion angle, Coulomb found a limiting value for & in equation ⑴ of & 彡 0.01，thus surpassing the precision of the previous experiments of Robison and Cavendish. The scalar expression for what has come to be known as Coulomb’s Law says that the force F between two charges q\ and q 2 separated by a distance r may be written in the simple formpublication of his results may signal that he was more aware than his colleagues of how fundamental and important this work was. 3. Null tests of Coulomb’s Law: theory The technique employed by Cavendish has been used in most of the experimental work done since then, as it turned out to be potentially the most sensitive. It is intrinsically a null experiment, in the sense that the experimentalist seeks to verify with great precision the absence of charge from the inner sphere, rather than having to measure with less precision a non-null physical quantity, such as the twist in the fibre, as in the torsion balance approach. Following Robison and Maxwell and supposing that the exponent in Coulomb’s Law is not —2 but — (2 + s), to first order in & the electric potential at a point r due to the charge density distribution p(r r ) is given by where Coulomb’s Law is perfectly valid, d(cos 0 0 1 (r 2 + a 2 — 2ar cos 0,)1/2 a ⑶ so that V ^^)—V (a) = 0 and the electric field inside the charged spherical shell vanishes. Thus, in tests of Coulomb’s Law, we are interested in the potential induced on a sphere of radius r by a charge distributed uniformly on a concentric sphere of radius a > r , i.e. If the charge is uniformly distributed on a spherical shell of radius a > r , then p(r !, = a8(r — a) and we may arbitrarily choose r to coincide with the z axis and expression (3) becomes a sin 01 d 沒'd# | r — r' |1+s P(r') V(r) V(r)G Spavieri et alE ♦ dl (9) 1 2/ 2 2、 {a—r ).(10) (11)As an alternative to equations (7) and (8), de Broglie [9] considered a simple generalization of Maxwell’s equations involving a small non-zero rest mass of the photon. In this case, two charges will repel each other by a Yukawa force derived from the potential The voltage across the inductor of capacity C is then given [15] bya V(r) — V(a)e —^r e -r/入 c=—= --------- ， r r where ^ = m y c/h =入—1 is the inverse Comptonwavelength of the photon. In the limit ^a 《1, U(r) = 1/r — ^ + 1 ^2r and equation (6)yieldsV(r) - V ⑷ ~Via)~ Although U(r) containsthe term i 丄,what is tested experimentally is the result of equation (10). Since the other tests of Coulomb’s Law are explicitly sensitive to |2 and not to i, the quadratic dependence of V (r) — V (a) on i makes a test based on this approach comparable to other tests. Thus, the potential difference V (r) — V (a) is not zero if Coulomb’s Law is invalid or, equivalently, if the photon rest mass is non-zero. For direct tests of Coulomb’s Law that consist of measuring the static potential difference of charged concentric shells, one may use either equation (7) or equation (10). However, one can also test Coul omb’s Law by determining i with independent, indirect methods. In general, these would rely on either finding possible variations due to the presence of the Yukawa potential(9) or on the standard fields of massless electrodynamics, such as, e.g., measurements at either large distances or long times, where the percentage effect would be much higher. Typical of these approaches are those that involve the magnetic field of the Earth. For example, one might consider (a) satellite verification that the magnetic field of the Earth falls off as 1/r 3 out to distances at which the solar wind is appreciable[10] , (b) observation of the propagation of hydromagnetic waves through the magnetosphere [11], (c) application of the Schrodinger external field method [12], or other methods such as those described below. The three approaches outlined above should all give roughly the same limit, | 彡 10-11 cm —1.In the high-frequency (direct) null test of Coulomb’s Law described below, it is convenient to start from a relativistically invariant linear generalization ofMaxwell’s equations, namely the Proca equations [13], which allow for a finite rest mass of the photon. Proca’s equations for a particle of spin 1 and mass m y are [14]4n(口 + ^ ~)A V = — J vc and Gauss’ Law becomes(12)Equation (12) may be applied to two concentric, conducting, spherical shells of radii r and a (a > r ) with an inductor across (i.e. in parallel with) this spherical capacitor. If a potential Voe_ is applied to the outer shell, the resulting electric field is [15]E(r) = (qr-2 — 1 ^2Voe 1(^t r)i where q is thetotal charge on the inner shell.(13) Save for the standard term q/C (which is zero when there is no charge on the inner shell), the term dependent on i in equation (14) coincides with that of equation (10). 4. Direct tests of Coulomb’s Law After the development of the phase-sensitive detectors such as lock-in amplifiers, new and more sensitive attempts to test Coulomb’s Law were made such as the ones by Plimpton and Lawton [16], Cochran and Franken [17], and Bartlett and Phillips [18]. In this section, we consider Maxwell’s derivation (equations (6) and (7)) applied to the simple case of a conducting sphere containing a smaller concentric sphere. The potential of the outer sphere is raised to a value V and the potential difference between them is measured. The actual shape of these conductors should not be relevant because the electric field inside a cavity of any shape vanishes unless Coulomb’s Law is violated. Thus, Cochran and Franken [17] could use conducting rectangular boxes in their experiment and set a limit of e 彡 0.9 x 10—11. The experiments of both Cavendish and Maxwell required connecting the inner sphere to an electrometer. The accuracy of the experiment was thus limited by fluctuations in the contact potentials while measuring the inner sphere’s voltage. Another problem was that of spontaneous ionization between the spheres. These problems were overcome by Plimpton and Lawton [16] by using alternating potentials. They developed a quasi-static method and charged the outer sphere with a slowly alternating current. The potential difference between the inner and outer spheres was detected with a resonant frequency electrometer. It consisted of an undamped galvanometer with amplifier, placed within the globes, and with the input resistor of the amplifier forming a permanent link connecting them, so as to measure any variable potential difference. No effect was observed when a harmonically alternating high potential V (>3000 V), from a condenser generator operating at the low resonance frequency of the galvanometer, was applied to the outer globe. The sensitivity was such that a voltage of 10—6 V was easily observable above the small level of background noise. With this technique they succeeded in reducing Maxwell’s limit to e ^ 2 x 10—9. Another of the classic ‘null experiments’ that tests the exactness of the electrostatic inverse square law was performed by Bartlett et al [19]. In this experiment, the outer shell of a spherical capacitor was raised to a potential V with respect to a distant ground and the potential difference V(r) — V(a) of equations (7) and (10) induced between the inner and outer shells was measured. Five concentric spheres were used and a potential difference of 40 kV at 2500 Hz was imposed between the two outer spheres. A lock-in detector with a sensitivity of about 0.2 nV measured the potentialPhysical implications of Coulomb’s Lawdifference between the inner two spheres. Any deviation inCoulomb’s law should lead to a non-null result for V (r)—V(a)proportional to e as shown by equation (7). The resultobtained by these authors was e彡 1 x 10—13. A comparableresult was found even whenG Spavieri et althe frequency was reduced to 250 Hz and the detector was synchronized with the charging current rather than with the charge itself.The best result obtained so far through developments of the original Cavendish technique is still that from 1971 by Williams et al [15], who improved an earlier experiment [20]. They used five concentric metallic shells in the form of icosahedra rather than spheres in order to reduce the errors due to charge dispersion. A high voltage and frequency signal was applied to the external shells and a very sensitive detector checked for any trace of a signal related to variable charging of the internal shell. The detector worked by amplifying the signal of the internal shell and comparing it with an identical reference signal, progressively out of phase atarhythmof 360° per half hour. Any signal from the detector would indicate a violation of Coulomb’s Law. In order to avoid introducing unrelated fields, the reference signal and the detector output signal were transmitted by means of optical fibres. The outer shell, of about 1.5 mdiameter, was charged 10 kV peak-to-peak with a 4 MHz sinusoidal voltage. Centred inside this charged conducting shell is a smaller conducting shell. Any deviation from Coulomb’s Law is detected by measuring the line integral of the electric field between these two shells with a detection sensitivity of about 10—12 V peak-to-peak.The null result of this experiment expressed in the form of the photon rest mass squared (equation (14) or equation (10)) is fj2 = 2.3 x 10—19 cm-2. Expressed as a deviation from Coulomb’s Law in the form of equation (7), their result is £ = 6 x 10—16, extending the validity of Coulomb’s Law by two orders of magnitude beyond the findings of Bartlett et al.5.Limits due to the effects of gravityWe have mentioned above that null experiments that test the validity of Coulomb’s Law are typically more precise than those that attempt to directly measure the interaction force between charges. One of the problems arising when making direct measurements of the force between two macroscopic charged bodies, as done when using a torsion balance, is that the charges are distributed over conducting surfaces of finite size. In the ideal case, Coulomb’s Law describes the interaction between two point charges separated by a precisely known distance. In any practical arrangement, even the charge on a microscopically small conducting ball cannot be considered to be truly point-like—as if placed at the centre— but rather distributed over the ball’s surface. If the charged ball is interacting with another charged ball, the distribution on the surface is no longer uniform and has to be determined using the method of images. Saranin [21] has studied in detail the departures from Coulomb’s La w that can occur when two conducting spheres interact electrostatically with each other. By computing forces on them as a function of their separation, he found that at small distances a switch from repulsion to attraction occurs in the general case of arbitrarily but similarly charged spheres. The only exception—and in it they always repel each other—is the case in which the charges on the spheres are related as the squares of their radii. The results of Saranin help corroborate the idea that, even in principle, null experiments can be more precise than tests based on the direct measurement of interaction forces between two macroscopic charged bodies.In view of the high levels of precision achieved in several of these tests, it is interesting to consider what possible competing effects gravity might introduce into them. The result f(a, r) in equation (5) was derived strictly from classical electrodynamics. In it, a uniform charge distribution is assumed and the effect of gravity is neglected. As noted by Plimpton and Lawton [16], if electrons have weight meg the electron density on the conducting sphere must be asymmetrical, being greater at the bottom where the electrons are pulled by the force of gravity. For the experiment of Plimpton and Lawton this effect is insignificant as it leads to a maximum potential difference over the globe of 10—10V, which is far less than the minimum detectable voltage of 10—6 V.Thus, while such a gravitational effect shouldbe negligible in the relatively low sensitivity experiment of Plimpton and Lawton, it could conceivably be important in experimental tests of higher sensitivity. According to this model, the overall effect of gravity is to produce a distortion in what should otherwise be a uniform charge distribution. Of course, the more general problem is to account for effects of a nonuniform charge distribution regardless of the origin of the non-uniformity. In equation (5), the null result comes from the assumption that Coulomb’s Law is valid and that the charge is distributed uniformly on the sphere. However, Shaw [22] objected to the assumption that the charge will distribute itself uniformly over a conducting spherical shell, even in the absence of any gravitational effect. In conventional electrostatics, the uniform charge distribution for Coulomb and Yukawa potentials follows from the symmetry of the problem and the uniqueness of the solution. If these potentials are not valid there is no guarantee of a uniform charge distribution and thus irregularities in the spherical surface would bias the concept that the inner potential does not depend on the shape of the outer sphere. However, considering that any violation of Coulomb’s Law is very small, departures from the expected uniformity should give [19] only second-order corrections to equations (7) and (8).6.Indirect tests of Coulomb’s LawIn addition to the tests discussed in the previous sections, there have also been a number of indirect experimental verifications of Coulomb’s Law, and these will be discussed briefly in what follows.6.1.Geomagnetic and astronomical testsA consequence of Coulomb’s Law is that the magnetic field produced by a dipole goes as 1/r3 at distances from its centre for which the dipole approximation is valid. For the magnetic field of a planet, this distance is equivalent to about two planetary radii (at least). If the photon rest mass is not zero—which is equivalent to a violation of Coulomb’s Law— a Yukawa factor e—r/lC is introduced in the 1/r terms for the electrostatic and magnetostatic potentials. In this case, the magnetic field produced by a dipole no longer goes as 1/r3 but。

压力限制肿瘤增长翻译中英

最后译文：压力限制肿瘤生长法国物理学家发现了简单的力压在医学上可应用于降低肿瘤的生长速度并限制其生长大小。

通过使用老鼠细胞来完成这项工作的研究者说这个结果可以引生出更好的癌症诊断工具并很可能最终实现用药物治疗癌症。

众所周知当生长细胞中的DNA发生突变时就会形成肿瘤并发展为癌症, .但是这种发展是如何受到肿瘤周围环境的影响仍是一个需要讨论的课题。

由巴黎居里学院的让.弗朗斯科乔尼和其他一些院校进行了一项新的调查，研究肿瘤的生长是如何受到它所经受的压力的限制的，如同按压周围的健康组织一样。

很难把基因学、生物化学和力学在生物机体内的肿瘤中所扮演的角色分离出来。

为了解释这一问题，乔尼的团队用老鼠细胞中的一个直径十余毫米的类似肿瘤的球在实验台上进行了这项工作，工作者们把这个模拟肿瘤放入一个由半渗透聚合物制成的几毫米长的袋子中，这之后就进入到一个滋生细胞的包含营养物的研究方案中。

肿瘤在这种自由的状态下会继续生长两周或者三周, 直到达到细胞的死亡和分裂刚好平衡的稳态。

糖分的严厉打击为了找出在这个生长过程中是什么影响到了压力, 小组在此方案中加入了很多糖分这些糖分由于颗粒太大而无法穿过袋子的微小孔洞所以仍在袋子外面，造成了一种浓度的不平衡，而使其迫切的要解决掉袋子外的溶液以努力恢复其浓度的平衡，袋子外较大浓度的溶液随即对袋子产生了力度的压迫，并且这种压迫被里面的肿瘤所感应到。

这种方法被重复用于同样的肿瘤上，每个不同袋子中的肿瘤被不同浓度的糖分溶液所浸透，因此揭示出每个肿瘤都受到了不同的压力。

该小组发现压力越大，肿瘤生长越慢并且最终尺寸越小。

比如施加500帕的压力，仅仅百分之两点五的气压），便可将肿瘤的增长率和稳态量减半。

为了精准地确立压力是如何减弱增长的，乔恩和他的同事将肿瘤冰冻起来，将其切成非常薄的薄片，.并在薄片上覆盖两种抗体，这个方法显示出了在每个肿瘤上已死亡而被分离的细胞----这两种细胞发出的荧光波长不同-。

Calculation of the Self Force using the Extended-Object Approach

1
Throughout the paper we use the metric ηµν = diag(−1, 1, 1, 1), and units where c =rces does not vanish (this has been established by many authors, as we discuss below, and it is also demonstrated explicitly later in this paper). This nonvanishing overall electromagnetic force does not conﬂict with the momentum conservation law, because the electromagnetic ﬁeld itself contains a time-varying amount of momentum and energy; A non-vanishing overall electromagnetic force acting on the object is thus a manifestation of a momentum transfer between the charged object and the surrounding electromagnetic ﬁeld. In particular, the electromagnetic radiation ﬁeld carries energy and momentum away from the object to inﬁnity (hence the name ”radiation-reaction force”). Recognizing that the overall mutual electromagnetic force does not vanish, one is tempted to identify this overall force with the notion of the self force acting on a charged particle. Thus, one would hope that at the limit were the object’s size is taken to zero, a universal result (independent of the object’s size and shape) will be obtained, which will coincide with Eq. (1). Many attempts have been made to derive this extended-object total force. Two types of models have been considered: objects that are continuously charged [3, 5, 6, 7], and objects with a ﬁnite number of discrete charges [7]. The simplest model of a discretelycharged rigid object is the ”dumbbell”, i.e. a ﬁxed-length rod with two point charges located at its two edges. The previous analyses of both the continuous and discrete models revealed that indeed the overall electromagnetic force does not generally vanish. But these analyses also indicated a fundamental diﬃculty (which we shortly explain), that made it impossible to derive the universal small-size limit of this force. The goal of this paper is to provide a simple resolution to this diﬃculty.

自由落体定律英语

自由落体定律英语The Law of Free FallThe law of free fall, also known as the law of gravitational acceleration, is a fundamental principle in physics that describes the motion of objects under the influence of gravity. This law, which was first formulated by Galileo Galilei in the early 17th century, states that the acceleration of an object due to the force of gravity is constant and independent of the object's mass or the medium through which it is falling.The basic premise of the law of free fall is that when an object is released from a certain height, it will accelerate downward at a constant rate, regardless of its weight or composition. This acceleration, known as the acceleration due to gravity, is typically denoted by the symbol "g" and has a value of approximately 9.8 meters per second squared (m/s²) near the Earth's surface.The mathematical expression of the law of free fall can be written as follows:s = 1/2 * g * t²where:- s is the distance traveled by the object (in meters)- g is the accel eration due to gravity (in m/s²)- t is the time elapsed since the object was released (in seconds)This equation demonstrates that the distance traveled by a falling object is proportional to the square of the time elapsed. In other words, as the time increases, the distance covered by the object increases exponentially.One of the key implications of the law of free fall is that all objects, regardless of their mass or composition, will fall at the same rate in a vacuum. This is because the acceleration due to gravity is independent of the object's mass. However, in the presence of air resistance or other external forces, the motion of a falling object can be affected, and the actual acceleration may deviate from the theoretical value of "g".The law of free fall has numerous applications in various fields, including physics, engineering, and astronomy. For example, it is used to calculate the trajectory of projectiles, the motion of satellites and spacecraft, and the behavior of objects in freefall experiments. It also plays a crucial role in the understanding of gravitational forces and the dynamics of planetary motion.Furthermore, the study of the law of free fall has led to the development of important concepts in physics, such as the conservation of energy, the concept of potential and kinetic energy, and the principles of classical mechanics.In conclusion, the law of free fall is a fundamental principle that describes the motion of objects under the influence of gravity. It has been extensively studied and applied in various scientific and technological fields, and its understanding continues to be a vital part of our knowledge of the physical world.。

弗思词项搭配的相互预见

弗思词项搭配的相互预见
剑桥改良英语词典（Collin's Cobuild Dictionary）中对Forces
的定义是：Forces 指人们为了实现某种目标而组织实施活动的一组力量。

1、Forces of nature：自然力量，指大自然力量，如风、雨、地震等，它们会影响人类未来发展。

2、Forces of gravity：重力力，指地球引力和太阳引力，它们影响
物体的运动。

3、Forces of public opinion：公众舆论力量，指公众的思想和情绪，它们能够影响政府的政策和行动。

4、Forces of the market：市场力量，指市场行为的力量，如供需
关系、竞争格局等，它们能够影响商品价格和供应量。

5、Forces of history：历史力量，指历史的推动力，指一个国家的
过去、现在和未来，它们在社会上留下无声的影响。

6、Forces of tradition：传统力量，指社会历史和文化背景下，社
会各个阶层传承并延续的行为习惯，它们影响着社会的发展方向。

8、Forces of technology：科技力量，指科学技术的发展和创新，
它们是推动社会进步的动力。

9、Forces of progress：进步力量，指社会的发展活动形成的力量，它们催生社会的先进思想，推动社会的前进。

10、Forces of inertia：惯性力量，指社会没有能力改变既有状态
的力量，它们会制约社会发展步伐。

安庆2024年06版小学第2次英语自测题(含答案)

安庆2024年06版小学英语自测题(含答案)考试时间：80分钟（总分:110）B卷考试人：_________题号一二三四五总分得分一、综合题(共计100题共100分)1. 填空题：A sloth moves very _______ (慢), hanging from trees.2. 听力题：I love to _______ (explore) new places.3. 听力题：They are learning to ________.4. 听力题：A garden needs _______ to thrive.5. 听力题：My ______ enjoys hiking in the mountains.6. 选择题：What color is the grass?A. BlueB. GreenC. RedD. Yellow7. 听力题：The chemical formula for calcium chloride is ______.8. 听力题：We see a _____ (car/bird) in the tree.9. 听力题：The turtle is ______ (slow) but steady.10. 选择题：What do we call the device used to look at distant objects?A. MicroscopeB. TelescopeC. PeriscopeD. Kaleidoscope11. 填空题：My dad works as a ________ (工程师).12. 选择题：What is the name of the famous river in South America?A. AmazonB. OrinocoC. ParanáD. All of the above13. 填空题：He is a _____ (评论员) who analyzes sports games.14. 填空题：A _____ (果汁) can be made from fresh fruits.15. 填空题：A squirrel has sharp ______ (爪子) for climbing.16. 选择题：What is the frozen form of water called?A. IceB. SnowC. HailD. Fog答案:A. Ice17. 填空题：The ________ is a friend to everyone it meets.18. 选择题：What do we call a young horse?A. FoalB. CalfC. KidD. Puppy答案:A19. 填空题：The ________ was a famous philosopher known for his teachings.The ancient Greeks developed the concept of ________.21. 填空题：The _______ (NATO) alliance was formed for mutual defense.22. 填空题：We have a ______ (愉快的) family day every month.23. 选择题：Which of these is a natural resource?A. PlasticB. WoodC. GlassD. Metal答案: B24. 听力题：Rust is a result of the reaction between iron and ______.25. 选择题：What do we use to write on paper?A. PaintB. PencilC. GlueD. Scissors26. 选择题：What is the name of the chemical element with the symbol "O"?A. OxygenB. HydrogenC. CarbonD. Nitrogen答案:A27. 听力题：A _______ grows close to the ground.28. 填空题：I saw a _______ (蟋蟀) in the grass.29. 听力题：I saw a _______ (butterfly) in the garden.30. ocean) is home to many fish and other marine life. 填空题：The ____The best time for a picnic is on a ______ (温暖的) day.32. 听力题：A ______ is a small, furry animal that lives in burrows.33. 听力题：A ______ is a cold-blooded animal.34. 听力题：A _______ is a substance that can conduct electricity when dissolved in water.35. 填空题：In geography, a ________ (平原) is a flat area of land.36. 听力题：The _______ of light can create shadows.37. 听力题：In a chemical reaction, the starting materials are called _____.38. 听力题：The flowers are very ______. (pretty)39. 选择题：How many continents are there in the world?A. SevenB. SixC. FiveD. Eight答案: A40. 听力题：I want to _____ (join/start) a club.41. 填空题：She is an athlete, ______ (她是一位运动员), and runs fast.42. 听力题：The puppy is _____ in the yard. (running)43. 填空题：The __________ is a famous city known for its flowers. (阿姆斯特丹)44. 填空题：In the garden, we have many ________ (树) and flowers that attract ________ (蜜蜂).My dad loves __________ (参观博物馆).46. 听力题：An extinct volcano is one that is unlikely to ______ again.47. 填空题：I like to draw ______ (漫画) in my free time. It allows me to express my creativity and tell funny ______ (故事).48. 听力题：The main gas that plants take in is __________.49. 选择题：How many continents are there?A. FiveB. SixC. SevenD. Eight50. 填空题：We have a ______ (精彩的) event planned for next month.51. 选择题：What is the primary function of the kidneys?A. To pump bloodB. To filter wasteC. To digest foodD. To produce hormones答案: B. To filter waste52. 填空题：I saw a _______ (小蝴蝶) fluttering by.53. 选择题：Which season comes after winter?A. FallB. SummerC. SpringD. Rainy54. 选择题：What is the name of the famous British writer who created Sherlock Holmes?A. Charles DickensB. J.K. RowlingC. Agatha ChristieD. Arthur Conan Doyle答案:D55. 填空题：The __________ (冷战) led to the space race between the USA and USSR.56. 填空题：I love the feeling of the ______ (微风) on my face.57. 选择题：What do we call a person who creates art?A. ArtistB. ScientistC. WriterD. Musician答案：A58. 选择题：What is 8 x 2?A. 12B. 14C. 16D. 18答案:C59. 填空题：My ________ (玩具) is full of surprises.60. 选择题：What do we call the temperature at which a liquid boils?A. Freezing pointB. Melting pointC. Boiling pointD. Critical point答案: C. Boiling point61. 听力题：My mom loves to decorate our ____ (home).62. 选择题：What is the name of the largest rainforest in the world?A. Amazon RainforestB. Congo RainforestC. TaigaD. Temperate Rainforest答案:A63. 选择题：What is the hardest natural substance on Earth?A. GoldB. DiamondC. IronD. Quartz答案:B64. 填空题：The flowers in the garden attract _______ and happy bees buzzing around.65. 听力题：The Earth’s crust is made up of many different _______.66. 听力题：An ion is an atom that has gained or lost ______.67. 听力题：My cousin is a ______. She loves to design clothes.68. 填空题：A penguin waddles when it ________________ (走).69. 选择题：What is the capital of Iceland?A. ReykjavikB. OsloC. HelsinkiD. Copenhagen答案: A70. 填空题：_____ (地下根系) stabilize plants during storms.71. 选择题：What do we call the time when the sun rises?A. SunsetB. SunriseC. NoonD. Midnight72. 填空题：We should _______ the environment.What is the name of the famous battle fought in 1066?A. Battle of HastingsB. Battle of WaterlooC. Battle of GettysburgD. Battle of Agincourt74. 听力题：She is ___ (reading/writing) a poem.75. 选择题：What do we call the study of the universe?A. BiologyB. AstronomyC. GeologyD. Physics答案: B76. 选择题：Which animal is known for its speed?A. TortoiseB. HareC. SlothD. Snail答案:B77. 听力题：A chemical reaction can be influenced by temperature, concentration, and _____.78. 填空题：The __________ (绿叶) produce oxygen for us to breathe.79. 填空题：We should reduce ______ (浪费) to protect nature.80. 填空题：The ancient Romans were known for their ________ (法律).81. 选择题：What is the name of the device used to see small things?A. MicroscopeB. TelescopeC. BinocularsD. Magnifying Glass答案:AWhat do you call a vehicle that travels on tracks?A. BusB. TrainC. CarD. Bicycle答案:B83. 听力题：The ____ has bright feathers and sings sweetly.84. 选择题：What do we call a material that can conduct electricity?A. InsulatorB. ConductorC. ResistorD. Capacitor答案: B85. 听力题：A __________ is a small animal that loves to dig.86. 填空题：I find ________ (生态学) very interesting.87. 选择题：What is the capital of Egypt?A. CairoB. AlexandriaC. LuxorD. Giza答案: A88. 选择题：What is the capital of Azerbaijan?A. BakuB. GanjaC. LankaranD. Mingachevir答案: A89. 选择题：What is the main ingredient in mayonnaise?A. EggB. OilC. VinegarD. All of the above90. 填空题：A __________ (合成材料) is made from natural or artificial substances.91. 填空题：The __________ during the summer can be very humid. (天气)92. 听力题：I enjoy ______ (listening) to music.93. 填空题：Mount Kilimanjaro is found in _____ (14).94. 填空题：Abraham Lincoln delivered the Gettysburg __________ (演讲) during the Civil War.95. 听力题：We go to school _____ foot. (on)96. 填空题：The bus driver, ______ (公交司机), drives us to school.97. 听力题：A chemical that can be oxidized is called a ______.98. 填空题：The _____ (pampas grass) sways in the wind.99. 听力题：The _____ (ball/box) is round.100. 选择题：Which animal is known for its long ears and hopping?A. SquirrelB. RabbitC. KangarooD. Deer答案: B。

the forces of attraction on h2 bubbles 英语

the forces of attraction on h2 bubbles 英语The Forces of Attraction on H₂ BubblesHydrogen gas (H₂) bubbles are a fascinating subject in the study of chemistry and physics. These bubbles, often observed in various chemical reactions or electrolysis processes, are influenced by several forces of attraction that dictate their behavior and stability. Understanding these forces is crucial for comprehending the dynamics of gas bubbles and their applications in different scientific and industrial contexts.Firstly, the **van der Waals forces** play a significant role in the interaction between hydrogen molecules within the bubbles. These are weak,non-covalent forces that arise from temporary dipole moments in the molecules. Although hydrogen molecules are nonpolar, van der Waals forces can still cause slight attractions between them. In a bubble, these forces contribute to the cohesion of the hydrogen molecules, helping to maintain the bubble's structure.Secondly, the **surface tension** of the liquid in which the hydrogen bubbles are present also affects their behavior. Surface tension is the result of cohesive forces between the molecules in the liquid, which tends to minimize the surface area of the bubble. For hydrogen bubbles, surface tension acts to keep the bubble spherical, reducing its surface area and stabilizing its shape. This force is particularly important in determining the size and stability of the bubbles.Additionally, **hydrophobic interactions** can be relevant when hydrogen bubbles are in a non-polar environment or when there are other substances present that interact weakly with water. These interactions can influence how the bubbles rise or coalesce with other bubbles. In a solution where hydrogen is being produced, such as during electrolysis, these interactions can affect how the bubbles form and aggregate.Moreover, the **pressure difference** between theinside and outside of the bubble also plays a crucial role. This difference in pressure, known as Laplace pressure, is influenced by the surface tension and can affect the stability and size of the bubble. A higher internal pressure compared to the external pressure can cause the bubble to expand or even burst if the pressure difference becomes too great.In conclusion, the forces of attraction on H₂ bubbles are multifaceted and involve a combination of van der Waals forces, surface tension, hydrophobic interactions, and pressure differences. Each of these forces contributes to the behavior, stability, and dynamics of hydrogen bubbles in various environments. By understanding these forces, scientists and engineers can better control and utilize hydrogen bubbles in a range of applications, from industrial processes to scientific experiments.---。

吉林2024年05版小学4年级第十一次英语第五单元暑期作业

吉林2024年05版小学4年级英语第五单元暑期作业考试时间：90分钟（总分:120）A卷考试人：_________题号一二三四五总分得分一、综合题(共计100题)1、填空题：The _______ (D-Day) invasion occurred on June 6, 1944, during WWII.2、填空题：A rabbit's fur can be very ______ (温暖).3、What do we call a building where we learn?A. LibraryB. SchoolC. HospitalD. Market答案:B4、How many sides does a square have?A. ThreeB. FourC. FiveD. Six5、听力题：The chemical formula for sodium acetate is _______.6、填空题：The first archaeological site to be excavated was in ________ (美索不达米亚).7、听力题：I see a _______ (fox) in the forest.8、填空题：I call my mom “.”9、填空题：The ancient Egyptians used ________ to write their history.10、填空题：My dog gets excited when it's time for a _______ (散步).11、听力填空题：I love exploring different cuisines. My favorite dish is __________.12、填空题：I have a _____ (画板) where I draw pictures of animals.我有一个画板，画动物的图画。

包头2024年02版小学6年级第13次英语第三单元测验试卷

包头2024年02版小学6年级英语第三单元测验试卷考试时间：100分钟（总分:140）A卷考试人：_________题号一二三四五总分得分一、综合题(共计100题)1、听力题：A ____ is a loyal companion that loves to be with humans.2、What do we call the study of the atmosphere and weather?A. MeteorologyB. ClimatologyC. GeographyD. Environmental Science3、填空题：The penguin waddles _______ (走路) on ice.4、听力题：The chemical formula for calcium acetate is ______.5、听力题：A precipitate forms when two liquids react to form a ______.6、填空题：The sun is _______ in the sky.7、What is the capital of Argentina?A. Buenos AiresB. SantiagoC. LimaD. Bogotá答案:A8、听力题：The park is ________ from my house.I have a _____ (玩具飞机) that flies high.10、听力题：The chemical symbol for vanadium is ______.11、填空题：The _____ (企鹅) waddles across the ice, looking for fish.企鹅在冰上摇摇晃晃地走，寻找鱼。

12、What do we call the first month of the year?A. FebruaryB. MarchC. JanuaryD. April13、填空题：The ________ is a smart animal that can learn tricks.14、听力题：My favorite place is the ________.15、听力题：The _______ needs care and attention.16、听力题：Animals that eat both plants and meat are called ______.17、填空题：I learned about different types of ______ (树) in science class. They are very ______ (重要).18、听力题：My mom _____ breakfast every morning. (prepares)19、听力题：Asteroids are rocky objects that orbit the ______.20、What do you call a baby shark?A. PupB. CalfC. KitD. Cub21、填空题：In winter, I wear _______ (厚衣服) to stay warm.The ______ is home to many fish.23、填空题：The porcupine has sharp _________ (刺).24、听力题：The chemical symbol for carbon is ______.25、填空题：The _____ (袋鼠) carries its baby in a pouch.26、填空题：The _____ (草) is soft and green.27、听力题：I can speak ________ languages.28、Which season comes after winter?A. FallB. SummerC. SpringD. Autumn答案: C29、填空题：The owl has a ______ (敏锐的) sense of hearing.30、听力题：I have _____ (three/four) pets.31、填空题：The first hydrogen bomb was tested in ________ (1952).32、听力题：My sister is _____ a song. (singing)33、填空题：__________ (化学危险性) must be assessed before handling reagents.34、听力填空题：I love exploring new hobbies. Recently, I tried __________.35、选择题：What is the main ingredient in a smoothie?A. MilkB. IceC. FruitD. All of the above36、听力题：A non-renewable resource is one that cannot be _______ quickly.37、填空题：I want to be a ________ (记者) when I grow up.38、What do we call the act of improving one's skills?A. TrainingB. DevelopmentC. EducationD. All of the Above答案：D39、听力题：A saturated solution contains the maximum amount of solute that can be _____ at a given temperature.40、听力题：I like to play ______ (puzzles) with my family.41、填空题：My pet has a _______ (特别的) toy it loves.42、填空题：The goldfish is one of the most popular ______ (宠物) in homes.43、听力题：The simplest type of sugar is called a ______.44、What type of animal is a dolphin?A. FishB. ReptileC. MammalD. Amphibian答案:C45、填空题：A ______ (学习) about botany can lead to new discoveries.46、填空题：I have a ________ that tells time.The _______ Pole is located at the top of the Earth.48、填空题：A peacock spreads its ______ (羽毛) to attract mates.49、What is the capital of Micronesia?A. PalikirB. KoloniaC. WenoD. Yap答案:A50、填空题：I want to _______ a new adventure.51、填空题：I have a _______ (宠物) that loves to cuddle.52、听力题：The chemical symbol for tungsten is __________.53、听力题：A balanced chemical equation has the same number of _____ (atoms) on both sides.54、What do you call a person who helps sick people?A. DoctorB. TeacherC. NurseD. Scientist答案:A55、填空题：A ________ (青蛙) jumps from lily pad to lily pad in the pond.56、听力题：A __________ is a measure of how acidic or basic a solution is.57、What is the term for the scientific study of plants?A. BiologyB. BotanyC. ChemistryD. Physics答案:BThe main gas produced during respiration is __________.59、听力题：The _____ (car/bike) is red.60、Which animal is known as the king of the jungle?A. ElephantB. LionC. TigerD. Bear61、听力题：I have a ________ in my backpack.62、填空题：A hamster loves to run on its ______ (轮子).63、填空题：The ant builds its ______ (巢) underground.64、听力题：I enjoy ________ in the garden.65、听力题：The product of a chemical reaction is found on the _______ side of the equation.66、What do you call a young deer?A. CalfB. FawnC. KitD. Cub67、填空题：My ________ (玩具名称) can float on water.68、填空题：The _____ (气候变化) impacts many plant species.69、听力题：The chemical formula for table salt is _______.70、听力题：All living things are made up of _____.The flamingo stands on one _______ (腿).72、Which fruit is yellow and curved?A. OrangeB. BananaC. PearD. Apple73、选择题：What is the capital of Latvia?A. RigaB. VilniusC. TallinnD. Minsk74、填空题：Many flowers have a specific ______ that makes them attractive to insects. (许多花都有特定的颜色，使它们对昆虫有吸引力。