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Josephson Constant

Josephson constant

The magnetic flux quantum Φ₀ is the quantum of magnetic flux passing through a superconductor. The inverse of the flux quantum, 1/Φ₀, is called the Josephson constant, and is denoted K_J. The quantization of magnetic flux is closely related to the Aharonov-Bohm effect, but was predicted earlier by F. London in 1948 using a phenomenological model.

Introduction

It is a property of a supercurrent (superconducting electrical current) that the magnetic flux passing through any area bounded by such a current is quantized. The quantum of magnetic flux is a physical constant, as it is independent of the underlying material as long as it is a superconductor. Its value is :

\Phi_0 = \frac = 2.067833636 \times 10^\,\mathrm

If the area under consideration consists entirely of superconducting material, the magnetic flux through it will be zero, for supercurrents always flow in such a way as to expel magnetic fields from the interior of a superconductor, a phenomenon known as the Meissner effect. A non-zero magnetic flux may be obtained by embedding a ring of superconducting material in a normal (non-superconducting) medium. There are no supercurrents present at the center of the ring, so magnetic fields can pass through. However, the supercurrents at the boundary will arrange themselves so that the total magnetic flux through the ring is quantized in units of Φ₀. This is the idea behind SQUIDs, which are the most accurate type of magnetometer available. A similar effect occurs when a superconductor is placed in a magnetic field. At sufficiently high field strengths, some of the magnetic field may penetrate the superconductor in the form of thin threads of material that have turned normal. These threads, which are sometimes called fluxons because they carry magnetic flux, are in fact the central regions ("cores") of vortices in the supercurrent. Each fluxon carries an integer number of magnetic flux quanta.

Measuring the magnetic flux

The magnetic flux quantum may be measured with great precision by exploiting the Josephson effect. In fact, when coupled with the measurement of the quantum Hall resistance quantum R_H = h / e², this provides the most precise values of Planck's constant h obtained to date. This is remarkable since h is generally associated with the behavior of microscopically small systems, whereas the quantization of magnetic flux in a superconductor and the quantum Hall effect are both collective phenomena associated with thermodynamically large numbers of particles. Category:Superconductivity Category:Magnetism

Quantum

:For the article about the manufacturer of computer peripherals, see Quantum Corporation. :For the comic book character, see Quantum (comics). The word quantum, pl. "quanta", comes from the Latin "quantus", for "how much". In general, it refers to an "amount of something". But, the term is often used in the more specific sense which it has in physics, where a quantum refers to an indivisible, and perhaps elementary entity. For instance, a "light quantum", being a unit of light (that is, a photon). In combinations like "quantum mechanics", "quantum optics", etc., it distinguishes a more specialized field of study. Behind this, one finds the fundamental notion that a physical property may be "quantized", referred to as "quantization". This means that the magnitude can take on only certain numerical values, rather than any value, at least within a range. For example, the energy of an electron bound to an atom (at rest) is quantized. This accounts for the stability of atoms, and matter in general. An entirely new conceptual framework was developed around this idea, during the first half of the 1900s. Usually referred to as quantum "mechanics", it is regarded by virtually every professional physicist as the most fundamental framework we have for understanding and describing nature, for the very practical reason that it works. It is "in the nature of things", not a more or less arbitrary human preference.

Discovery of quantum theory

Quantum theory, the branch of physics based on quantization, began in 1900 when Max Planck published his theory explaining the emission spectrum of black bodies. In that paper Planck used the Natural system of units invented by him the previous year. The consequences of the differences between classical and quantum mechanics quickly became obvious. But it was not until 1926, by the work of Werner Heisenberg, Erwin Schrödinger, and others, that quantum mechanics became correctly formulated and understood mathematically. Despite tremendous experimental success, the philosophical interpretations of quantum theory are still widely debated. Planck was reluctant to accept the new idea of quantization, as were many others. But, with no acceptable alternative, he continued to work with the idea, and found his efforts were well received. Eighteen years later, he called it, "a few weeks of the most strenuous work" of his life, when he accepted the Nobel Prize in Physics for his contributions. During those few weeks, he even had to discard much of his own theoretical work from the preceding years. Quantization turned out to be the only way to describe the new, and detailed experiments which were just then being performed. He did this practically overnight, openly reporting his change of mind to his scientific colleagues, in the October, November, and December meetings of the German Physical Society, in Berlin, where the black body work was being intensely discussed. In this way, careful experimentalists (including F. Paschen, O.R. Lummer, E. Pringsheim, H.L. Rubens, and F. Kurlbaum), and a reluctant theorist, ushered in the greatest revolution science has ever seen.

The quantum black-body radiation formula

When a body is heated, it emits radiant heat, a form of electromagnetic radiation in the infrared region of the EM spectrum. All of this was well understood at the time, and of considerable practical importance. When the body becomes red-hot, the red wavelength parts start to become visible. This had been studied over the previous years, as the instruments were being developed. However, most of the heat radiation remains infrared, until the body becomes as hot as the surface of the Sun (about 6000 °C, where most of the light is green in color). This was not achievable in the laboratory at that time. What is more, measuring specific infrared wavelengths was only then becoming feasible, due to newly developed experimental techniques. Until then, most of the electromagnetic spectrum was not measurable, and therefore blackbody emission had not been mapped out in detail. The quantum black-body radiation formula, being the very first piece of quantum mechanics, appeared Sunday evening October 7, 1900, in a so-called back-of-the-envelope calculation by Planck. It was based on a report by Rubens (visiting with his wife) of the very latest experimental findings in the infrared. Later that evening, Planck sent the formula on a postcard, which Rubens had the following morning. A couple of days later, he could tell Planck that it worked perfectly. As it does to this day. At first, it was just a fit to the data. Only weeks later did it turn out to enforce quantization. That the latter became possible involved a certain amount of luck (or skill, even though Planck himself called it "a fortuitous guess at an interpolation formula"). It only had that drastic "side effect" because the formula happened to become fundamentally correct, in regard to the as yet non-existent quantum theory. And normally, that much is not at all expected. The skill lay in simplifying the mathematics, so that this could happen. And here Planck used hard won experience from the previous years. Briefly stated, he had two mathematical expressions:
- (i) from the previous work on the red parts of the spectrum, he had x;
- (ii) now, from the new infrared data, he got x². Combining these as x(a+x), he still has x, approximately, when x is much smaller than a ( the red end of the spectrum). But now also x², again approximately, when x is much larger than a (in the infrared). The luck part is that, this procedure turned out to actually give something completely right, far beyond what could reasonably be expected. The formula for the energy E, in a single mode of radiation at frequency f, and temperature T, can be written :

E = \frac

This is (essentially) what is being compared with the experimental measurements. There are two parameters to determine from the data, written in the present form by the symbols used today: h is the new Planck's constant, and k is Boltzmann's constant. Both have now become fundamental in physics, but that was by no means the case at the time. The "elementary quantum of energy" is hf. But such a unit does not normally exist, and is not required for quantization.

The birthday of quantum mechanics

From the experiments, Planck deduced the numerical values of h and k. Thus he could report, in the German Physical Society meeting on December 14, 1900, where quantization (of energy) was revealed for the first time, values of the Avogadro-Loschmidt number, the number of real molecules in a mole, and the unit of electrical charge, which were more accurate than those known until then. This event has been referred to as "the birthday of quantum mechanics".

Quantization in antiquity

In a sense, it can be said that the quantization idea is very old. A string under tension, and fixed at both ends, will vibrate at certain quantized frequencies, corresponding to various standing waves. This, of course, is the basis of music. The basic idea was regarded as essential by the Pythagoreans, who are reported to have held numbers in high esteem. It is a curious fact that, the famous formula, named after Pythagoras, for the side lengths of a right triangle, today serves as a cornerstone of quantum mechanics as well. The very existence of atoms and molecules can be ascribed to various forms of quantization contrary to notions of matter as some form of continuous medium. This was also understood already in antiquity, particularly by Leucippos and Democritos, although not generally appreciated, even by physicists, until the late 19th- and early 20th- centuries, shortly before the invention of quantum mechanics. It should be mentioned, though, that later works within the Epicurean school of thought played a significant role in forming the physics and chemistry of the Renaissance period in Europe. In particular the famous tutorial poem "De rerum natura" by the Roman author Titus Lucretius Carus.

References

- J. Mehra and H. Rechenberg, The Historical Development of Quantum Theory, Vol.1, Part 1, Springer-Verlag New York Inc., New York 1982.
- Lucretius, "On the Nature of the Universe", transl. from the Latin by R.E. Latham, Penguin Books Ltd., Harmondsworth 1951. There are, of course, many translations, and the translation's title varies. Some put emphasis on how things work, others on what things are found in nature.
- M. Planck, A Survey of Physical Theory, transl. by R. Jones and D.H. Williams, Methuen & Co., Ltd., London 1925 (Dover editions 1960 and 1993) including the Nobel lecture.

Magnetic flux

Magnetic flux, is a measure of quantity of magnetism, taking account of the strength and the extent of a magnetic field. The flux through an element of area perpendicular to the direction of magnetic field is given by the product of the magnetic field density and the area element. More generally, magnetic flux is defined by a scalar product of the magnetic field density and the area element vector. Gauss's law for magnetism, which is one of the four Maxwell's equations, states that the total magnetic flux through a closed surface is zero. This law is a consequence of the empirical observation that magnetic monopoles do not exist or are not measureable. The SI unit of magnetic flux is the weber, and the unit of magnetic flux density is the weber per square meter. In symbols, this means: :

\Phi_m \equiv \int \!\!\! \int \mathbf \cdot d\mathbf S

where

\Phi_m \

is the magnetic flux and B is the magnetic flux density. We know from Gauss's law that :

\nabla \cdot \mathbf=0

This equation, in combination with the divergence theorem, provides the following result: :

\oint \!\!\! \oint_ \mathbf \cdot d\mathbf=\int \!\!\! \int \!\!\! \int_V \nabla \cdot \mathbf \, d\tau = 0

. In other words, the magnetic flux through any closed surface must be zero. By way of contrast, Gauss's law for electric fields, another of Maxwell's equations, is :

\nabla \cdot \mathbf =

indicating the presence of electric monopoles. By the same token, there are no magnetic monopoles. The direction or vector of the magnetic flux is by definition from the south to the north pole of a magnet (within the magnet). Outside of the magnet, the field lines will go from north to south. A change of magnetic flux in a spool of electrical conductive wire called a solenoid will cause an electric current in the spool. This is the basis of the production of electricity. When turned around, that is, running a current through a spool, a magnetic flux will be produced in the spool. This is electromagnetism. The relationship is given by Faraday's Law: :

\mathcal = \oint \mathbf \cdot d\mathbf = -

Superconductor

underneath) demonstrates the Meissner effect.]] Superconductivity is a phenomenon occurring in certain materials at low temperatures, characterised by the complete absence of electrical resistance and the damping of the interior magnetic field (the Meissner effect). In conventional superconductors, superconductivity is caused by a force of attraction between certain conduction electrons arising from the exchange of phonons, which causes the conduction electrons to exhibit a superfluid phase composed of correlated pairs of electrons. There also exists a class of materials, known as unconventional superconductors, that exhibit superconductivity but whose physical properties contradict the theory of conventional superconductors. In particular, the so-called high-temperature superconductors superconduct at temperatures much higher than should be possible according to the conventional theory (though still far below room temperature.) There is currently no complete theory of high-temperature superconductivity. Superconductivity occurs in a wide variety of materials, including simple elements like tin and aluminium, various metallic alloys, some heavily-doped semiconductors, and certain ceramic compounds containing planes of copper and oxygen atoms. The latter class of compounds, known as the cuprates, are high-temperature superconductors. Superconductivity does not occur in noble metals like gold and silver, nor in most ferromagnetic metals, though a number of materials displaying both superconductivity and ferromagnetism have been discovered in recent years. Superconductivity is an essentially quantum mechanical phenomenon, and cannot be understood simply as the idealization of "perfect conductivity" in classical physics.

Elementary properties of superconductors

Most of the physical properties of superconductors vary from material to material, such as the heat capacity and the critical temperature at which superconductivity is destroyed. On the other hand, there is a class of properties that are independent of the underlying material. For instance, all superconductors have exactly zero resistivity to low applied currents when there is no magnetic field present. The existence of these "universal" properties imply that superconductivity is a thermodynamic phase, and thus possess certain distinguishing properties which are largely independent of microscopic details.

Zero electrical resistance

The simplest method to measure the electrical resistance of a superconductor is to place the sample in an electrical circuit, in series with a voltage (potential difference) source V (such as a battery), and measure the resulting current. If the resistance of the remaining circuit elements (such as the leads connecting the sample to the rest of the circuit, and the source's internal resistance) is R, the current passing through the sample is V/R. According to Ohm's law, this means that the resistance of the superconducting sample is zero. Superconductors are also able to maintain a current with no applied voltage whatsoever, a property exploited in superconducting electromagnets such as those found in MRI machines. Experiments have demonstrated that currents in superconducting coils can persist for years without any measurable degradation. Experimental evidence points to a current lifetime of at least 100,000 years, and theoretical estimates for the lifetime of persistent current exceed the lifetime of the universe. In a normal conductor, an electrical current may be visualized as a fluid of electrons moving across a heavy ionic lattice. The electrons are constantly colliding with the ions in the lattice, and during each collision some of the energy carried by the current is absorbed by the lattice and converted into heat (which is essentially the vibrational kinetic energy of the lattice ions.) As a result, the energy carried by the current is constantly being dissipated. This is the phenomenon of electrical resistance. The situation is different in a superconductor. In a conventional superconductor, the electronic fluid cannot be resolved into individual electrons, instead consisting of bound pairs of electrons known as Cooper pairs. This pairing is caused by an attractive force between electrons from the exchange of phonons. Due to quantum mechanics, the energy spectrum of this Cooper pair fluid possesses an energy gap, meaning there is a minimum amount of energy ΔE that must be supplied in order to excite the fluid. Therefore, if ΔE is larger than the thermal energy of the lattice (given by kT, where k is Boltzmann's constant and T is the temperature), the fluid will not be scattered by the lattice. The Cooper pair fluid is thus a superfluid, meaning it can flow without energy dissipation. In a class of superconductors known as type II superconductors (including all known high-temperature superconductors), an extremely small amount of resistivity appears at temperatures not too far below the nominal superconducting transition when an electrical current is applied in conjunction with a strong magnetic field (which may be caused by the electrical current). This is due to the motion of vortices in the electronic superfluid, which dissipates some of the energy carried by the current. If the current is sufficiently small, the vortices are stationary, and the resistivity vanishes. The resistance due to this effect is tiny compared with that of non-superconducting materials, but must be taken into account in sensitive experiments. However, as the temperature decreases far enough below the nominal superconducting transition, these vortice can become frozen into a disordered but stationary phase known as a "vortex glass". Below this vortex glass transition temperature, the resistance of the material becomes truly zero.

Superconducting phase transition

superfluid In superconducting materials, the characteristics of superconductivity appear when the temperature T is lowered below a critical temperature T_c. The value of this critical temperature varies from material to material. Conventional superconductors usually have critical temperatures ranging from less than 1K to around 20K. Solid mercury, for example, has a critical temperature of 4.2K. As of 2001, the highest critical temperature found for a conventional superconductor is 39 K for magnesium diboride (MgB₂), although this material displays enough exotic properties that there is doubt about classifying it as a "conventional" superconductor. Cuprate superconductors can have much higher critical temperatures: YBa₂Cu₃O₇, one of the first cuprate superconductors to be discovered, has a critical temperature of 92 K, and mercury-based cuprates have been found with critical temperatures in excess of 130 K. The explanation for these high critical temperatures remains unknown. (Electron pairing due to phonon exchanges explains superconductivity in conventional superconductors, but it does not explain superconductivity in the newer superconductors that have a very high T_c.) The onset of superconductivity is accompanied by abrupt changes in various physical properties, which is the hallmark of a phase transition. For example, the electronic heat capacity is proportional to the temperature in the normal (non-superconducting) regime. At the superconducting transition, it suffers a discontinuous jump and thereafter ceases to be linear. At low temperatures, it varies instead as e^−α/T for some constant α. (This exponential behavior is one of the pieces of evidence for the existence of the energy gap.) The order of the superconducting phase transition is still a matter of debate. It had long been thought that the transition is second-order, meaning there is no latent heat. However, recent calculations have suggested that it may actually be weakly first-order due to the effect of long-range fluctuations in the electromagnetic field.

Meissner effect

When a superconductor is placed in a weak external magnetic field H, the field penetrates the superconductor for only a short distance λ, called the penetration depth, after which it decays rapidly to zero. This is called the Meissner effect, and is a defining characteristic of superconductivity. For most superconductors, the penetration depth is on the order of 100 nm. The Meissner effect is sometimes confused with the kind of diamagnetism one would expect in a perfect electrical conductor: according to Lenz's law, when a changing magnetic field is applied to a conductor, it will induce an electrical current in the conductor that creates an opposing magnetic field. In a perfect conductor, an arbitrarily large current can be induced, and the resulting magnetic field exactly cancels the applied field. The Meissner effect is distinct from this because a superconductor expels all magnetic fields, not just those that are changing. Suppose we have a material in its normal state, containing a constant internal magnetic field. When the material is cooled below the critical temperature, we would observe the abrupt expulsion of the internal magnetic field, which we would not expect based on Lenz's law. The Meissner effect was explained by London and London, who showed that the electromagnetic free energy in a superconductor is minimized provided :

\nabla^2\mathbf = \lambda^ \mathbf\,

where :H is the magnetic field and λ is the penetration depth. This equation, which is known as the London equation, predicts that the magnetic field in a superconductor decays exponentially from whatever value it possesses at the surface. decays exponentially The Meissner effect breaks down when the applied magnetic field is too large. Superconductors can be divided into two classes according to how this breakdown occurs. In Type I superconductors, superconductivity is abruptly destroyed when the strength of the applied field rises above a critical value H_c. Depending on the geometry of the sample, one may obtain an intermediate state consisting of regions of normal material carrying a magnetic field mixed with regions of superconducting material containing no field. In Type II superconductors, raising the applied field past a critical value H_c1 leads to a mixed state in which an increasing amount of magnetic flux penetrates the material, but there remains no resistance to the flow of electrical current as long as the current is not too large. At a second critical field strength H_c2, superconductivity is destroyed. The mixed state is actually caused by vortices in the electronic superfluid, sometimes called fluxons because the flux carried by these vortices is quantized. Most pure elemental superconductors (except niobium, technetium, vanadium and carbon nanotubes) are Type I, while almost all impure and compound superconductors are Type II.

Theories of superconductivity

Since the discovery of superconductivity, great efforts have been devoted to finding out how and why it works. During the 1950s, theoretical condensed matter physicists arrived at a solid understanding of "conventional" superconductivity, through a pair of remarkable and important theories: the phenomenological Ginzburg-Landau theory (1950) and the microscopic BCS theory (1957). Generalizations of these theories form the basis for understanding the closely related phenomenon of superfluidity, but the extent to which similar generalizations can be applied to unconventional superconductors as well is still controversial.

History of superconductivity

Main article : History of superconductivity Superconductivity was discovered in 1911 by Heike Kamerlingh Onnes, who was studying the resistivity of solid mercury at cryogenic temperatures using the recently-discovered liquid helium as a refrigerant. At the temperature of 4.2 K, he observed that the resistivity abruptly disappeared. For this discovery, he was awarded the Nobel Prize in Physics in 1913. In subsequent decades, superconductivity was found in several other materials. In 1913, lead was found to superconduct at 7 K, and in 1941 niobium nitride was found to superconduct at 16 K. The next important step in understanding superconductivity occurred in 1933, when Meissner and Ochsenfeld discovered that superconductors expelled applied magnetic fields, a phenomenon which has come to be known as the Meissner effect. In 1935, F. and H. London showed that the Meissner effect was a consequence of the minimization of the electromagnetic free energy carried by superconducting current. In 1950, the phenomenological Ginzburg-Landau theory of superconductivity was devised by Landau and Ginzburg. This theory, which combined Landau's theory of second-order phase transitions with a Scrödinger-like wave equation, had great success in explaining the macroscopic properties of superconductors. In particular, Abrikosov showed that Ginzburg-Landau theory predicts the division of superconductors into the two categories now referred to as Type I and Type II. Abrikosov and Ginzburg were awarded the 2003 Nobel Prize for their work (Landau having died in 1968.) Also in 1950, Maxwell and Reynolds et. al. found that the critical temperature of a superconductor depends on the isotopic mass of the constituent element. This important discovery pointed to the electron-phonon interaction as the microscopic mechanism responsible for superconductivity. The complete microscopic theory of superconductivity was finally proposed in 1957 by Bardeen, Cooper, and Schrieffer. This BCS theory explained the superconducting current as a superfluid of Cooper pairs, pairs of electrons interacting through the exchange of phonons. For this work, the authors were awarded the Nobel Prize in 1972. The BCS theory was set on a firmer footing in 1958, when Bogoliubov showed that the BCS wavefunction, which had originally been derived from a variational argument, could be obtained using a canonical transformation of the electronic Hamiltonian. In 1959, Gor'kov showed that the BCS theory reduced to the Ginzburg-Landau theory close to the critical temperature. In 1962, the first commercial superconducting wire, a niobium-titanium alloy, was developed by researchers at Westinghouse. In the same year, Josephson made the important theoretical prediction that a supercurrent can flow between two pieces of superconductor separated by a thin layer of insulator. This phenomenon, now called the Josephson effect, is exploited by superconducting devices such as SQUIDs. It is used in the most accurate available measurements of the magnetic flux quantum h/e, and thus (coupled with the quantum Hall resistivity) for Planck's constant h. Josephson was awarded the Nobel Prize for this work in 1973. Until 1986, physicists had believed that BCS theory forbade superconductivity at temperatures above about 30 K. In that year, Bednorz and Müller discovered superconductivity in a lanthanum-based cuprate perovskite material, which had a transition temperature of 35 K (Nobel Prize in Physics, 1987). It was shortly found by Paul C. W. Chu of the University of Houston and M.K. Wu at the University of Alabama in Huntsville [http://64.233.161.104/search?q=cache:Ld0r1qeeJNgJ:www.the-scientist.com/yr1988/jul/letters_p14_880711.html+Huntsville++%22paul+chu%22&hl=en] that replacing the lanthanum with yttrium, i.e. making YBCO, raised the critical temperature to 92 K, which was important because liquid nitrogen could then be used as a refrigerant (at atmospheric pressure, the boiling point of nitrogen is 77 K.) This is important commercially because liquid nitrogen can be produced cheaply on-site with no raw materials, and is not prone to some of the problems (solid air plugs, etc) of helium in piping. Many other cuprate superconductors have since been discovered, and the theory of superconductivity in these materials is one of the major outstanding challenges of theoretical condensed matter physics.

Technological applications of superconductivity

There have been many technological innovations based on superconductivity. Superconductors are used to make the most powerful electromagnets known to man, including those used in MRI machines and the beam-steering magnets used in particle accelerators. Another application is for magnetic separation where weakly magnetic particles are extracted from a background of less or non-magnetic particles (used in a large scale in pigment industries). Superconductors are also used to make SQUIDs (superconducting quantum interference devices), the most sensitive magnetometers known. Superconductors have also been used to make digital circuits (e.g. based on the Rapid Single Flux Quantum technology) and microwave filters for mobile phone base stations. Many promising applications of superconductivity have been stalled by the impracticality of maintaining large systems (e.g. long stretches of cable) at cryogenic temperatures. These problems may soon be alleviated with the continued development of high temperature superconductors, as these can be cooled by using liquid nitrogen rather than liquid helium (which is much more expensive and difficult to handle) or by using cryocoolers. However, the currently known high-temperature superconductors are brittle ceramics which are not easily turned into wires or other useful shapes. Promising future applications include high-performance transformers, power storage devices, electric power transmission, electric motors (e.g. for vehicle propulsion), magnetic levitation devices, and Fault Current Controllers.

Superconductors in science fiction

Superconductivity has long been a staple of science fiction. One of the first mentions of the phenomenon occurred in Robert A. Heinlein's novel Beyond This Horizon (1942). Notably, the use of a fictional room temperature superconductor was a major plot point in the Ringworld novels by Larry Niven, first published in 1970. Superconductivity is a popular device in science fiction due to the simplicity of the underlying concept - zero electrical resistance - and the rich technological possibilities. For example, superconducting magnets could be used to generate the powerful magnetic fields used by Bussard ramjets, a type of spacecraft commonly encountered in science fiction. The most troublesome property of real superconductors, the need for cryogenic cooling, is often circumvented by postulating the existence of room temperature superconductors. Many stories attribute additional properties to their fictional superconductors, ranging from infinite heat conductivity in Niven's novels (real superconductors conduct heat poorly, though superfluid helium has immense but finite heat conductivity) to providing power to an interstellar travel device in the Stargate movie and TV series. In the movie Terminator 2: Judgment Day, the CPU of the T-101 destroyed in Terminator 1 is found to be superconductive at room temperature.

References

Books

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Journal Articles

- H.K. Onnes, Commun. Phys. Lab. 12, 120 (1911)
- W. Meissner and R. Oschenfeld, Naturwiss. 21, 787 (1933)
- F. London and H. London, Proc. R. Soc. London A149, 71 (1935)
- V.L. Ginzburg and L.D. Landau, Zh. Eksp. Teor. Fiz. 20, 1064 (1950)
- E.Maxwell, Phys. Rev. 78, 477 (1950)
- C.A. Reynolds et. al., Phys. Rev. 78, 487 (1950)
- J. Bardeen, L.N. Cooper, and J.R. Schrieffer, Phys. Rev. 108, 1175 (1957)
- N.N. Bogoliubov, Zh. Eksp. Teor. Fiz. 34, 58 (1958)
- L.P. Gor'kov, Zh. Eksp. Teor. Fiz. 36, 1364 (1959)
- B.D. Josephson, Phys. Lett. 1, 251 (1962)
- J.G. Bednorz and K.A. Mueller, Z. Phys. B64, 189 (1986)
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External links

- [http://www.eere.energy.gov/EE/power_superconductivity.html US, EREN: superconductivity]
- [http://www.superconductors.org/ superconductors.org]
- [http://www.ornl.gov/reports/m/ornlm3063r1/pt1.html Introduction to superconductivity]
- [http://www.sns.gov/partnerlabs/jlab.htm Superconducting Niobium Cavities]
- [http://www.ornl.gov/sci/fed/applied/ Superconductivity at ORNL]
- [http://www.superlife.info Superconductivity in everyday life : Interactive exhibition]
- Category:Materials science ja:超伝導

Aharonov-Bohm effect

The Aharonov-Bohm effect, sometimes called the Ehrenberg-Siday-Aharonov-Bohm effect, is a quantum mechanical phenomenon by which a charged particle is affected by electromagnetic fields in regions from which the particle is excluded. The earliest form of this effect was predicted by Werner Ehrenberg and R.E. Siday in 1949, and similar effects were later rediscovered by Aharonov and Bohm in 1959. Such effects are predicted to arise from both magnetic fields and electric fields, but the magnetic version has been easier to observe. In general, the profound consequence of Aharonov-Bohm effects is that knowledge of the classical electromagnetic field acting locally on a particle is not sufficient to predict its quantum-mechanical behavior. After the 1959 paper was published, Bohm was informed that the effect had been predicted by Rory E. Siday and Werner Ehrenberg a decade earlier; Bohm and Aharonov duly cited this in their second paper (Peat, 1997, p. 192). The most commonly described case, sometimes called the Aharonov-Bohm solenoid effect, is when the wave function of a charged particle passing around a long solenoid experiences a phase shift as a result of the enclosed magnetic field, despite the magnetic field being zero in the region through which the particle passes. This phase shift has been observed experimentally by its effect on interference fringes. (There are also magnetic Aharonov-Bohm effects on bound energies and scattering cross sections, but these cases have not been experimentally tested.) An electric Aharonov-Bohm phenomenon was also predicted, in which a charged particle is affected by regions with different electrical potentials but zero electric field, and this has also seen experimental confirmation. A separate "molecular" Aharonov-Bohm effect was proposed for nuclear motion in multiply-connected regions, but this has been argued to be essentially different, depending only on local quantities along the nuclear path (Sjöqvist, 2002). A general review can be found in Peshkin and Tonomura (1989).

Magnetic Aharonov-Bohm effect

The magnetic Aharonov-Bohm effect can be seen as a result of the requirement that quantum physics be invariant with respect to the gauge choice for the vector potential A. This implies that a particle with charge q travelling along some path P in a region with zero magnetic field (

\mathbf = 0 = \nabla \times \mathbf

) must acquire a phase φ given in SI units by :

\phi = \frac \int_P \mathbf \cdot d\mathbf,

with a phase difference Δφ between any two paths with the same endpoints therefore determined by the magnetic flux Φ through the area between the paths (via Stokes theorem and

\nabla  \times \mathbf = \mathbf

), and given by: :

\Delta\phi = \frac.

Stokes theorem This phase difference can be observed by placing a solenoid between the slits of a double-slit experiment (or equivalent). A solenoid encloses a magnetic field B, but does not produce any magnetic field outside of its cylinder, and thus the charged particle (e.g. an electron) passing outside experiences no classical effect. However, there is a (curl-free) vector potential outside the solenoid with an enclosed flux, and so the relative phase of particles passing through one slit or the other is altered by whether the solenoid current is turned on. This corresponds to an observable shift of the interference fringes on the observation plane. The same phase effect is responsible for the quantized-flux requirement in superconducting loops. This quantization is due to the fact that the superconducting wave function must be single valued: its phase difference Δφ around a closed loop must be an integer multiple of 2π (with the charge q=2e for the electron Cooper pairs), and thus the flux Φ must be a multiple of h/2e. The superconducting flux quantum was actually predicted prior to Aharonov and Bohm, by London (1948) using a phenomenological model. The magnetic Aharonov-Bohm effect is also closely related to Dirac's argument that the existence of a magnetic monopole necessarily implies that both electric and magnetic charges are quantized. A magnetic monopole implies a mathematical singularity in the vector potential, which can be expressed as an infinitely long Dirac string of infinitesimal diameter that contains the equivalent of all of the 4πg flux from a monopole "charge" g. Thus, assuming the absence of an infinite-range scattering effect by this arbitrary choice of singularity, the requirement of single-valued wave functions (as above) necessitates charge-quantization:

2qg/c\hbar

must be an integer (in cgs units) for any electric charge q and magnetic charge g. The magnetic Aharonov-Bohm effect was experimentally confirmed by Osakabe et al. (1986), following earlier work summarized in Olariu and Popèscu (1984). Its scope and application continues to expand. Webb et al. (1985) demonstrated Aharonov-Bohm oscillations in ordinary, non-superconducting metallic rings; for a discussion, see Schwarzschild (1986) and Imry & Webb (1989). Bachtold et al. (1999) detected the effect in carbon nanotubes; for a discussion, see Kong et al. (2004).

Electric Aharonov-Bohm effect

Just as the phase of the wave function depends upon the magnetic vector potential, it also depends upon the scalar electric potential. By constructing a situation in which the electrostatic potential varies for two paths of a particle, through regions of zero electric field, an observable Aharonov-Bohm interference phenomenon from the phase shift has been predicted; again, the absence of an electric field means that, classically, there would be no effect. From the Schrödinger equation, the phase of an eigenfunction with energy E goes as

\exp(-iEt/\hbar)

. The energy, however, will depend upon the electrostatic potential V for a particle with charge q. In particular, for a region with constant potential V (zero field), the electric potential energy qV is simply added to E, resulting in a phase shift: :

\Delta\phi = -\frac ,

where t is the time spent in the potential. The initial theoretical proposal for this effect suggested an experiment where charges pass through conducting cylinders along two paths, which shield the particles from external electric fields in the regions where they travel, but still allow a varying potential to be applied by charging the cylinders. This proved difficult to realize, however. Instead, a different experiment was proposed involving a ring geometry interrupted by tunnel barriers, with a bias voltage V relating the potentials of the two halves of the ring. This situation results in an Aharonov-Bohm phase shift as above, and was observed experimentally in 1998.

Mathematical interpretation

In the terms of modern differential geometry, the Aharonov-Bohm effect can be understood to be the holonomy of the complex-valued line bundle representing the electromagentic field. The connection on the line bundle is given by the electromagnetic potential A, and thus the electromagnetic field strength is the curvature of the line bundle F=dA. The integral of A around a closed loop is the holonomy, which, by Stokes theorem, is the magnetic field threading the loop. Thus the wave function of the electron can be seen to be directly coupled to the complex line bundle representing the electromagnetic field. See also a related effect, the Berry phase.

References

- Ehrenberg, W. and R. E. Siday, "The Refractive Index in Electron Optics and the Principles of Dynamics," Proc. Phys. Soc. London Sect. B 62, 8–21 (1949).
- Aharonov, Y. and D. Bohm, "Significance of electromagnetic potentials in quantum theory," Phys. Rev. 115, 485–491 (1959).
- Peshkin, M. and A. Tonomura, The Aharonov-Bohm Effect (Springer-Verlag: Berlin, 1989).
- Olariu, S. and I. Iovitzu Popèscu, "The quantum effects of electromagnetic fluxes," Rev. Mod. Phys. 57, 339–436 (1985).
- Bachtold, A., C. Strunk, J. P. Salvetat, J. M. Bonard, L. Forro, T. Nussbaumer and [http://pages.unibas.ch/phys-meso/ C. Schonenberger], “Aharonov-Bohm oscillations in carbon nanotubes”, Nature 397, 673 (1999).
- Imry, Y. and R. A. Webb, "Quantum Interference and the Aharonov-Bohm Effect," Scientific American, 260(4), April 1989.
- Kong, J., L. Kouwenhoven, and C. Dekker, "Quantum change for nanotubes", [http://physicsweb.org/articles/world/17/7/3/1 Physics Web] (July 2004).
- London, F. "On the problem of the molecular theory of superconductivity," Phys. Rev. 74, 562–573 (1948).
- Murray, M. [http://www.maths.adelaide.edu.au/people/mmurray/dg99/line_bundles.pdf Line Bundles], (2002).
- Osakabe, N., T. Matsuda, T. Kawasaki, J. Endo, A. Tonomura, S. Yano, and H. Yamada, "Experimental confirmation of Aharonov-Bohm effect using a toroidal magnetic field confined by a superconductor." Phys Rev A. 34(2): 815-822 (1986). [http://prola.aps.org/abstract/PRA/v34/i2/p815_1 Abstract and full text.]
- [http://www.fdavidpeat.com/ Peat, F. David], Infinite Potential: The Life and Times of David Bohm (Addison-Wesley: Reading, MA, 1997). ISBN 0-201-40635-7.
- Schwarzschild, B. "Currents in Normal-Metal Rings Exhibit Aharonov-Bohm Effect." Phys. Today 39, 17–20, Jan. 1986.
- Sjöqvist, E. "Locality and topology in the molecular Aharonov-Bohm effect," Phys. Rev. Lett. 89 (21), 210401/1–3 (2002).
- van Oudenaarden, A., M. H. Devoret, Yu. V. Nazarov, and J. E. Mooij, "Magneto-electric Aharonov-Bohm effect in metal rings," Nature 391, 768–770 (1998).
- Webb, R., S. Washburn, C. Umbach, and R. Laibowitz. Phys. Rev. Lett. 54, 2696 (1985). Category:Quantum mechanics ja:アハラノフ=ボーム効果

Electrical current

In electricity, current refers to electric current, which is the flow of electric charge. Lightning is an example of an electric current, as is the solar wind, the source of the polar aurora. Probably the most familiar form of electric current is the flow of conduction electrons in a metallic wire. This is how utility companies deliver electricity. In electronics, electric current is most often the flow of electrons through conductors and devices such as resistors, but it is also the flow of ions inside a battery or the flow of holes within a semiconductor.

Relation between current and charge

The symbol typically used for the amount of current (the amount of charge Q flowing per unit of time t) is I, from the German word Intensität, which means 'intensity'. :

I =

Formally this is written as :

i(t) =

or inversely as

q(t) = \int_^ i(x)\, dx

Conventional current

Conventional current was defined early in the history of electrical science as a flow of positive charge. In solid metals, like wires, the positive charges are immobile, and only the negatively charged electrons flow in the direction opposite conventional current, but this is not the case in most non-metallic conductors. In other materials, charged particles flow in both directions at the same time. Electric currents in electrolytes are flows of electrically charged atoms (ions), which exist in both positive and negative varieties. For example, an electrochemical cell may be constructed with salt water (a solution of sodium chloride) on one side of a membrane and pure water on the other. The membrane lets the positive sodium ions pass, but not the negative chlorine ions, so a net current results. Electric currents in plasma are flows of electrons as well as positive and negative ions. In ice and in certain solid electrolytes, flowing protons constitute the electric current. To simplify this situation, the original definition of conventional current still stands. There are also instances where the electrons are the charge that is physically moving, but where it makes more sense to think of the current as the movement of positive "holes" (the spots that should have an electron to make the conductor neutral). This is the case in a p-type semiconductor. The SI unit of electrical current is the ampere. Electric current is therefore sometimes informally referred to as amperage or ampage, by analogy with the term voltage. Though this is a valid term, some engineers frown on it.

The speed of an electric current

The charged particles whose movement causes an electric current do not always move in straight lines. In metals, for example, they follow an erratic path, bouncing from atom to atom, but generally drifting in the direction of the electric field. The speed at which they drift can be calculated from the equation: :

I=nAvQ \!\

where :I is the current :n is number of charged particles per unit volume :A is the cross-sectional area of the conductor :v is the drift velocity, and :Q is the charge on each particle. For example, in a copper wire of cross-section 0.5 mm², carrying a current of 5 A, the drift velocity of the electrons is of the order of a millimetre per second. To take a different example, in the near-vacuum inside a cathode ray tube, the electrons travel in near-straight lines ("ballistically") at about a tenth of the speed of light. However, we know that an electric signal travels much faster than this; usually close to the speed of light. These results show that the speed of the charged particles is not necessarily related to the speed of the electric signal. To understand how signals travel faster than the particles that carry them, it is necessary to understand the properties of electromagnetic waves (see article).

Current density

Current density is the current per unit (cross-sectional) area. Mathematically, current is defined as the net flux through an area. Thus: :

I = j \cdot A

where, in the MKS or SI system of measurement, :I is the current, measured in amperes :j is the "current density" measured in amperes per square metre :A is the area through which the current is flowing, measured in square metres The current density is defined as: :

j=\int_i n_i \cdot x_i \cdot \mathbf

where :n is the particle density (number of particles per unit volume) :x is the mass, charge, or any other characteristic whose flow one would like to measure. :u is the average velocity of the particles in each volume Current density is an important consideration in the design of electrical and electronic systems. Most electrical conductors have a finite, positive resistance, making them dissipate power in the form of heat. The current density must be kept sufficiently low to prevent the conductor from melting or burning up, or the insulating material failing. In superconductors, excessive current density may generate a strong enough magnetic field to cause spontaneous loss of the superconductive property.

Electromagnetism

Every electric current produces a magnetic field. The magnetic field can be visualized as a pattern of circular field lines surrounding the wire. Electric current can be directly measured with a galvanometer, but this method involves breaking the circuit, which is sometimes inconvenient. Current can also be measured without breaking the circuit by detecting the magnetic field it creates. Devices used for this include Hall effect sensors, current clamps and Rogowski coils.

Ohm's law

Ohm's law predicts the current in an (ideal) resistor (or other ohmic device) to be the quotient of applied voltage over electrical resistance: :

I = \frac

where :I is the current, measured in amperes :V is the potential difference measured in volts :R is the resistance measured in ohms

Electrical safety

The danger of an electric shock depends on the current (in milliamperes), duration and the current's path in the body:
- 1 mA causes a tingle
- 5 mA causes a slight shock
- 50 to 150 mA may result in death, e.g. through rhabdomyolysis (muscle breakdown) and resultant acute renal failure
- 1-4 A causes ventricular fibrillation
- 10 A causes cardiac arrest (only at this current will a typical home fuse break the circuit) Currents through the heart and the nervous system are the most dangerous. As most dangerous sources are voltage sources, the current present depends on the resistance of the body between the points of contact and any current limiting built into the source. The comparison between the dangers of alternating current and direct current has been a subject of debate ever since the War of Currents in the 1880s. DC tends to cause continuous muscular contractions that make the victim hold on to a live conductor, thereby increasing the risk of deep tissue burns. On the other hand, mains-frequency AC tends to interfere more with the heart's electrical pacemaker, leading to an increased risk of fibrillation. AC at higher frequencies holds a different mixture of hazards, such as RF burns and the possibility of tissue damage with no immediate sensation of pain.

External links

- [http://www.unitconversion.org/unit_converter/current.html Online Current Converter] - convert between various units of current, such as ampere, biot, abampere, statampere, and so on
- [http://www.unitconversion.org/unit_converter/current-v.html Interactive Current Conversion Table] - convert selected unit to all other units of current
- [http://amasci.com/amateur/elecdir.html Which direction does electricity really flow?] Category:Electromagnetism Category:Magnetism ko:전류 ja:電流 th:กระแสไฟฟ้า

Area

:This article explains the meaning of area as a physical quantity. The article area (geometry) is more mathematical. See also area (disambiguation). Area is a quantity expressing the size of a part of a surface. Surface area is the summation of the areas of the exposed sides of an object.

Units

Units for measuring surface area include: :square metre = SI derived unit :are = 100 square metres :hectare = 10,000 square metres :square kilometre = 1,000,000 square metres :square megametre = 10¹² square metres Imperial units, as currently defined from the metre: :square foot (plural square feet) = 0.09290304 square metres. :square yard = 9 square feet = 0.83612736 square metres :square perch = 30.25 square yards = 25.2928526 square metres :acre = 160 square perches or 43,560 square feet = 4046.8564224 square metres :square mile = 640 acres = 2.5899881103 square kilometres Old European area units, still in used in some private matters (e.g. land sale advertisements) :square fathom = 3.5967 square metres :cadastral moon(acre) = 1600� square fathoms = 5755 square metres The article Orders of magnitude links to lists of objects of comparable surface area.

Useful formulas

- Area of a rectangle (and, in particular, a square): length × width
- Area of a triangle: ½ × base × height
- Area of a disk: π × r²
- Area of an ellipse: π × a × b
- Area of a sphere: 4 × π × r² = π × d²
- Area of a trapezoid: If a and b are the two parallel sides and h is the distance (height) between the parallels, the area formula is as below: :

A=\frac(a+b)h

A=\frac

- Total surface area of a right circular cylinder: 2 × π × r × (h + r)
- Lateral surface area of a right circular cylinder: 2 × π × r × h
- Total surface area of a right circular cone: π × r × (l + r)
- Lateral surface area of a right circular cone: π × r × l

External links

- [http://www.unitconversion.org/unit_converter/area.html Online Area Converter - convert between various units of area, such as square meter, hectare, rood, and so on]
- [http://www.unitconversion.org/unit_converter/area-v.html Interactive Area Conversion table - convert selected unit to all other units of area]
- [http://calc.skyrocket.de/en/ Online Unit Converter - Conversion of many different units]
- als:Fläche ja:面積 ko:면적 simple:Area th:พื้นที่ zh-min-nan:Bīn-chek

Physical constant

In science, a physical constant is a physical quantity whose numerical value does not change. It can be contrasted with a mathematical constant, which is a fixed value that does not directly involve a physical measurement. There are many physical constants in science, some of the most famous being Planck's constant

\hbar \

, the gravitational constant

G \

, the speed of light

c \

, the electric constant

\epsilon_0 \

, and the elementary charge

e \

. Constants can take many forms: the speed of light in a vacuum signifies a maximum speed limit of the universe; while the fine-structure constant

\alpha \

characterizes the interaction between electrons and photons, is dimensionless. Beginning with Paul Dirac in 1937, some scientists have speculated that physical constants may actually decrease in proportion to the age of the universe. Scientific experiments have not yet pinpointed any definite evidence that this is the case, although they have placed upper bounds on the maximum possible relative change per year at very small amounts (roughly 10^-5 per year for the fine structure constant

\alpha \,\!

and 10^-11 for the gravitational constant

G \

). However it is currently disputed [http://www.arxiv.org/abs/hep-th/0208093] [http://xxx.lanl.gov/pdf/physics/0110060] that any changes in dimensionful physical constants such as

G \

c \

\hbar \

, or

\epsilon_0 \

are operationally meaningless, however a change in a dimensionless constant such as

\alpha \

is something that would definitely be noticed. If a measurement indicated that a dimensionful physical constant had changed, that is the result or interpretation of a more fundamental dimensionless constant changing, which is the salient metric. Unless the system of natural units is used, the numerical values of dimensionful physical constants are artifacts of the unit system used, such as SI or cgs; that is, they are are essentially conversion factors of human construct. While some properties of materials and particles are constant, they do not show up on this page because they are specific to their respective materials or properties alone. Constants that are independent of systems of units are typically dimensionless numbers, are known as fundamental physical constants, and are truly meaningful parameters of nature, not merely human constructs. The fine-structure constant

\alpha \

is probably the most well known dimensionless fundamental physical constant. The dimensionless ratios of masses (or other like dimensioned properties) of fundamental particles are also fundamental physical constants as are the measure of these properties in terms of natural units. Some people claim that if the physical constants had slightly different values, our universe would be so different that intelligent life would probably not have emerged, and that our universe seems to be fine-tuned for intelligent life. The weak anthropic principle simply says that only because these fundamental constants came out to be the values they are, that there was sufficient order and richness in elemental diversity, that life could have formed and eventually evolved with sufficient intelligence to observe that these constants have taken on the values they have.

Table of universal constants

Table of electromagnetic constants

Table of atomic and nuclear constants

Table of physico-chemical constants

Table of adopted values

Notes

¹The values are given in the so-called concise form; the number in brackets is the standard uncertainty, which is the value multiplied by the relative standard uncertainty.
²This is the value adopted internationally for realizing representations of the volt using the Josephson effect.
³This is the value adopted internationally for realizing representations of the ohm using the quantum Hall effect.

References

- [http://physics.nist.gov/cuu/Constants CODATA Recommendations] - 2002 CODATA Internationally recommended values of the Fundamental Physical Constants Category:Measurement ko:물리 상수 ja:物理定数

Magnetic field

:For other senses of this term, see magnetic field (disambiguation). In physics, a magnetic field is an entity produced by moving electric charges (electric currents) that exerts a force on other moving charges. (The quantum-mechanical spin of a particle produces magnetic fields and is acted on by them as though it were a current; this accounts for the fields produced by "permanent" ferromagnets.) A magnetic field is a vector field: it associates with every point in space a (pseudo-)vector that may vary in time. The direction of the field is the equilibrium direction of a compass needle placed in the field.

Symbols and terminology

Magnetic field is usually denoted by the symbol

\mathbf \

. Historically,

\mathbf \

was called the magnetic flux density, magnetic induction, or magnetic field strength.

\mathbf

was called the magnetic field (or magnetic field intensity), and this terminology is still often used to distinguish the two in the context of magnetic materials (non-trivial permeability μ). Otherwise, however, this distinction is often ignored, and both symbols are frequently referred to as the magnetic field. (Some authors call H the auxiliary field, instead.) In linear materials, such as air or free space, the two quantities are linearly related: :

\mathbf = \mu \mathbf \

where

\ \mu

is the magnetic permeability (in henries per meter) of the medium. In SI units,

\mathbf \

and

\mathbf \

are measured in teslas (T) and amperes per meter (A/m), respectively; or, in cgs units, in gauss (G) and oersteds (Oe), respectively. Two parallel wires carrying an electric current in the same sense will generate a magnetic field which will cause a force of attraction to each other. This fact is used to generate the value of an ampere of electric current. Note that while like charges repel and unlike ones attract, the opposite holds for currents: if the current in one of the two parallel wires is reversed, the two will repel.

Definition

Like the electric field, the magnetic field can be defined by the force it produces. In SI units, this is: :

\mathbf = q \mathbf \times \mathbf

where :F is the force produced, measured in newtons :

\times \

indicates a vector cross product :

q \

is electric charge that the magnetic field is acting on, measured in coulombs :

\mathbf \

is velocity of the electric charge

q \

, measured in metres per second :B is magnetic flux density, measured in teslas This law is called the Lorentz force law. (More precisely, it is the special case of that law when there is no electric field. It holds in any reference frame, although the force due to the magnetic field may be different in different frames because magnetic fields transform into electric fields under Lorentz transformations. The total force due to the electric and magnetic fields is the same in any frame.)

Current loop

A simpler form of the force equation in a wire current loop is: Force = BLi = (Tesla)x(meter length of wire)x(ampere current of wire). A more complex explanation is that if the moving charge is part of a current in a wire, then an equivalent form of the law is :

\frac   = \mathbf \times \mathbf

In words, this equation says that the force per unit length of wire is the cross product of the current vector and the magnetic field. In the equation above, the current vector,

\mathbf

, is a vector with magnitude equal to the usual scalar current,

i

, and direction pointing along the wire that the current is flowing.

Point charge generating magnetic field

The field can be computed as the sum of the contributions from individual charged particles. The magnetic flux density from a point charge is: :

\mathbf = \frac\mathbf \times \mathbf

which, for constant velocities, can be expanded into the Biot-Savart law: :

\mathbf = \frac\frac\mathbf \times \mathbf

q \

is electric charge generating the magnetic field, measured in coulombs :

\mathbf \

is velocity of the electric charge

q \

that is generating B, measured in metres per second :B is magnetic flux density, measured in teslas

Vector calculus

The most compact and elegant mathematical statements describing how magnetic fields are produced makes use of vector calculus. In free space: :

\nabla \times \mathbf = \mu_0 \mathbf + \mu_0 \epsilon_0 \frac

\nabla \cdot \mathbf = 0

where :

\nabla \times

is the curl operator :

\nabla \cdot

is the divergence operator :

\mu_0 \

is permeability :

\mathbf \

is current density :

\partial \

is the partial derivative :

\epsilon_0 \

is the free-space permittivity :

\mathbf \

is the electric field :

t \

is time The first equation is known as Ampère's law with James Clerk Maxwell's correction. The second term of this equation (Maxwell's correction) disappears in static or quasi-static systems. The second equation is a statement of the observed non-existence of magnetic monopoles. These are two of four Maxwell's equations; the notation is due to Oliver Heaviside.

Energy in the magnetic field

The general relation for nonlinear materials, the differential energy is: :

dU_H = \int_^ H \cdot dB \, dV

Where V is the volume and dV is the differential volume. For linear materials, H is proportional to B, so the above equation can be simplified: :

U_H = \frac\int_^ B \cdot H \, dV

For linear materials and a constant volume: :

U_H = \frac

Energy can produce a force, so :

F = \frac

F = \frac

Where dl is differential distance and A is the surface area. Force per unit area (pressure) is :

P = \frac

In the case of free space (air),

\mu_o = 4 \pi \cdot 10^ \frac

: :

P \approx 398 \, \mbox \, \approx 57.7 \, \frac

at B = 1 tesla :

P \approx 1592 \, \mbox \, \approx 231 \, \frac

at B = 2 teslas This is the force observed when a high permeability, ferromagnetic materials, such as iron and steel alloys, are in the proximity of magnetic fields.

Properties

Maxwell did much to unify static electricity and magnetism, producing a set of four equations relating the two fields. However, under Maxwell's formulation, there were still two distinct fields describing different phenomena. It was Albert Einstein who showed, using special relativity, that electric and magnetic fields are two aspects of the same thing (a rank-2 tensor), and that one observer may perceive a magnetic force where a moving observer perceives only an electrostatic force. Thus, using special relativity, magnetic forces are a manifestation of electrostatic forces of charges in motion and may be predicted from knowledge of the electrostatic forces and the movement (relative to some observer) of the charges. A thought experiment one can do to show this is with two identical infinite and parallel lines of charge having no motion relative to each other but moving together relative to an observer. Another observer is moving alongside the two lines of charge (at the same velocity) and observes only electrostatic repulsive force and acceleration. The first or "stationary" observer seeing the two lines (and second observer) moving past with some known velocity also observes that the "moving" observer's clock is ticking more slowly (due to time dilation) and thus observes the repulsive acceleration of the lines more slowly than that which the "moving" observer sees. The reduction of repulsive acceleration can be thought of as an attractive force, in a classical physics context, that reduces the electrostatic repulsive force and also that is increasing with increasing velocity. This pseudo-force is precisely the same as the electromagnetic force in a classical context. Changing magnetic fields, according to Faraday's law of induction, can induce an electric field and thus an electric current; similar currents can be induced by conductors moving in a fixed magnetic field. These phenomena are the basis for many electric generators and electric motors.

Magnetic field lines

electric motor Formally, the magnetic field is not a vector, it is a pseudovector. That is, it gains an extra sign flip under improper rotations of the coordinate system. (The distinction is important when using symmetry to analyze magnetic-field problems.) This is a consequence of the fact that B is related to two true vectors by a cross product (e.g. in the Lorentz force law). To simplify the study of magnets an arbitrary (but valid) description of magnetic field lines was created. 1 magnetic field line = 1 gauss line. 10,000 gauss lines per square meter is equal to 1 tesla. The total number of lines emanating from a magnet pole is the magnetic flux. Count only north or only south pole lines, i.e. monopole or one sided value. Although the field line orientation is typically indicated in diagrams with an arrow, the arrow should not be interpreted to indicate any actual movement or flow of the field line.

Pole labeling confusions

It is necessary to note that the labeling of north and south on a compass is in opposition to the labeling of the north and south pole of the Earth. If you have two labeled magnets, it is clear that like poles repel, while opposing poles attract. However, this is clearly wrong when using a compass to find the North Pole of the Earth, because the "north" end of the compass points to the "North" Pole. By convention, the pole of a magnet is labelled according to the direction it points, hence when we speak of the "north pole" of a magnet, we really mean the "north-seeking pole". Magnetic field lines point from north to south of a magnet, and hence the natural magnetic field lines run from south to north along the Earth's surface. This choice, along with the choice of sign convention in the Biot-Savart law, is equivalent to choosing a sign convention for electric charge.

Rotating magnetic fields

A rotating magnetic field is a magnetic field which rotates in polarity at non-relativistic speeds. This is a key principle to the operation of alternating-current motor. A permanent magnet in such a field will rotate so as to maintain its alignment with the external field. This effect is utilised in alternating current electric motors. A good rotating magnetic field can be constructed using three phase alternating currents (or even with higher order polyphase systems). Synchronous motors and induction motors use a stator's rotating magnetic fields to turn rotors. In 1882, Nikola Tesla identified the concept of the rotary magnetic field. In 1885, Galileo Ferraris independently researched the concept. In 1888, Tesla gained for his work. Also in 1888, Ferraris published his research in a paper to the Royal Academy of Sciences in Turin.

References

Books
-
-
-

External articles

Information
- Nave, R., "[http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magfie.html Magnetic Field]". HyperPhysics.
- "Magnetism", [http://theory.uwinnipeg.ca/physics/mag/node2.html#SECTION00110000000000000000 The Magnetic Field]. theory.uwinnipeg.ca.
- Hoadley, Rick, "[http://my.execpc.com/~rhoadley/magfield.htm What do magnetic fields look like]?" 17 July 2005. Rotating magnetic fields
- "[http://www.tpub.com/neets/book5/18a.htm Rotating magnetic fields]". Integrated Publishing.
- "Introduction to Generators and Motors", [http://www.tpub.com/content/neets/14177/css/14177_87.htm rotating magnetic field]. Integrated Publishing.
- "[http://www.egr.msu.edu/~jurkovi4/Experiment4.pdf Induction Motor-Rotating Fields]". Diagrams
- McCulloch, Malcolm,"A2: Electrical Power and Machines", [http://www.eng.ox.ac.uk/~epgmdm/A2/img89.htm Rotating magnetic field]. eng.ox.ac.uk.
- "AC Motor Theory" [http://www.tpub.com/content/doe/h1011v4/css/h1011v4_23.htm Figure 2 Rotating Magnetic Field]. Integrated Publishing. Journal Articles
- Yaakov Kraftmakher, "[http://www.iop.org/EJ/abstract/0143-0807/22/5/302 Two experiments with rotating magnetic field]". 2001 Eur. J. Phys. 22 477-482.
- Bogdan Mielnik and David J. Fernández C., "[http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=JMAPAQ000030000002000537000001&idtype=cvips&gifs=yes An electron trapped in a rotating magnetic field]". Journal of Mathematical Physics, February 1989, Volume 30, Issue 2, pp. 537-549.
- Sonia Melle, Miguel A. Rubio and Gerald G. Fuller "[http://prola.aps.org/abstract/PRE/v61/i4/p4111_1 Structure and dynamics of magnetorheological fluids in rotating magnetic fields]". Phys. Rev. E 61, 4111–4117 (2000). Category:Magnetism Category:Physical quantity Category:Introductory physics ja:磁場 th:สนามแม่เหล็ก

Meissner effect

The Meissner Effect (or Meissner-Ochsenfeld Effect) is the total exclusion of any magnetic flux from the interior of a superconductor. It is often referred to as perfect diamagnetism. It was discovered by Walther Meißner and Robert Ochsenfeld in 1933. In the effect, there is an exclusion of magnetic flux brought about by electrical "screening currents" that flow at the surface of the superconducting metal and which generate a magnetic field that exactly cancels the externally applied field inside the superconductor. The Meissner effect is one of the defining features of superconductivity, and its discovery served to establish that the onset of superconductivity is a phase transition. Superconducting magnetic levitation is due to the Meissner Effect (which repels a permanent magnet) and flux pinning, which stops the magnet from sliding away. Note that there is a difference between a Perfect Diamagnet and a Superconductor.

Squid

Squids are the large, diverse group of marine cephalopods popular as food in cuisines as widely separated as the Korean and the Italian. In fish markets and restaurants in English-speaking countries, it is often known by the name calamari, from the Greek-Italian word for these animals. English family.]] Squids are members of the class Cephalopoda, subclass Coleoidea, order Teuthida, of which there are two major suborders, Myopsina and Oegopsina (including the giant squids like Architeuthis dux). Teuthida is the largest of the cephalopod orders, edging out the octopuses (order Octopoda) for total number of species, with 298 classified into 28 families. The order Teuthida is a member of the superorder Decapodiformes (from the Greek for "ten legs"). Two other orders of decapodiform cephalopods are also called squid, although they are taxonomically distinct from Teuthida and differ recognizably in their gross anatomical features. They are the bobtail squids of order Sepiolida and the Ram's Horn Squid of the single species order Spirulida. The Vampire Squid, however, is more closely related to the octopuses than to any of the squids. Like all cephalopods, squids are distinguished by having a distinct head, bilateral symmetry, a mantle, and tentacles with suckers; squid, like cuttlefish, have eight arms and two tentacles arranged in pairs. These are a type of muscular hydrostat. If accidentally cut off, the tentacles do not grow back[http://www.thestar.com/NASApp/cs/ContentServer?pagename=thestar/Layout/Article_Type1&call_pageid=971358637177&c=Article&cid=1127944212147&DPL=IvsNDS%2f7ChAX&tacodalogin=yes]. Squids can blend in with their surroundings to avoid predators. They also have chromatophores embedded in their skin and the ability to expel ink if threatened. Being coleoids means that their bony structure is internalized (in the octopus it is nonexistent); in squid there is a single flat bone plate buried within the soft tissue structure. They have a specialized foot called the siphon, or hyponome, that enables them to move by expelling water under pressure. Squid are the most skilled of the coleoids at this form of motion. The mouth of the squid is equipped with a sharp horny beak made of chitin, used to kill and tear prey into manageable pieces. Captured whales often have squid beaks in their stomachs, the beak being the only indigestible part of the squid. The mouth contains the radula (the rough tongue common to all mollusks except bivalvia and aplacophora). Squid have two gills, sometimes called ctenidia, and an extensive closed circulatory system consisting of a systemic heart and two gill hearts. They are exclusively carnivorous, feeding on fish and other invertebrates. Squid usually have two elongated tentacles especially for the capture of food. carnivorous]] The majority of squid are no more than 60 cm in length, but the giant squid is reportedly up to 20 m in length, which made it the largest invertebrate in the world, and it has the largest eyes of all. Recently, however, an even larger specimen of a poorly understood species, Mesonychoteuthis hamiltoni (the Colossal Squid) has been discovered. Giant squids are featured in literature and folklore, with a strongly frightening connotation. Colossal Squid Individual species of squid are found abundantly in certain areas and provide large catches for fisheries. A giant squid was observed for the first time on September 30, 2005, by two Japanese scientists: Tsunemi Kubodera of the National Science Museum (of Japan) and Kyoichi Mori of the Ogasawara Whale Watching Association. From their initial observations, the scientists concluded that giant squid appear to be more aggressive than previous thought. A 5.5 meter long tentacle was retrieved (accidentally) from the creature and DNA tests compared with other giant squid specimens previously washed up on shore confirmed that indeed they had observed a live giant squid. The scientists were able to estimate the total size to the squid to be eight meters.

Classification

giant squid
- CLASS CEPHALOPODA
- Subclass Nautiloidea: nautilus
- Subclass Coleoidea: squid, octopus, cuttlefish
- Superorder Decapodiformes
- Order Spirulida: Ram's Horn Squid
- Order Sepiida: cuttlefish
- Order Sepiolida: bobtail squid
- Order Teuthida: squid
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- Suborder Myopsina
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- Family Loliginidae: inshore, calamari, and grass squid
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- Suborder Oegopsina
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- Family Ancistrocheiridae: Sharpear Enope Squid
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- Family Architeuthidae: giant squid
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- Family Bathyteuthidae
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- Family Batoteuthidae: Bush-club Squid
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- Family Brachioteuthidae
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- Family Chiroteuthidae
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- Family Chtenopterygidae: comb-finned squid
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- Family Cranchiidae: glass squid
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- Family Cycloteuthidae
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- Family Enoploteuthidae
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- Family Gonatidae: armhook squid
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- Family Histioteuthidae: jewel squid
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- Family Joubiniteuthidae: Joubin's Squid
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- Family Lepidoteuthidae: Grimaldi Scaled Squid
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- Family Lycoteuthidae
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- Family Magnapinnidae: bigfin squid
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- Family Mastigoteuthidae: whip-lash squid
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- Family Neoteuthidae
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- Family Octopoteuthidae
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- Family Ommastrephidae: flying squid
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- Family Onychoteuthidae: hooked squid
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- Family Pholidoteuthidae
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- Family Promachoteuthidae
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- Family Psychroteuthidae: Glacial Squid
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- Family Pyroteuthidae: fire squid
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- Family Thysanoteuthidae: rhomboid squid
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- Family incertae sedis (uncertain group)
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- Family Walvisteuthidae
- Superorder Octopodiformes

External links

- [http://www.squidcam.info Squidcam] from New Zealand's The Science Site (very popular site, viewer operated camera on live baby squid).
- [http://www.cephbase.utmb.edu/spdb/squid.cfm CephBase: Teuthida]
- [http://encarta.msn.com/encyclopedia_761552165/Squid.html#461553803 MSN Encarta - Squid]
- [http://www.sciam.com/article.cfm?chanID=sa003&articleID=00030326-0783-133B-878383414B7F0000 Scientific American - Giant Squid] Category:Seafood

Magnetometer

A magnetometer is a scientific instrument used to measure the strength of magnetic fields. A magnetograph is a magnetometer that continuously records data. Earth's magnetism varies from place to place and differences in the Earth's magnetic field (the magnetosphere) can be caused by a couple of things: #The differing nature of rocks #The interaction between charged particles from the sun and the magnetosphere Magnetometers are used in geophysical surveys to find deposits of iron because they can measure the magnetic pull of iron. Magnetometers are also used to detect archeological sites, shipwrecks and other buried or submerged objects. A magnetometer can also be used by satellites like GOES to measure both the magnitude and direction of the earth's magnetic field. Magnetometers are very sensitive, and can give an indication of possible auroral activity before one can even see the light from the aurora. Magnetometers can be divided into two basic types:
- scalar magnetometers, that measure the total strength of the magnetic field to which they are subjected, and
- vector magnetometers, that have the capability to measure the component of the magnetic field in a particular direction. The use of three orthogonal vector magnetometers allows the magnetic field strength, inclination and declination to be uniquely defined. Examples of ve