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39-511: The symmetries of the causes are to be found in the effects. The idea was based on the ideas of Franz Ernst Neumann and Bernhard Minnigerode. Thus, it is sometimes known as the Neuman–Minnigerode–Curie principle . This science article is a stub . You can help Misplaced Pages by expanding it . Franz Ernst Neumann Franz Ernst Neumann (11 September 1798 – 23 May 1895) was a German mineralogist and physicist . He devised

78-419: A curl states that the divergence of the curl of a vector field must always be zero. Hence and so the original Ampère's circuital law implies that i.e. that the current density is solenoidal . But in general, reality follows the continuity equation for electric charge : which is nonzero for a time-varying charge density. An example occurs in a capacitor circuit where time-varying charge densities exist on

117-418: A dielectric the above contribution to displacement current is present too, but a major contribution to the displacement current is related to the polarization of the individual molecules of the dielectric material. Even though charges cannot flow freely in a dielectric, the charges in molecules can move a little under the influence of an electric field. The positive and negative charges in molecules separate under

156-514: A given current, or the current associated with a given magnetic field. The original circuital law only applies to a magnetostatic situation, to continuous steady currents flowing in a closed circuit. For systems with electric fields that change over time, the original law (as given in this section) must be modified to include a term known as Maxwell's correction (see below). The original circuital law can be written in several different forms, which are all ultimately equivalent: The integral form of

195-502: A particular direction, creating a microscopic current. When the currents from all these atoms are put together, they create the same effect as a macroscopic current, circulating perpetually around the magnetized object. This magnetization current J M is one contribution to "bound current". The other source of bound current is bound charge . When an electric field is applied, the positive and negative bound charges can separate over atomic distances in polarizable materials , and when

234-583: A renown mathematician and physicist; his younger son Franz Ernst Christian became professor of medicine in Königsberg. Amp%C3%A8re%27s circuital law In classical electromagnetism , Ampère's circuital law (not to be confused with Ampère's force law ) relates the circulation of a magnetic field around a closed loop to the electric current passing through the loop. James Clerk Maxwell derived it using hydrodynamics in his 1861 published paper " On Physical Lines of Force ". In 1865 he generalized

273-463: A student of theology , but soon turned to scientific subjects. His earlier papers were mostly concerned with crystallography , and the reputation they gained him led to his appointment as Privatdozent at the University of Königsberg , where in 1828 he became extraordinary, and in 1829 ordinary, professor of mineralogy and physics . His 1831 study on the specific heats of compounds included what

312-684: Is now known as Neumann's law : the molecular heat of a compound is equal to the sum of the atomic heats of its constituents. Devoting himself next to optics, he produced memoirs which earned him a high place among early searchers of a true dynamical theory of light. In 1832, by the aid of a particular hypothesis as to the constitution of the ether, he reached by a rigorous dynamical calculation results agreeing with those obtained by Augustin Louis Cauchy , and succeeded in deducing laws of double refraction closely resembling those of Augustin-Jean Fresnel . In studying double refraction, with his deduction of

351-408: Is possible. With the addition of the displacement current, Maxwell was able to hypothesize (correctly) that light was a form of electromagnetic wave . See electromagnetic wave equation for a discussion of this important discovery. Proof that the formulations of the circuital law in terms of free current are equivalent to the formulations involving total current In this proof, we will show that

390-432: Is the magnetic H field (also called "auxiliary magnetic field", "magnetic field intensity", or just "magnetic field"), D is the electric displacement field , and J f is the enclosed conduction current or free current density. In differential form, On the other hand, treating all charges on the same footing (disregarding whether they are bound or free charges), the generalized Ampère's equation, also called

429-448: Is the polarization density . Substituting this form for D in the expression for displacement current, it has two components: The first term on the right hand side is present everywhere, even in a vacuum. It doesn't involve any actual movement of charge, but it nevertheless has an associated magnetic field, as if it were an actual current. Some authors apply the name displacement current to only this contribution. The second term on

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468-456: The circulation of the magnetic field around some path (line integral) due to the current which passes through that enclosed path (surface integral). In terms of total current , (which is the sum of both free current and bound current) the line integral of the magnetic B -field (in teslas , T) around closed curve C is proportional to the total current I enc passing through a surface S (enclosed by C ). In terms of free current,

507-414: The 1850s Scottish mathematical physicist James Clerk Maxwell generalized these results and others into a single mathematical law. The original form of Maxwell's circuital law, which he derived as early as 1855 in his paper "On Faraday's Lines of Force" based on an analogy to hydrodynamics, relates magnetic fields to electric currents that produce them. It determines the magnetic field associated with

546-1190: The Maxwell–Ampère equation, is in integral form (see the " proof " section below): ∮ C B ⋅ d l = ∬ S ( μ 0 J + μ 0 ε 0 ∂ E ∂ t ) ⋅ d S {\displaystyle \oint _{C}\mathbf {B} \cdot \mathrm {d} {\boldsymbol {l}}=\iint _{S}\left(\mu _{0}\mathbf {J} +\mu _{0}\varepsilon _{0}{\frac {\partial \mathbf {E} }{\partial t}}\right)\cdot \mathrm {d} \mathbf {S} } In differential form, ∇ × B = μ 0 J + μ 0 ε 0 ∂ E ∂ t {\displaystyle \mathbf {\nabla } \times \mathbf {B} =\mu _{0}\mathbf {J} +\mu _{0}\varepsilon _{0}{\frac {\partial \mathbf {E} }{\partial t}}} In both forms J includes magnetization current density as well as conduction and polarization current densities. That is,

585-440: The applied field, causing an increase in the state of polarization, expressed as the polarization density P . A changing state of polarization is equivalent to a current. Both contributions to the displacement current are combined by defining the displacement current as: where the electric displacement field is defined as: where ε 0 is the electric constant , ε r the relative static permittivity , and P

624-555: The basis of his seminar research. This seminar was the model for many others of the same type established after 1834, including Kirchhoff's own at Heidelberg University . Neumann retired from his professorship in 1876, and died at Königsberg (now Kaliningrad , Russia ) in 1895 at the age of 96. Neumann had four children with his wife Luise Florentine Hagen (born 1800): Carl Gottfried Neumann (1832–1925), Franz Ernst Christian Neumann (1834–1818), Friedrich Julius Neumann (1835-1910), and Luise Neumann (1837-1934). His son Carl, became

663-467: The bound charges move, the polarization changes, creating another contribution to the "bound current", the polarization current J P . The total current density J due to free and bound charges is then: with J f   the "free" or "conduction" current density. All current is fundamentally the same, microscopically. Nevertheless, there are often practical reasons for wanting to treat bound current differently from free current. For example,

702-403: The bound current usually originates over atomic dimensions, and one may wish to take advantage of a simpler theory intended for larger dimensions. The result is that the more microscopic Ampère's circuital law, expressed in terms of B and the microscopic current (which includes free, magnetization and polarization currents), is sometimes put into the equivalent form below in terms of H and

741-459: The circuital equation is extended by including the polarization current, thereby remedying the limited applicability of the original circuital law. Treating free charges separately from bound charges, the equation including Maxwell's correction in terms of the H -field is (the H -field is used because it includes the magnetization currents, so J M does not appear explicitly, see H -field and also Note ): (integral form), where H

780-446: The circuital law. James Clerk Maxwell conceived of displacement current as a polarization current in the dielectric vortex sea, which he used to model the magnetic field hydrodynamically and mechanically. He added this displacement current to Ampère's circuital law at equation 112 in his 1861 paper " On Physical Lines of Force ". In free space , the displacement current is related to the time rate of change of electric field. In

819-515: The current density on the right side of the Ampère–Maxwell equation is: where current density J D is the displacement current , and J is the current density contribution actually due to movement of charges, both free and bound. Because ∇ ⋅  D = ρ , the charge continuity issue with Ampère's original formulation is no longer a problem. Because of the term in ε 0 ⁠ ∂ E / ∂ t ⁠ , wave propagation in free space now

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858-399: The current that passes through a wire or battery . In contrast, "bound current" arises in the context of bulk materials that can be magnetized and/or polarized . (All materials can to some extent.) When a material is magnetized (for example, by placing it in an external magnetic field), the electrons remain bound to their respective atoms, but behave as if they were orbiting the nucleus in

897-406: The elastic constants (on which the optical properties depend) Neumann employed the assumption that the symmetry of the elastic behavior of a crystal was equal to that of its form. In other words, he assumed that the magnitudes of the components of a physical property in symmetric positions are equivalent. This assumption substantially reduced the number of independent constants and greatly simplified

936-513: The elastic equations. However, four decades passed before Neumann elaborated his application of symmetry in a course on elasticity in 1873. This principle was later formalized by his student Woldemar Voigt (1850–1918) in 1885: " the symmetry of the physical phenomenon is at least as high as the crystallographic symmetry ", which became a fundamental postulate of crystal physics known as Neumann’s principle . In 1900, Voigt attributed this principle to Neumann's 1832 paper even though, at most, all that

975-478: The equation is equivalent to the equation Note that we are only dealing with the differential forms, not the integral forms, but that is sufficient since the differential and integral forms are equivalent in each case, by the Kelvin–Stokes theorem . We introduce the polarization density P , which has the following relation to E and D : Next, we introduce the magnetization density M , which has

1014-470: The equation to apply to time-varying currents by adding the displacement current term, resulting in the modern form of the law, sometimes called the Ampère–Maxwell law , which is one of Maxwell's equations that form the basis of classical electromagnetism . In 1820 Danish physicist Hans Christian Ørsted discovered that an electric current creates a magnetic field around it, when he noticed that

1053-476: The first formulas to calculate of inductance . He also formulated Neumann's law for molecular heat. In electromagnetism, he is credited for introducing the magnetic vector potential . Franz Ernst Neumann was born in Joachimsthal , Margraviate of Brandenburg , near Berlin , son of Ernst Neumann a farmer that became state agent. His mother was a Countess that was not allowed to marry Ernst. Franz Ernst Neumann

1092-404: The free current only. For a detailed definition of free current and bound current, and the proof that the two formulations are equivalent, see the " proof " section below. There are two important issues regarding the circuital law that require closer scrutiny. First, there is an issue regarding the continuity equation for electrical charge. In vector calculus, the identity for the divergence of

1131-405: The line integral of the magnetic H -field (in amperes per metre , A·m ) around closed curve C equals the free current I f,enc through a surface S . There are a number of ambiguities in the above definitions that require clarification and a choice of convention. The electric current that arises in the simplest textbook situations would be classified as "free current"—for example,

1170-445: The needle of a compass next to a wire carrying current turned so that the needle was perpendicular to the wire. He investigated and discovered the rules which govern the field around a straight current-carrying wire: This sparked a great deal of research into the relation between electricity and magnetism. André-Marie Ampère investigated the magnetic force between two current-carrying wires, discovering Ampère's force law . In

1209-405: The original circuital law is a line integral of the magnetic field around some closed curve C (arbitrary but must be closed). The curve C in turn bounds both a surface S which the electric current passes through (again arbitrary but not closed—since no three-dimensional volume is enclosed by S ), and encloses the current. The mathematical statement of the law is a relation between

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1248-417: The plates. Second, there is an issue regarding the propagation of electromagnetic waves. For example, in free space , where the circuital law implies that i.e. that the magnetic field is irrotational , but to maintain consistency with the continuity equation for electric charge , we must have To treat these situations, the contribution of displacement current must be added to the current term in

1287-455: The problem of giving mathematical expression to the conditions holding for a surface separating two crystalline media, and worked out from theory the laws of double refraction in strained crystalline bodies. He also made important contributions to the mathematical theory of electrodynamics, and in papers published in 1845 and 1847 established mathematically the laws of the induction of electric currents. His last publication, which appeared in 1878,

1326-422: The right hand side is the displacement current as originally conceived by Maxwell, associated with the polarization of the individual molecules of the dielectric material. Maxwell's original explanation for displacement current focused upon the situation that occurs in dielectric media. In the modern post-aether era, the concept has been extended to apply to situations with no material media present, for example, to

1365-437: The type of precision measurement perfected by his astronomer colleague Friedrich Wilhelm Bessel . The objective of his seminar exercises was to perfect one's ability to practice an exact experimental physics through the control of both constant and random experimental errors. Only a few students actually produced original research in the seminar; a notable exception was Gustav Robert Kirchhoff who formulated Kirchhoff's laws on

1404-455: The vacuum between the plates of a charging vacuum capacitor . The displacement current is justified today because it serves several requirements of an electromagnetic theory: correct prediction of magnetic fields in regions where no free current flows; prediction of wave propagation of electromagnetic fields; and conservation of electric charge in cases where charge density is time-varying. For greater discussion see Displacement current . Next,

1443-666: Was not able to meet his mother until he was 10. Neumann studied in a Gymnasium in Berlin, demonstrating good skills in mathematics. However his studies were interrupted by the war with France. In 1815 he interrupted his studies at Berlin to serve as a volunteer in the Hundred Days against Napoleon , and was wounded in the Battle of Ligny . He later returned to finish his studies in Berlin. Subsequently, he entered Berlin University in 1818 as

1482-523: Was on spherical harmonics ( Beiträge zur Theorie der Kugelfunctionen ). With the mathematician Carl Gustav Jacobi , he founded in 1834 the Mathematisch-physikalisches Seminar which operated in two sections for mathematics and for mathematical physics . Not every student took both sections. In his section on mathematical physics Neumann taught mathematical methods as well as the techniques of an exact experimental physics grounded in

1521-442: Was present in that work was an implicit assumption that the symmetry of the phenomenon was equal to that of the crystal. Bernhard Minnigerode (1837–1896), another student of Neumann, first expressed this relation in written form in 1887 in the journal Neues Jahrb. Mineral Geol. Paleontol . (Vol. 5, p. 145). In 1845, Neumann introduced the magnetic vector potential to discuss Ampère's circuital law . Later, Neumann attacked

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