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83-650: It was proposed by Bardeen, Cooper, and Schrieffer in 1957; they received the Nobel Prize in Physics for this theory in 1972. Rapid progress in the understanding of superconductivity gained momentum in the mid-1950s. It began with the 1948 paper, "On the Problem of the Molecular Theory of Superconductivity", where Fritz London proposed that the phenomenological London equations may be consequences of

166-478: A cornucopia . The Genius of Science holds the veil which covers Nature's "cold and austere face". It was designed by Erik Lindberg and is manufactured by Svenska Medalj in Eskilstuna . It is inscribed " Inventas vitam iuvat excoluisse per artes " ("It is beneficial to have improved (human) life through discovered arts"), an adaptation of " inventas aut qui vitam excoluere per artes " from line 663 of book 6 of

249-430: A bar suspended from its middle by a thin fiber. The fiber acts as a very weak torsion spring . In Coulomb's experiment, the torsion balance was an insulating rod with a metal -coated ball attached to one end, suspended by a silk thread. The ball was charged with a known charge of static electricity , and a second charged ball of the same polarity was brought near it. The two charged balls repelled one another, twisting

332-401: A charge q t {\textstyle q_{t}} depends on the electric field E {\textstyle \mathbf {E} } established by other charges that it finds itself in, such that F = q t E {\textstyle \mathbf {F} =q_{t}\mathbf {E} } . In the simplest case, the field is considered to be generated solely by

415-916: A charge, q 1 {\displaystyle q_{1}} at position r 1 {\displaystyle \mathbf {r} _{1}} , in the vicinity of another charge, q 2 {\displaystyle q_{2}} at position r 2 {\displaystyle \mathbf {r} _{2}} , in a vacuum is equal to F 1 = q 1 q 2 4 π ε 0 r ^ 12 | r 12 | 2 {\displaystyle \mathbf {F} _{1}={\frac {q_{1}q_{2}}{4\pi \varepsilon _{0}}}{{\hat {\mathbf {r} }}_{12} \over {|\mathbf {r} _{12}|}^{2}}} where r 12 = r 1 − r 2 {\textstyle \mathbf {r_{12}=r_{1}-r_{2}} }

498-648: A compact set V ⊆ R 3 {\displaystyle V\subseteq R^{3}} having a piecewise smooth boundary ∂ V {\displaystyle \partial V} such that Ω ∩ V = ∅ {\displaystyle \Omega \cap V=\emptyset } . It follows that e ( r , r ′ ) ∈ C 1 ( V × Ω ) {\displaystyle e(\mathbf {r,\mathbf {r} '} )\in C^{1}(V\times \Omega )} and so, for

581-428: A lot of such electron pairs in a superconductor, these pairs overlap very strongly and form a highly collective condensate. In this "condensed" state, the breaking of one pair will change the energy of the entire condensate - not just a single electron, or a single pair. Thus, the energy required to break any single pair is related to the energy required to break all of the pairs (or more than just two electrons). Because

664-492: A picture with the name of the laureate and a citation explaining their accomplishments. At the awards ceremony, the laureate is given a document indicating the award sum. The amount of the cash award may differ from year to year, based on the funding available from the Nobel Foundation . For example, in 2009 the total cash awarded was 10 million Swedish Kronor (SEK) (US$ 1.4 million), but in 2012 following

747-573: A piece of amber attract small objects. In 1600, English scientist William Gilbert made a careful study of electricity and magnetism, distinguishing the lodestone effect from static electricity produced by rubbing amber. He coined the Neo-Latin word electricus ("of amber" or "like amber", from ἤλεκτρον [ elektron ], the Greek word for "amber") to refer to the property of attracting small objects after being rubbed. This association gave rise to

830-498: A point charge due to a system of point charges is simply the vector addition of the individual forces acting alone on that point charge due to each one of the charges. The resulting force vector is parallel to the electric field vector at that point, with that point charge removed. Force F {\textstyle \mathbf {F} } on a small charge q {\displaystyle q} at position r {\displaystyle \mathbf {r} } , due to

913-618: A prize, as the discoverers have died by the time the impact of their work is appreciated. A Physics Nobel Prize laureate is awarded a gold medal, a diploma bearing a citation, and a sum of money. The medal for the Nobel Prize in Physics is identical in design to the Nobel Prize in Chemistry medal. The reverse of the physics and chemistry medals depicts the Goddess of Nature in the form of Isis as she emerges from clouds holding

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996-624: A series of prizes for those who confer the "greatest benefit on mankind" in the fields of physics , chemistry , peace , physiology or medicine, and literature. Though Nobel wrote several wills during his lifetime, the last one was written a year before he died and was signed at the Swedish-Norwegian Club in Paris on 27 November 1895. Nobel bequeathed 94% of his total assets, 31 million Swedish kronor (US$ 2.9 million, or €2.7 million in 2023), to establish and endow

1079-507: A single source point charge . More generally, the field can be generated by a distribution of charges who contribute to the overall by the principle of superposition . If the field is generated by a positive source point charge q {\textstyle q} , the direction of the electric field points along lines directed radially outwards from it, i.e. in the direction that a positive point test charge q t {\textstyle q_{t}} would move if placed in

1162-719: A small test charge q {\displaystyle q} at position r {\displaystyle {\boldsymbol {r}}} in vacuum is given by the integral over the distribution of charge F ( r ) = q 4 π ε 0 ∫ d q ′ r − r ′ | r − r ′ | 3 . {\displaystyle \mathbf {F} (\mathbf {r} )={\frac {q}{4\pi \varepsilon _{0}}}\int dq'{\frac {\mathbf {r} -\mathbf {r'} }{|\mathbf {r} -\mathbf {r'} |^{3}}}.} The "continuous charge" version of Coulomb's law

1245-409: A surface charge distribution (a good approximation for charge on a plate in a parallel plate capacitor ) where σ ( r ′ ) {\displaystyle \sigma (\mathbf {r} ')} gives the charge per unit area at position r ′ {\displaystyle \mathbf {r} '} , and d A ′ {\displaystyle dA'}

1328-601: A system of n {\textstyle n} discrete charges in vacuum is F ( r ) = q 4 π ε 0 ∑ i = 1 n q i r ^ i | r i | 2 , {\displaystyle \mathbf {F} (\mathbf {r} )={q \over 4\pi \varepsilon _{0}}\sum _{i=1}^{n}q_{i}{{\hat {\mathbf {r} }}_{i} \over {|\mathbf {r} _{i}|}^{2}},} where q i {\displaystyle q_{i}}

1411-575: A wire) where λ ( r ′ ) {\displaystyle \lambda (\mathbf {r} ')} gives the charge per unit length at position r ′ {\displaystyle \mathbf {r} '} , and d ℓ ′ {\displaystyle d\ell '} is an infinitesimal element of length, d q ′ = λ ( r ′ ) d ℓ ′ . {\displaystyle dq'=\lambda (\mathbf {r'} )\,d\ell '.} For

1494-952: Is a consequence of historical choices for units. The constant ε 0 {\displaystyle \varepsilon _{0}} is the vacuum electric permittivity . Using the CODATA 2022 recommended value for ε 0 {\displaystyle \varepsilon _{0}} , the Coulomb constant is k e = 1 4 π ε 0 = 8.987   551   7862 ( 14 ) × 10 9   N ⋅ m 2 ⋅ C − 2 . {\displaystyle k_{\text{e}}={\frac {1}{4\pi \varepsilon _{0}}}=8.987\ 551\ 7862(14)\times 10^{9}\ \mathrm {N{\cdot }m^{2}{\cdot }C^{-2}} .} There are three conditions to be fulfilled for

1577-399: Is a constant, q 1 and q 2 are the quantities of each charge, and the scalar r is the distance between the charges. The force is along the straight line joining the two charges. If the charges have the same sign, the electrostatic force between them makes them repel; if they have different signs, the force between them makes them attract. Being an inverse-square law , the law

1660-474: Is a macroscopic effect which results from the condensation of Cooper pairs. These have some bosonic properties, and bosons, at sufficiently low temperature, can form a large Bose–Einstein condensate . Superconductivity was simultaneously explained by Nikolay Bogolyubov , by means of the Bogoliubov transformations . In many superconductors, the attractive interaction between electrons (necessary for pairing)

1743-862: Is always discrete in reality, and the "continuous charge" assumption is just an approximation that is not supposed to allow | r − r ′ | = 0 {\displaystyle |\mathbf {r} -\mathbf {r'} |=0} to be analyzed. The constant of proportionality, 1 4 π ε 0 {\displaystyle {\frac {1}{4\pi \varepsilon _{0}}}} , in Coulomb's law: F 1 = q 1 q 2 4 π ε 0 r ^ 12 | r 12 | 2 {\displaystyle \mathbf {F} _{1}={\frac {q_{1}q_{2}}{4\pi \varepsilon _{0}}}{{\hat {\mathbf {r} }}_{12} \over {|\mathbf {r} _{12}|}^{2}}}

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1826-617: Is an annual award given by the Royal Swedish Academy of Sciences for those who have made the most outstanding contributions to mankind in the field of physics . It is one of the five Nobel Prizes established by the will of Alfred Nobel in 1895 and awarded since 1901, the others being the Nobel Prize in Chemistry , Nobel Prize in Literature , Nobel Peace Prize , and Nobel Prize in Physiology or Medicine . Physics

1909-411: Is an infinitesimal element of area, d q ′ = σ ( r ′ ) d A ′ . {\displaystyle dq'=\sigma (\mathbf {r'} )\,dA'.} For a volume charge distribution (such as charge within a bulk metal) where ρ ( r ′ ) {\displaystyle \rho (\mathbf {r} ')} gives

1992-456: Is brought about indirectly by the interaction between the electrons and the vibrating crystal lattice (the phonons ). Roughly speaking the picture is the following: An electron moving through a conductor will attract nearby positive charges in the lattice. This deformation of the lattice causes another electron, with opposite spin, to move into the region of higher positive charge density. The two electrons then become correlated. Because there are

2075-416: Is conventionally called the electrostatic force or Coulomb force . Although the law was known earlier, it was first published in 1785 by French physicist Charles-Augustin de Coulomb . Coulomb's law was essential to the development of the theory of electromagnetism and maybe even its starting point, as it allowed meaningful discussions of the amount of electric charge in a particle. The law states that

2158-1051: Is given by | E | = k e | q | r 2 {\displaystyle |\mathbf {E} |=k_{\text{e}}{\frac {|q|}{r^{2}}}} A system of n discrete charges q i {\displaystyle q_{i}} stationed at r i = r − r i {\textstyle \mathbf {r} _{i}=\mathbf {r} -\mathbf {r} _{i}} produces an electric field whose magnitude and direction is, by superposition E ( r ) = 1 4 π ε 0 ∑ i = 1 n q i r ^ i | r i | 2 {\displaystyle \mathbf {E} (\mathbf {r} )={1 \over 4\pi \varepsilon _{0}}\sum _{i=1}^{n}q_{i}{{\hat {\mathbf {r} }}_{i} \over {|\mathbf {r} _{i}|}^{2}}} Coulomb's law holds even within atoms , correctly describing

2241-420: Is less favorable. As the magnitude of opposing charges increases, energy increases and ionic bonding is more favorable. Strictly speaking, Gauss's law cannot be derived from Coulomb's law alone, since Coulomb's law gives the electric field due to an individual, electrostatic point charge only. However, Gauss's law can be proven from Coulomb's law if it is assumed, in addition, that the electric field obeys

2324-403: Is never supposed to be applied to locations for which | r − r ′ | = 0 {\displaystyle |\mathbf {r} -\mathbf {r'} |=0} because that location would directly overlap with the location of a charged particle (e.g. electron or proton) which is not a valid location to analyze the electric field or potential classically. Charge

2407-1291: Is no reason to expect Gauss's law to hold for moving charges based on this derivation alone. In fact, Gauss's law does hold for moving charges, and, in this respect, Gauss's law is more general than Coulomb's law. Let Ω ⊆ R 3 {\displaystyle \Omega \subseteq R^{3}} be a bounded open set, and E 0 ( r ) = 1 4 π ε 0 ∫ Ω ρ ( r ′ ) r − r ′ ‖ r − r ′ ‖ 3 d r ′ ≡ 1 4 π ε 0 ∫ Ω e ( r , r ′ ) d r ′ {\displaystyle \mathbf {E} _{0}(\mathbf {r} )={\frac {1}{4\pi \varepsilon _{0}}}\int _{\Omega }\rho (\mathbf {r} '){\frac {\mathbf {r} -\mathbf {r} '}{\left\|\mathbf {r} -\mathbf {r} '\right\|^{3}}}\mathrm {d} \mathbf {r} '\equiv {\frac {1}{4\pi \varepsilon _{0}}}\int _{\Omega }e(\mathbf {r,\mathbf {r} '} ){\mathrm {d} \mathbf {r} '}} be

2490-431: Is not realized in many unconventional superconductors such as the d-wave high-temperature superconductors. Extensions of BCS theory exist to describe these other cases, although they are insufficient to completely describe the observed features of high-temperature superconductivity. BCS is able to give an approximation for the quantum-mechanical many-body state of the system of (attractively interacting) electrons inside

2573-412: Is similar to Isaac Newton 's inverse-square law of universal gravitation , but gravitational forces always make things attract, while electrostatic forces make charges attract or repel. Also, gravitational forces are much weaker than electrostatic forces. Coulomb's law can be used to derive Gauss's law , and vice versa. In the case of a single point charge at rest, the two laws are equivalent, expressing

BCS theory - Misplaced Pages Continue

2656-533: Is the Dirac delta function , the result is ∇ ⋅ E ( r ) = 1 ε 0 ∫ ρ ( s ) δ ( r − s ) d 3 s {\displaystyle \nabla \cdot \mathbf {E} (\mathbf {r} )={\frac {1}{\varepsilon _{0}}}\int \rho (\mathbf {s} )\,\delta (\mathbf {r} -\mathbf {s} )\,\mathrm {d} ^{3}\mathbf {s} } Using

2739-393: Is the displacement vector between the charges, r ^ 12 {\textstyle {\hat {\mathbf {r} }}_{12}} a unit vector pointing from q 2 {\textstyle q_{2}} to q 1 {\textstyle q_{1}} , and ε 0 {\displaystyle \varepsilon _{0}}

2822-432: Is the charge density. If we take the divergence of both sides of this equation with respect to r, and use the known theorem ∇ ⋅ ( r | r | 3 ) = 4 π δ ( r ) {\displaystyle \nabla \cdot \left({\frac {\mathbf {r} }{|\mathbf {r} |^{3}}}\right)=4\pi \delta (\mathbf {r} )} where δ (r)

2905-457: Is the magnitude of the i th charge, r i {\textstyle \mathbf {r} _{i}} is the vector from its position to r {\displaystyle \mathbf {r} } and r ^ i {\textstyle {\hat {\mathbf {r} }}_{i}} is the unit vector in the direction of r i {\displaystyle \mathbf {r} _{i}} . In this case,

2988-408: Is traditionally the first award presented in the Nobel Prize ceremony. The prize consists of a medal along with a diploma and a certificate for the monetary award. The front side of the medal displays the same profile of Alfred Nobel depicted on the medals for Physics, Chemistry, and Literature. The first Nobel Prize in Physics was awarded to German physicist Wilhelm Röntgen in recognition of

3071-665: The Aeneid by the Roman poet Virgil . A plate below the figures is inscribed with the name of the recipient. The text " REG. ACAD. SCIENT. SUEC. " denoting the Royal Swedish Academy of Sciences is inscribed on the reverse. Nobel laureates receive a diploma directly from the hands of the King of Sweden . Each diploma is uniquely designed by the prize-awarding institutions for the laureate who receives it. The diploma contains

3154-524: The Fermi surface become unstable against the formation of Cooper pairs . Cooper showed such binding will occur in the presence of an attractive potential, no matter how weak. In conventional superconductors, an attraction is generally attributed to an electron-lattice interaction. The BCS theory, however, requires only that the potential be attractive, regardless of its origin. In the BCS framework, superconductivity

3237-485: The Great Recession , the amount was 8 million SEK, or US$ 1.1 million. If there are two laureates in a particular category, the award grant is divided equally between the recipients, but if there are three, the awarding committee may opt to divide the grant equally, or award half to one recipient and a quarter to each of the two others. The committee and institution serving as the selection board for

3320-592: The Nobel Committee for Physics , a Nobel Committee that consists of five members elected by The Royal Swedish Academy of Sciences . During the first stage which begins in September, a group of about 3,000 selected university professors, Nobel Laureates in Physics and Chemistry, and others are sent confidential nomination forms. The completed forms must arrive at the Nobel Committee by 31 January of

3403-500: The Weber force . When the charges are moving more quickly in relation to each other or accelerations occur, Maxwell's equations and Einstein 's theory of relativity must be taken into consideration. An electric field is a vector field that associates to each point in space the Coulomb force experienced by a unit test charge . The strength and direction of the Coulomb force F {\textstyle \mathbf {F} } on

BCS theory - Misplaced Pages Continue

3486-583: The coherence of a quantum state . In 1953, Brian Pippard , motivated by penetration experiments, proposed that this would modify the London equations via a new scale parameter called the coherence length . John Bardeen then argued in the 1955 paper, "Theory of the Meissner Effect in Superconductors", that such a modification naturally occurs in a theory with an energy gap. The key ingredient

3569-542: The electric constant . Here, r ^ 12 {\textstyle \mathbf {\hat {r}} _{12}} is used for the vector notation. The electrostatic force F 2 {\textstyle \mathbf {F} _{2}} experienced by q 2 {\displaystyle q_{2}} , according to Newton's third law , is F 2 = − F 1 {\textstyle \mathbf {F} _{2}=-\mathbf {F} _{1}} . If both charges have

3652-424: The force between the positively charged atomic nucleus and each of the negatively charged electrons . This simple law also correctly accounts for the forces that bind atoms together to form molecules and for the forces that bind atoms and molecules together to form solids and liquids. Generally, as the distance between ions increases, the force of attraction, and binding energy, approach zero and ionic bonding

3735-589: The superposition principle . The superposition principle states that the resulting field is the vector sum of fields generated by each particle (or the integral, if the charges are distributed smoothly in space). Coulomb's law states that the electric field due to a stationary point charge is: E ( r ) = q 4 π ε 0 e r r 2 {\displaystyle \mathbf {E} (\mathbf {r} )={\frac {q}{4\pi \varepsilon _{0}}}{\frac {\mathbf {e} _{r}}{r^{2}}}} where Using

3818-502: The " sifting property " of the Dirac delta function, we arrive at ∇ ⋅ E ( r ) = ρ ( r ) ε 0 , {\displaystyle \nabla \cdot \mathbf {E} (\mathbf {r} )={\frac {\rho (\mathbf {r} )}{\varepsilon _{0}}},} which is the differential form of Gauss's law, as desired. Since Coulomb's law only applies to stationary charges, there

3901-524: The English words "electric" and "electricity", which made their first appearance in print in Thomas Browne 's Pseudodoxia Epidemica of 1646. Early investigators of the 18th century who suspected that the electrical force diminished with distance as the force of gravity did (i.e., as the inverse square of the distance) included Daniel Bernoulli and Alessandro Volta , both of whom measured

3984-625: The Peace Prize were appointed soon after the will was approved. The other prize-awarding organisations followed: Karolinska Institutet on 7 June, the Swedish Academy on 9 June, and the Royal Swedish Academy of Sciences on 11 June. The Nobel Foundation then established guidelines for awarding the prizes. In 1900, the Nobel Foundation's newly created statutes were promulgated by King Oscar II . According to Nobel's will,

4067-572: The Prize. Nomination records are sealed for fifty years. While posthumous nominations are not permitted, awards can be made if the individual died in the months between the decision of the committee (typically in October) and the ceremony in December. Prior to 1974, posthumous awards were permitted if the candidate had died after being nominated. The rules for the Nobel Prize in Physics require that

4150-455: The Royal Swedish Academy of Sciences would award the Prize in Physics. A maximum of three Nobel laureates and two different works may be selected for the Nobel Prize in Physics. Compared with other Nobel Prizes, the nomination and selection process for the prize in physics is long and rigorous. This is a key reason why it has grown in importance over the years to become the most important prize in Physics. The Nobel laureates are selected by

4233-431: The charge per unit volume at position r ′ {\displaystyle \mathbf {r} '} , and d V ′ {\displaystyle dV'} is an infinitesimal element of volume, d q ′ = ρ ( r ′ ) d V ′ . {\displaystyle dq'=\rho ({\boldsymbol {r'}})\,dV'.} The force on

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4316-532: The charges have opposite signs then the product q 1 q 2 {\displaystyle q_{1}q_{2}} is negative and the direction of the force on q 1 {\displaystyle q_{1}} is − r ^ 12 {\textstyle -{\hat {\mathbf {r} }}_{12}} ; the charges attract each other. The law of superposition allows Coulomb's law to be extended to include any number of point charges. The force acting on

4399-469: The collective behavior of the condensate is a crucial ingredient necessary for superconductivity. BCS theory starts from the assumption that there is some attraction between electrons, which can overcome the Coulomb repulsion . In most materials (in low temperature superconductors), this attraction is brought about indirectly by the coupling of electrons to the crystal lattice (as explained above). However,

4482-429: The dense limit of pairs. Note that the continuous crossover between the dilute and dense regimes of attracting pairs of fermions is still an open problem, which now attracts a lot of attention within the field of ultracold gases. The hyperphysics website pages at Georgia State University summarize some key background to BCS theory as follows: BCS derived several important theoretical predictions that are independent of

4565-491: The details of the interaction, since the quantitative predictions mentioned below hold for any sufficiently weak attraction between the electrons and this last condition is fulfilled for many low temperature superconductors - the so-called weak-coupling case. These have been confirmed in numerous experiments: Nobel Prize in Physics The Nobel Prize in Physics ( Swedish : Nobelpriset i fysik )

4648-1145: The divergence theorem: ∮ ∂ V E 0 ⋅ d S = ∫ V ∇ ⋅ E 0 d V {\displaystyle \oint _{\partial V}\mathbf {E} _{0}\cdot d\mathbf {S} =\int _{V}\mathbf {\nabla } \cdot \mathbf {E} _{0}\,dV} But because e ( r , r ′ ) ∈ C 1 ( V × Ω ) {\displaystyle e(\mathbf {r,\mathbf {r} '} )\in C^{1}(V\times \Omega )} , ∇ ⋅ E 0 ( r ) = 1 4 π ε 0 ∫ Ω ∇ r ⋅ e ( r , r ′ ) d r ′ = 0 {\displaystyle \mathbf {\nabla } \cdot \mathbf {E} _{0}(\mathbf {r} )={\frac {1}{4\pi \varepsilon _{0}}}\int _{\Omega }\nabla _{\mathbf {r} }\cdot e(\mathbf {r,\mathbf {r} '} ){\mathrm {d} \mathbf {r} '}=0} for

4731-516: The electric attraction and repulsion must be inversely as some power of the distance between that of the 2 + ⁠ 1 / 50 ⁠ th and that of the 2 − ⁠ 1 / 50 ⁠ th , and there is no reason to think that it differs at all from the inverse duplicate ratio". Finally, in 1785, the French physicist Charles-Augustin de Coulomb published his first three reports of electricity and magnetism where he stated his law. This publication

4814-540: The electric field, with ρ ( r ′ ) {\displaystyle \rho (\mathbf {r} ')} a continuous function (density of charge). It is true for all r ≠ r ′ {\displaystyle \mathbf {r} \neq \mathbf {r'} } that ∇ r ⋅ e ( r , r ′ ) = 0 {\displaystyle \nabla _{\mathbf {r} }\cdot \mathbf {e} (\mathbf {r,r'} )=0} . Consider now

4897-707: The expression from Coulomb's law, we get the total field at r by using an integral to sum the field at r due to the infinitesimal charge at each other point s in space, to give E ( r ) = 1 4 π ε 0 ∫ ρ ( s ) ( r − s ) | r − s | 3 d 3 s {\displaystyle \mathbf {E} (\mathbf {r} )={\frac {1}{4\pi \varepsilon _{0}}}\int {\frac {\rho (\mathbf {s} )(\mathbf {r} -\mathbf {s} )}{|\mathbf {r} -\mathbf {s} |^{3}}}\,\mathrm {d} ^{3}\mathbf {s} } where ρ

4980-553: The extraordinary services he rendered by the discovery of X-rays . This award is administered by the Nobel Foundation and is widely regarded as the most prestigious award that a scientist can receive in physics. It is presented in Stockholm at an annual ceremony on the 10th of December, the anniversary of Nobel's death. As of 2024 , a total of 226 individuals have been awarded the prize. Alfred Nobel , in his last will and testament, stated that his wealth should be used to create

5063-415: The fiber through a certain angle, which could be read from a scale on the instrument . By knowing how much force it took to twist the fiber through a given angle, Coulomb was able to calculate the force between the balls and derive his inverse-square proportionality law. Coulomb's law states that the electrostatic force F 1 {\textstyle \mathbf {F} _{1}} experienced by

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5146-421: The field. For a negative point source charge, the direction is radially inwards. The magnitude of the electric field E can be derived from Coulomb's law. By choosing one of the point charges to be the source, and the other to be the test charge, it follows from Coulomb's law that the magnitude of the electric field E created by a single source point charge Q at a certain distance from it r in vacuum

5229-534: The five Nobel Prizes. Owing to the level of skepticism surrounding the will, it was not until 26 April 1897 that it was approved by the Storting (Norwegian Parliament). The executors of his will were Ragnar Sohlman and Rudolf Lilljequist, who formed the Nobel Foundation to take care of Nobel's fortune and organise the prizes. The members of the Norwegian Nobel Committee who were to award

5312-654: The following year. The nominees are scrutinized and discussed by experts and are narrowed to approximately fifteen names. The committee submits a report with recommendations on the final candidates to the Academy, where, in the Physics Class, it is further discussed. The Academy then makes the final selection of the Laureates in Physics by a majority vote. The names of the nominees are never publicly announced, and neither are they told that they have been considered for

5395-505: The force between charges varied as the inverse square of the distance. In 1769, Scottish physicist John Robison announced that, according to his measurements, the force of repulsion between two spheres with charges of the same sign varied as x . In the early 1770s, the dependence of the force between charged bodies upon both distance and charge had already been discovered, but not published, by Henry Cavendish of England. In his notes, Cavendish wrote, "We may therefore conclude that

5478-420: The force between plates of a capacitor , and Franz Aepinus who supposed the inverse-square law in 1758. Based on experiments with electrically charged spheres, Joseph Priestley of England was among the first to propose that electrical force followed an inverse-square law , similar to Newton's law of universal gravitation . However, he did not generalize or elaborate on this. In 1767, he conjectured that

5561-427: The joint administrative body of the prize-awarding institutions, but it is not concerned with the prize deliberations or decisions, which rest exclusively with the four institutions. Coulomb repulsion Coulomb's inverse-square law , or simply Coulomb's law , is an experimental law of physics that calculates the amount of force between two electrically charged particles at rest. This electric force

5644-405: The magnitude, or absolute value, of the attractive or repulsive electrostatic force between two point charges is directly proportional to the product of the magnitudes of their charges and inversely proportional to the square of the distance between them. Coulomb discovered that bodies with like electrical charges repel: It follows therefore from these three tests, that the repulsive force that

5727-411: The metal. This state is now known as the BCS state. In the normal state of a metal, electrons move independently, whereas in the BCS state, they are bound into Cooper pairs by the attractive interaction. The BCS formalism is based on the reduced potential for the electrons' attraction. Within this potential, a variational ansatz for the wave function is proposed. This ansatz was later shown to be exact in

5810-420: The pairing increases this energy barrier, kicks from oscillating atoms in the conductor (which are small at sufficiently low temperatures) are not enough to affect the condensate as a whole, or any individual "member pair" within the condensate. Thus the electrons stay paired together and resist all kicks, and the electron flow as a whole (the current through the superconductor) will not experience resistance. Thus,

5893-625: The phase transition is second order, that it reproduces the Meissner effect and the calculations of specific heats and penetration depths appeared in the December 1957 article, "Theory of superconductivity". They received the Nobel Prize in Physics in 1972 for this theory. In 1986, high-temperature superconductivity was discovered in La-Ba-Cu-O, at temperatures up to 30 K. Following experiments determined more materials with transition temperatures up to about 130 K, considerably above

5976-453: The previous limit of about 30  K . It is experimentally very well known that the transition temperature strongly depends on pressure. In general, it is believed that BCS theory alone cannot explain this phenomenon and that other effects are in play. These effects are still not yet fully understood; it is possible that they even control superconductivity at low temperatures for some materials. At sufficiently low temperatures, electrons near

6059-441: The principle of linear superposition is also used. For a continuous charge distribution, an integral over the region containing the charge is equivalent to an infinite summation, treating each infinitesimal element of space as a point charge d q {\displaystyle dq} . The distribution of charge is usually linear, surface or volumetric. For a linear charge distribution (a good approximation for charge in

6142-622: The prize typically announce the names of the laureates during the first week of October. The prize is then awarded at formal ceremonies held annually in Stockholm Concert Hall on 10 December, the anniversary of Nobel's death. The laureates receive a diploma, a medal, and a document confirming the prize amount. After Nobel's death, the Nobel Foundation was set up to carry out the provisions of his will and to administer his funds. In his will, he had stipulated that four different institutions—three Swedish and one Norwegian—should award

6225-609: The prizes. From Stockholm, the Royal Swedish Academy of Sciences confers the prizes for physics, chemistry, and economics, the Karolinska Institute confers the prize for physiology or medicine, and the Swedish Academy confers the prize for literature. The Norwegian Nobel Committee based in Oslo confers the prize for peace. The Nobel Foundation is the legal owner and functional administrator of the funds and serves as

6308-401: The results of BCS theory do not depend on the origin of the attractive interaction. For instance, Cooper pairs have been observed in ultracold gases of fermions where a homogeneous magnetic field has been tuned to their Feshbach resonance . The original results of BCS (discussed below) described an s-wave superconducting state, which is the rule among low-temperature superconductors but

6391-405: The same sign (like charges) then the product q 1 q 2 {\displaystyle q_{1}q_{2}} is positive and the direction of the force on q 1 {\displaystyle q_{1}} is given by r ^ 12 {\textstyle {\widehat {\mathbf {r} }}_{12}} ; the charges repel each other. If

6474-542: The same physical law in different ways. The law has been tested extensively , and observations have upheld the law on the scale from 10 m to 10 m. Ancient cultures around the Mediterranean knew that certain objects, such as rods of amber , could be rubbed with cat's fur to attract light objects like feathers and pieces of paper. Thales of Miletus made the first recorded description of static electricity around 600 BC, when he noticed that friction could make

6557-563: The significance of achievements being recognized has been "tested by time". In practice, that means that the lag between the discovery and the award is typically on the order of 20 years and can be much longer. For example, half of the 1983 Nobel Prize in Physics was awarded to Subrahmanyan Chandrasekhar for his work on stellar structure and evolution that was done during the 1930s. As a downside of this tested-by-time rule, not all scientists live long enough for their work to be recognized. Some important scientific discoveries are never considered for

6640-506: The two balls – [that were] electrified with the same kind of electricity – exert on each other, follows the inverse proportion of the square of the distance. Coulomb also showed that oppositely charged bodies attract according to an inverse-square law: | F | = k e | q 1 | | q 2 | r 2 {\displaystyle |F|=k_{\text{e}}{\frac {|q_{1}||q_{2}|}{r^{2}}}} Here, k e

6723-454: The validity of Coulomb's inverse square law: The last of these is known as the electrostatic approximation . When movement takes place, an extra factor is introduced, which alters the force produced on the two objects. This extra part of the force is called the magnetic force. For slow movement, the magnetic force is minimal and Coulomb's law can still be considered approximately correct. A more accurate approximation in this case is, however,

6806-468: Was Leon Cooper's calculation of the bound states of electrons subject to an attractive force in his 1956 paper, "Bound Electron Pairs in a Degenerate Fermi Gas". In 1957 Bardeen and Cooper assembled these ingredients and constructed such a theory, the BCS theory, with Robert Schrieffer. The theory was first published in April 1957 in the letter, "Microscopic theory of superconductivity". The demonstration that

6889-411: Was essential to the development of the theory of electromagnetism . He used a torsion balance to study the repulsion and attraction forces of charged particles , and determined that the magnitude of the electric force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. The torsion balance consists of

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