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Ampère's Circuital Law
In classical electromagnetism, Ampère's circuital law, often simply called Ampère's law, and sometimes Oersted's 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 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. Ampère's original circuital law Until the early 19th century, electricity and magnetism were thought to be completely separate phenomena. This view changed in 1820 when Danish physicist Hans Christian Ørsted discovered that an electric current produces a magnetic effect. He observed that a compass needle placed near a current-carrying wire deflect ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Classical Electromagnetism
Classical electromagnetism or classical electrodynamics is a branch of physics focused on the study of interactions between electric charges and electrical current, currents using an extension of the classical Newtonian model. It is, therefore, a classical field theory. The theory provides a description of electromagnetic phenomena whenever the relevant length scales and field strengths are large enough that quantum mechanical effects are negligible. For small distances and low field strengths, such interactions are better described by quantum electrodynamics which is a quantum field theory. History The physical phenomena that electromagnetism describes have been studied as separate fields since antiquity. For example, there were many advances in the field of History of optics, optics centuries before light was understood to be an electromagnetic wave. However, the theory of electromagnetism, as it is currently understood, grew out of Michael Faraday's experiments suggesting t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
On Physical Lines Of Force
"On Physical Lines of Force" is a four-part paper written by James Clerk Maxwell, published in 1861. In it, Maxwell derived the Maxwell's equations, equations of electromagnetism in conjunction with a "sea" of "molecule, molecular vortex, vortices" which he used to model Michael Faraday, Faraday's lines of force. Maxwell had studied and commented on the field of electricity and magnetism as early as 1855/56 when "On Faraday's Lines of Force" was read to the Cambridge Philosophical Society. Maxwell made an analogy between the density of this medium and the magnetic permeability, as well as an analogy between the transverse elasticity and the dielectric constant, and using the results of a prior experiment by Wilhelm Eduard Weber and Rudolf Kohlrausch performed in 1856, he established a connection between the speed of light and the speed of propagation of waves in this medium. The paper ushered in a new era of classical electrodynamics and catalyzed further progress in the mathemati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Three-dimensional Space
In geometry, a three-dimensional space (3D space, 3-space or, rarely, tri-dimensional space) is a mathematical space in which three values ('' coordinates'') are required to determine the position of a point. Most commonly, it is the three-dimensional Euclidean space, that is, the Euclidean space of dimension three, which models physical space. More general three-dimensional spaces are called '' 3-manifolds''. The term may also refer colloquially to a subset of space, a ''three-dimensional region'' (or 3D domain), a '' solid figure''. Technically, a tuple of numbers can be understood as the Cartesian coordinates of a location in a -dimensional Euclidean space. The set of these -tuples is commonly denoted \R^n, and can be identified to the pair formed by a -dimensional Euclidean space and a Cartesian coordinate system. When , this space is called the three-dimensional Euclidean space (or simply "Euclidean space" when the context is clear). In classical physics, it serve ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Surface (topology)
In the part of mathematics referred to as topology, a surface is a two-dimensional manifold. Some surfaces arise as the boundaries of three-dimensional solid figures; for example, the sphere is the boundary of the solid ball. Other surfaces arise as graphs of functions of two variables; see the figure at right. However, surfaces can also be defined abstractly, without reference to any ambient space. For example, the Klein bottle is a surface that cannot be embedded in three-dimensional Euclidean space. Topological surfaces are sometimes equipped with additional information, such as a Riemannian metric or a complex structure, that connects them to other disciplines within mathematics, such as differential geometry and complex analysis. The various mathematical notions of surface can be used to model surfaces in the physical world. In general In mathematics, a surface is a geometrical shape that resembles a deformed plane. The most familiar examples arise as boundaries ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Closed Curve
In mathematics, a curve (also called a curved line in older texts) is an object similar to a line (geometry), line, but that does not have to be Linearity, straight. Intuitively, a curve may be thought of as the trace left by a moving point (geometry), point. This is the definition that appeared more than 2000 years ago in Euclid's Elements, Euclid's ''Elements'': "The [curved] line is […] the first species of quantity, which has only one dimension, namely length, without any width nor depth, and is nothing else than the flow or run of the point which […] will leave from its imaginary moving some vestige in length, exempt of any width." This definition of a curve has been formalized in modern mathematics as: ''A curve is the image (mathematics), image of an interval (mathematics), interval to a topological space by a continuous function''. In some contexts, the function that defines the curve is called a ''parametrization'', and the curve is a parametric curve. In this artic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Line Integral
In mathematics, a line integral is an integral where the function (mathematics), function to be integrated is evaluated along a curve. The terms ''path integral'', ''curve integral'', and ''curvilinear integral'' are also used; ''contour integral'' is used as well, although that is typically reserved for #Complex line integral, line integrals in the complex plane. The function to be integrated may be a scalar field or a vector field. The value of the line integral is the sum of values of the field at all points on the curve, weighted by some scalar function on the curve (commonly arc length or, for a vector field, the Dot product, scalar product of the vector field with a Differential (infinitesimal), differential vector in the curve). This weighting distinguishes the line integral from simpler integrals defined on interval (mathematics), intervals. Many simple formulae in physics, such as the definition of Work (physics), work as have natural continuous analogues in terms of l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Magnetic Constant
The vacuum magnetic permeability (variously ''vacuum permeability'', ''permeability of free space'', ''permeability of vacuum'', ''magnetic constant'') is the magnetic permeability in a classical vacuum. It is a physical constant, conventionally written as ''μ''0 (pronounced "mu nought" or "mu zero"), approximately equal to 4π × 10−7 H/m (by the former definition of the ampere). It quantifies the strength of the magnetic field induced by an electric current. Expressed in terms of SI base units, it has the unit kg⋅ m⋅ s−2⋅A−2. It can be also expressed in terms of SI derived units, N⋅A−2, H·m−1, or T·m·A−1, which are all equivalent. Since the revision of the SI in 2019 (when the values of '' e'' and '' h'' were fixed as defined quantities), ''μ''0 is an experimentally determined constant, its value being proportional to the dimensionless fine-structure constant, which is known to a relative uncertainty of with no other dependencies ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Constitutive Equation
In physics and engineering, a constitutive equation or constitutive relation is a relation between two or more physical quantities (especially kinetic quantities as related to kinematic quantities) that is specific to a material or substance or field, and approximates its response to external stimuli, usually as applied fields or forces. They are combined with other equations governing physical laws to solve physical problems; for example in fluid mechanics the flow of a fluid in a pipe, in solid state physics the response of a crystal to an electric field, or in structural analysis, the connection between applied stresses or loads to strains or deformations. Some constitutive equations are simply phenomenological; others are derived from first principles. A common approximate constitutive equation frequently is expressed as a simple proportionality using a parameter taken to be a property of the material, such as electrical conductivity or a spring constant. Howe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
SI Units
The International System of Units, internationally known by the abbreviation SI (from French ), is the modern form of the metric system and the world's most widely used system of measurement. It is the only system of measurement with official status in nearly every country in the world, employed in science, technology, industry, and everyday commerce. The SI system is coordinated by the International Bureau of Weights and Measures, which is abbreviated BIPM from . The SI comprises a coherent system of units of measurement starting with seven base units, which are the second (symbol s, the unit of time), metre (m, length), kilogram (kg, mass), ampere (A, electric current), kelvin (K, thermodynamic temperature), mole (mol, amount of substance), and candela (cd, luminous intensity). The system can accommodate coherent units for an unlimited number of additional quantities. These are called coherent derived units, which can always be represented as products of powers of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proof Of Equivalence
Proof most often refers to: * Proof (truth), argument or sufficient evidence for the truth of a proposition * Alcohol proof, a measure of an alcoholic drink's strength Proof may also refer to: Mathematics and formal logic * Formal proof, a construct in proof theory * Mathematical proof, a convincing demonstration that some mathematical statement is necessarily true * Proof complexity, computational resources required to prove statements * Proof procedure, method for producing proofs in proof theory * Proof theory, a branch of mathematical logic that represents proofs as formal mathematical objects * Statistical proof, demonstration of degree of certainty for a hypothesis Law and philosophy * Evidence, information which tends to determine or demonstrate the truth of a proposition * Evidence (law), tested evidence or a legal proof * Legal burden of proof, duty to establish the truth of facts in a trial * Philosophic burden of proof, obligation on a party in a dispute to provide ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kelvin–Stokes Theorem
Stokes' theorem, also known as the Kelvin–Stokes theorem after Lord Kelvin and George Stokes, the fundamental theorem for curls, or simply the curl theorem, is a theorem in vector calculus on \R^3. Given a vector field, the theorem relates the integral of the curl of the vector field over some surface, to the line integral of the vector field around the boundary of the surface. The classical theorem of Stokes can be stated in one sentence: : The line integral of a vector field over a loop is equal to the surface integral of its ''curl'' over the enclosed surface. Stokes' theorem is a special case of the generalized Stokes theorem. In particular, a vector field on \R^3 can be considered as a 1-form in which case its curl is its exterior derivative, a 2-form. Theorem Let \Sigma be a smooth oriented surface in \R^3 with boundary \partial \Sigma \equiv \Gamma . If a vector field \mathbf(x,y,z) = (F_x(x, y, z), F_y(x, y, z), F_z(x, y, z)) is defined and has continuous first ord ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
