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Maxwell's equations

Index Maxwell's equations

Maxwell's equations are a set of partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits. [1]

200 relations: A Dynamical Theory of the Electromagnetic Field, A Treatise on Electricity and Magnetism, Aharonov–Bohm effect, Albert Einstein, Algebra of physical space, Ampère's circuital law, Ampère's force law, Artech House, Atomic nucleus, Atomic spacing, Bit, Boundary (topology), Boundary value problem, Capacitor, Charge conservation, Charge density, Circulation (fluid dynamics), Classical electromagnetism, Classical field theory, Cohomology, Computational electromagnetics, Conformal geometry, Constitutive equation, Cornell University Press, Coulomb's law, Covariant derivative, Covariant formulation of classical electromagnetism, Curl (mathematics), Current density, David J. Griffiths, De Rham cohomology, Del, Dielectric, Differential form, Dimensional analysis, Dipole, Dispersion (optics), Displacement current, Divergence, Divergence theorem, Duane–Hunt law, Electric charge, Electric current, Electric dipole moment, Electric displacement field, Electric field, Electric flux, Electric generator, Electric potential, Electrical network, ..., Electromagnetic four-potential, Electromagnetic induction, Electromagnetic radiation, Electromagnetic spectrum, Electromagnetic tensor, Electromagnetic wave equation, Electromagnetism, Electron, Elementary charge, Euclidean vector, Euler–Heisenberg Lagrangian, Exterior derivative, Faraday's law of induction, Finite element method, Finite-difference time-domain method, Flow velocity, Fluid dynamics, Frequency, Fresnel equations, Galilean transformation, Gamma ray, Gauge theory, Gauss's law, Gauss's law for magnetism, Gaussian surface, General relativity, Google Books, Gravitational constant, Gravitoelectromagnetism, Gravity, Gyromagnetic ratio, Hendrik Lorentz, Henri Poincaré, History of Maxwell's equations, Hodge star operator, Homology (mathematics), Hysteresis, If and only if, Inertial frame of reference, Initial condition, Integral, Interface conditions for electromagnetic fields, International System of Units, James Clerk Maxwell, Jefimenko's equations, Joseph Larmor, Julius Adams Stratton, Kelvin–Stokes theorem, Laplace–Beltrami operator, Leibniz integral rule, Leyden jar, Liénard–Wiechert potential, Light, Line integral, List of textbooks in electromagnetism, Lorentz force, Lorentz–Heaviside units, Lorenz gauge condition, Magnet, Magnetic core, Magnetic field, Magnetic flux, Magnetic monopole, Magnetic potential, Magnetization, Manifest covariance, Mathematical descriptions of the electromagnetic field, Matrix representation of Maxwell's equations, Metric tensor, Minkowski space, Moving magnet and conductor problem, Nabla symbol, Nonclassical light, Nonlinear optics, Normal (geometry), Numerical partial differential equations, Ohm's law, Oliver Heaviside, Optics, Overdetermined system, Partial differential equation, Particle physics, Perfectly matched layer, Periodic boundary conditions, Permeability (electromagnetism), Permittivity, Phase (waves), Phase velocity, Photoelectric effect, Photon, Physical constant, Physical law, Planck constant, Planck units, Planck's law, Poincaré group, Polarization density, Position (vector), Prentice Hall, Proposed redefinition of SI base units, Pseudovector, Quantum cryptography, Quantum electrodynamics, Quantum entanglement, Quantum field theory, Quantum mechanics, Quantum optics, Quaternion, Radio wave, Relative permittivity, Resonator, Riemann–Silberstein vector, Rudolf Kohlrausch, Scalar (physics), Science and Hypothesis, Sine wave, Single-photon avalanche diode, Solenoidal vector field, Spacetime, Spacetime algebra, Special relativity, Speed of light, Spin ice, Stokes' theorem, Surface (topology), Surface integral, Tensor, Tensor calculus, The Maxwellians, Theoretical physics, Topological insulator, Two-photon physics, Vacuum permeability, Vacuum permittivity, Vector area, Vector calculus, Vector field, Vector potential, Virtual particle, Volume element, Volume integral, Vorticity, Walter Lewin, Wave equation, Waveguide, Wheeler–Feynman absorber theory, Wilhelm Eduard Weber, Wireless, Work (physics), X-ray. Expand index (150 more) »

A Dynamical Theory of the Electromagnetic Field

"A Dynamical Theory of the Electromagnetic Field" is a paper by James Clerk Maxwell on electromagnetism, published in 1865.

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A Treatise on Electricity and Magnetism

A Treatise on Electricity and Magnetism is a two-volume treatise on electromagnetism written by James Clerk Maxwell in 1873.

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Aharonov–Bohm effect

The Aharonov–Bohm effect, sometimes called the Ehrenberg–Siday–Aharonov–Bohm effect, is a quantum mechanical phenomenon in which an electrically charged particle is affected by an electromagnetic potential (V, A), despite being confined to a region in which both the magnetic field B and electric field E are zero.

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Albert Einstein

Albert Einstein (14 March 1879 – 18 April 1955) was a German-born theoretical physicist who developed the theory of relativity, one of the two pillars of modern physics (alongside quantum mechanics).

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Algebra of physical space

In physics, the algebra of physical space (APS) is the use of the Clifford or geometric algebra Cl3,0(R) of the three-dimensional Euclidean space as a model for (3+1)-dimensional spacetime, representing a point in spacetime via a paravector (3-dimensional vector plus a 1-dimensional scalar).

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Ampère's circuital law

In classical electromagnetism, Ampère's circuital law (not to be confused with Ampère's force law that André-Marie Ampère discovered in 1823) relates the integrated magnetic field around a closed loop to the electric current passing through the loop.

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Ampère's force law

In magnetostatics, the force of attraction or repulsion between two current-carrying wires (see first figure below) is often called Ampère's force law.

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Artech House

Artech House (a.k.a. Artech House Publishers) is a publisher of professional scientific and engineering books.

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Atomic nucleus

The atomic nucleus is the small, dense region consisting of protons and neutrons at the center of an atom, discovered in 1911 by Ernest Rutherford based on the 1909 Geiger–Marsden gold foil experiment.

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Atomic spacing

Atomic spacing refers to the distance between the nuclei of atoms in a material.

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Bit

The bit (a portmanteau of binary digit) is a basic unit of information used in computing and digital communications.

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Boundary (topology)

In topology and mathematics in general, the boundary of a subset S of a topological space X is the set of points which can be approached both from S and from the outside of S. More precisely, it is the set of points in the closure of S not belonging to the interior of S. An element of the boundary of S is called a boundary point of S. The term boundary operation refers to finding or taking the boundary of a set.

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Boundary value problem

In mathematics, in the field of differential equations, a boundary value problem is a differential equation together with a set of additional constraints, called the boundary conditions.

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Capacitor

A capacitor is a passive two-terminal electrical component that stores potential energy in an electric field.

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Charge conservation

In physics, charge conservation is the principle that the total electric charge in an isolated system never changes.

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Charge density

In electromagnetism, charge density is a measure of the amount of electric charge per unit length, surface area, or volume.

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Circulation (fluid dynamics)

In fluid dynamics, circulation is the line integral around a closed curve of the velocity field.

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Classical electromagnetism

Classical electromagnetism or classical electrodynamics is a branch of theoretical physics that studies the interactions between electric charges and currents using an extension of the classical Newtonian model.

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Classical field theory

A classical field theory is a physical theory that predicts how one or more physical fields interact with matter through field equations.

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Cohomology

In mathematics, specifically in homology theory and algebraic topology, cohomology is a general term for a sequence of abelian groups associated to a topological space, often defined from a cochain complex.

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Computational electromagnetics

Computational electromagnetics, computational electrodynamics or electromagnetic modeling is the process of modeling the interaction of electromagnetic fields with physical objects and the environment.

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Conformal geometry

In mathematics, conformal geometry is the study of the set of angle-preserving (conformal) transformations on a space.

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Constitutive equation

In physics and engineering, a constitutive equation or constitutive relation is a relation between two physical quantities (especially kinetic quantities as related to kinematic quantities) that is specific to a material or substance, and approximates the response of that material to external stimuli, usually as applied fields or forces.

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Cornell University Press

The Cornell University Press is a division of Cornell University housed in Sage House, the former residence of Henry William Sage.

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Coulomb's law

Coulomb's law, or Coulomb's inverse-square law, is a law of physics for quantifying the amount of force with which stationary electrically charged particles repel or attract each other.

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Covariant derivative

In mathematics, the covariant derivative is a way of specifying a derivative along tangent vectors of a manifold.

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Covariant formulation of classical electromagnetism

The covariant formulation of classical electromagnetism refers to ways of writing the laws of classical electromagnetism (in particular, Maxwell's equations and the Lorentz force) in a form that is manifestly invariant under Lorentz transformations, in the formalism of special relativity using rectilinear inertial coordinate systems.

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Curl (mathematics)

In vector calculus, the curl is a vector operator that describes the infinitesimal rotation of a vector field in three-dimensional Euclidean space.

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Current density

In electromagnetism, current density is the electric current per unit area of cross section.

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David J. Griffiths

David Jeffrey Griffiths (born 1942) is a U.S. physicist and educator.

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De Rham cohomology

In mathematics, de Rham cohomology (after Georges de Rham) is a tool belonging both to algebraic topology and to differential topology, capable of expressing basic topological information about smooth manifolds in a form particularly adapted to computation and the concrete representation of cohomology classes.

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Del

Del, or nabla, is an operator used in mathematics, in particular in vector calculus, as a vector differential operator, usually represented by the nabla symbol ∇.

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Dielectric

A dielectric (or dielectric material) is an electrical insulator that can be polarized by an applied electric field.

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Differential form

In the mathematical fields of differential geometry and tensor calculus, differential forms are an approach to multivariable calculus that is independent of coordinates.

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Dimensional analysis

In engineering and science, dimensional analysis is the analysis of the relationships between different physical quantities by identifying their base quantities (such as length, mass, time, and electric charge) and units of measure (such as miles vs. kilometers, or pounds vs. kilograms) and tracking these dimensions as calculations or comparisons are performed.

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Dipole

In electromagnetism, there are two kinds of dipoles.

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Dispersion (optics)

In optics, dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency.

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Displacement current

In electromagnetism, displacement current density is the quantity appearing in Maxwell's equations that is defined in terms of the rate of change of, the electric displacement field.

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Divergence

In vector calculus, divergence is a vector operator that produces a scalar field, giving the quantity of a vector field's source at each point.

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Divergence theorem

In vector calculus, the divergence theorem, also known as Gauss's theorem or Ostrogradsky's theorem, reprinted in is a result that relates the flow (that is, flux) of a vector field through a surface to the behavior of the vector field inside the surface.

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Duane–Hunt law

The Duane–Hunt law, named after the American physicists William Duane and Franklin Hunt, gives the maximum frequency of X-rays that can be emitted by Bremsstrahlung in an X-ray tube by accelerating electrons through an excitation voltage V into a metal target.

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Electric charge

Electric charge is the physical property of matter that causes it to experience a force when placed in an electromagnetic field.

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Electric current

An electric current is a flow of electric charge.

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Electric dipole moment

The electric dipole moment is a measure of the separation of positive and negative electrical charges within a system, that is, a measure of the system's overall polarity.

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Electric displacement field

In physics, the electric displacement field, denoted by D, is a vector field that appears in Maxwell's equations.

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Electric field

An electric field is a vector field surrounding an electric charge that exerts force on other charges, attracting or repelling them.

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Electric flux

In electromagnetism, electric flux is the measure of flow of the electric field through a given area.

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Electric generator

In electricity generation, a generator is a device that converts motive power (mechanical energy) into electrical power for use in an external circuit.

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Electric potential

An electric potential (also called the electric field potential, potential drop or the electrostatic potential) is the amount of work needed to move a unit positive charge from a reference point to a specific point inside the field without producing any acceleration.

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Electrical network

An electrical network is an interconnection of electrical components (e.g. batteries, resistors, inductors, capacitors, switches) or a model of such an interconnection, consisting of electrical elements (e.g. voltage sources, current sources, resistances, inductances, capacitances).

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Electromagnetic four-potential

An electromagnetic four-potential is a relativistic vector function from which the electromagnetic field can be derived.

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Electromagnetic induction

Electromagnetic or magnetic induction is the production of an electromotive force (i.e., voltage) across an electrical conductor in a changing magnetic field.

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Electromagnetic radiation

In physics, electromagnetic radiation (EM radiation or EMR) refers to the waves (or their quanta, photons) of the electromagnetic field, propagating (radiating) through space-time, carrying electromagnetic radiant energy.

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Electromagnetic spectrum

The electromagnetic spectrum is the range of frequencies (the spectrum) of electromagnetic radiation and their respective wavelengths and photon energies.

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Electromagnetic tensor

In electromagnetism, the electromagnetic tensor or electromagnetic field tensor (sometimes called the field strength tensor, Faraday tensor or Maxwell bivector) is a mathematical object that describes the electromagnetic field in spacetime.

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Electromagnetic wave equation

The electromagnetic wave equation is a second-order partial differential equation that describes the propagation of electromagnetic waves through a medium or in a vacuum.

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Electromagnetism

Electromagnetism is a branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electrically charged particles.

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Electron

The electron is a subatomic particle, symbol or, whose electric charge is negative one elementary charge.

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Elementary charge

The elementary charge, usually denoted as or sometimes, is the electric charge carried by a single proton, or equivalently, the magnitude of the electric charge carried by a single electron, which has charge.

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Euclidean vector

In mathematics, physics, and engineering, a Euclidean vector (sometimes called a geometric or spatial vector, or—as here—simply a vector) is a geometric object that has magnitude (or length) and direction.

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Euler–Heisenberg Lagrangian

In physics, the Euler–Heisenberg Lagrangian describes the non-linear dynamics of electromagnetic fields in vacuum.

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Exterior derivative

On a differentiable manifold, the exterior derivative extends the concept of the differential of a function to differential forms of higher degree.

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Faraday's law of induction

Faraday's law of induction is a basic law of electromagnetism predicting how a magnetic field will interact with an electric circuit to produce an electromotive force (EMF)—a phenomenon called electromagnetic induction.

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Finite element method

The finite element method (FEM), is a numerical method for solving problems of engineering and mathematical physics.

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Finite-difference time-domain method

Finite-difference time-domain or Yee's method (named after the Chinese American applied mathematician Kane S. Yee, born 1934) is a numerical analysis technique used for modeling computational electrodynamics (finding approximate solutions to the associated system of differential equations).

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Flow velocity

In continuum mechanics the macroscopic velocity, also flow velocity in fluid dynamics or drift velocity in electromagnetism, is a vector field used to mathematically describe the motion of a continuum.

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Fluid dynamics

In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids - liquids and gases.

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Frequency

Frequency is the number of occurrences of a repeating event per unit of time.

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Fresnel equations

The Fresnel equations (or Fresnel coefficients) describe the reflection and transmission of light (or electromagnetic radiation in general) when incident on an interface between different optical media.

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Galilean transformation

In physics, a Galilean transformation is used to transform between the coordinates of two reference frames which differ only by constant relative motion within the constructs of Newtonian physics.

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Gamma ray

A gamma ray or gamma radiation (symbol γ or \gamma), is penetrating electromagnetic radiation arising from the radioactive decay of atomic nuclei.

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Gauge theory

In physics, a gauge theory is a type of field theory in which the Lagrangian is invariant under certain Lie groups of local transformations.

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Gauss's law

In physics, Gauss's law, also known as Gauss's flux theorem, is a law relating the distribution of electric charge to the resulting electric field.

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Gauss's law for magnetism

In physics, Gauss's law for magnetism is one of the four Maxwell's equations that underlie classical electrodynamics.

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Gaussian surface

A Gaussian surface (sometimes abbreviated as G.S.) is a closed surface in three-dimensional space through which the flux of a vector field is calculated; usually the gravitational field, the electric field, or magnetic field.

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General relativity

General relativity (GR, also known as the general theory of relativity or GTR) is the geometric theory of gravitation published by Albert Einstein in 1915 and the current description of gravitation in modern physics.

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Google Books

Google Books (previously known as Google Book Search and Google Print and by its codename Project Ocean) is a service from Google Inc. that searches the full text of books and magazines that Google has scanned, converted to text using optical character recognition (OCR), and stored in its digital database.

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Gravitational constant

The gravitational constant (also known as the "universal gravitational constant", the "Newtonian constant of gravitation", or the "Cavendish gravitational constant"), denoted by the letter, is an empirical physical constant involved in the calculation of gravitational effects in Sir Isaac Newton's law of universal gravitation and in Albert Einstein's general theory of relativity.

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Gravitoelectromagnetism

Gravitoelectromagnetism, abbreviated GEM, refers to a set of formal analogies between the equations for electromagnetism and relativistic gravitation; specifically: between Maxwell's field equations and an approximation, valid under certain conditions, to the Einstein field equations for general relativity.

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Gravity

Gravity, or gravitation, is a natural phenomenon by which all things with mass or energy—including planets, stars, galaxies, and even light—are brought toward (or gravitate toward) one another.

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Gyromagnetic ratio

In physics, the gyromagnetic ratio (also sometimes known as the magnetogyric ratio in other disciplines) of a particle or system is the ratio of its magnetic moment to its angular momentum, and it is often denoted by the symbol γ, gamma.

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Hendrik Lorentz

Hendrik Antoon Lorentz (18 July 1853 – 4 February 1928) was a Dutch physicist who shared the 1902 Nobel Prize in Physics with Pieter Zeeman for the discovery and theoretical explanation of the Zeeman effect.

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Henri Poincaré

Jules Henri Poincaré (29 April 1854 – 17 July 1912) was a French mathematician, theoretical physicist, engineer, and philosopher of science.

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History of Maxwell's equations

In electromagnetism, one of the fundamental fields of physics, the introduction of Maxwell's equations (mainly in "A Dynamical Theory of the Electromagnetic Field") was one of the most important aggregations of empirical facts in the history of physics.

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Hodge star operator

In mathematics, the Hodge isomorphism or Hodge star operator is an important linear map introduced in general by W. V. D. Hodge.

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Homology (mathematics)

In mathematics, homology is a general way of associating a sequence of algebraic objects such as abelian groups or modules to other mathematical objects such as topological spaces.

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Hysteresis

Hysteresis is the dependence of the state of a system on its history.

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If and only if

In logic and related fields such as mathematics and philosophy, if and only if (shortened iff) is a biconditional logical connective between statements.

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Inertial frame of reference

An inertial frame of reference in classical physics and special relativity is a frame of reference in which a body with zero net force acting upon it is not accelerating; that is, such a body is at rest or it is moving at a constant speed in a straight line.

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Initial condition

In mathematics and particularly in dynamic systems, an initial condition, in some contexts called a seed value, is a value of an evolving variable at some point in time designated as the initial time (typically denoted t.

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Integral

In mathematics, an integral assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data.

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Interface conditions for electromagnetic fields

Interface conditions describe the behaviour of electromagnetic fields; electric field, electric displacement field, and the magnetic field at the interface of two materials.

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International System of Units

The International System of Units (SI, abbreviated from the French Système international (d'unités)) is the modern form of the metric system, and is the most widely used system of measurement.

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James Clerk Maxwell

James Clerk Maxwell (13 June 1831 – 5 November 1879) was a Scottish scientist in the field of mathematical physics.

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Jefimenko's equations

In electromagnetism, Jefimenko's equations (named after Oleg D. Jefimenko) give the electric field and magnetic field due to a distribution of electric charges and electric current in space, that takes into account the propagation delay (retarded time) of the fields due to the finite speed of light and relativistic effects.

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Joseph Larmor

Sir Joseph Larmor FRS FRSE DCL LLD (11 July 1857 – 19 May 1942) was an Irish physicist and mathematician who made innovations in the understanding of electricity, dynamics, thermodynamics, and the electron theory of matter.

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Julius Adams Stratton

Julius Adams Stratton (May 18, 1901 – June 22, 1994) was a U.S. electrical engineer and university administrator.

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Kelvin–Stokes theorem

The Kelvin–Stokes theoremThis proof is based on the Lecture Notes given by Prof.

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Laplace–Beltrami operator

In differential geometry, the Laplace operator, named after Pierre-Simon Laplace, can be generalized to operate on functions defined on surfaces in Euclidean space and, more generally, on Riemannian and pseudo-Riemannian manifolds.

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Leibniz integral rule

In calculus, Leibniz's rule for differentiation under the integral sign, named after Gottfried Leibniz, states that for an integral of the form where -\infty, the derivative of this integral is expressible as where the partial derivative indicates that inside the integral, only the variation of f(x, t) with x is considered in taking the derivative.

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Leyden jar

A Leyden jar (or Leiden jar) stores a high-voltage electric charge (from an external source) between electrical conductors on the inside and outside of a glass jar.

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Liénard–Wiechert potential

Liénard–Wiechert potentials describe the classical electromagnetic effect of a moving electric point charge in terms of a vector potential and a scalar potential in the Lorenz gauge.

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Light

Light is electromagnetic radiation within a certain portion of the electromagnetic spectrum.

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Line integral

In mathematics, a line integral is an integral where the function to be integrated is evaluated along a curve.

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List of textbooks in electromagnetism

Following is a list of notable textbooks in electromagnetism.

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Lorentz force

In physics (particularly in electromagnetism) the Lorentz force is the combination of electric and magnetic force on a point charge due to electromagnetic fields.

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Lorentz–Heaviside units

Lorentz–Heaviside units (or Heaviside–Lorentz units) constitute a system of units (particularly electromagnetic units) within CGS, named for Hendrik Antoon Lorentz and Oliver Heaviside.

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Lorenz gauge condition

In electromagnetism, the Lorenz gauge condition or Lorenz gauge is a partial gauge fixing of the electromagnetic vector potential.

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Magnet

A magnet is a material or object that produces a magnetic field.

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Magnetic core

A magnetic core is a piece of magnetic material with a high magnetic permeability used to confine and guide magnetic fields in electrical, electromechanical and magnetic devices such as electromagnets, transformers, electric motors, generators, inductors, magnetic recording heads, and magnetic assemblies.

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Magnetic field

A magnetic field is a vector field that describes the magnetic influence of electrical currents and magnetized materials.

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Magnetic flux

In physics, specifically electromagnetism, the magnetic flux (often denoted or) through a surface is the surface integral of the normal component of the magnetic field B passing through that surface.

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Magnetic monopole

A magnetic monopole is a hypothetical elementary particle in particle physics that is an isolated magnet with only one magnetic pole (a north pole without a south pole or vice versa).

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Magnetic potential

The term magnetic potential can be used for either of two quantities in classical electromagnetism: the magnetic vector potential, or simply vector potential, A; and the magnetic scalar potential ψ. Both quantities can be used in certain circumstances to calculate the magnetic field B. The more frequently used magnetic vector potential is defined so that its curl is equal to the magnetic field: curl A.

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Magnetization

In classical electromagnetism, magnetization or magnetic polarization is the vector field that expresses the density of permanent or induced magnetic dipole moments in a magnetic material.

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Manifest covariance

In general relativity, a manifestly covariant equation is one in which all expressions are tensors.

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Mathematical descriptions of the electromagnetic field

There are various mathematical descriptions of the electromagnetic field that are used in the study of electromagnetism, one of the four fundamental interactions of nature.

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Matrix representation of Maxwell's equations

In electromagnetism, a branch of fundamental physics, the matrix representations of the Maxwell's equations are a formulation of Maxwell's equations using matrices, complex numbers, and vector calculus.

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Metric tensor

In the mathematical field of differential geometry, a metric tensor is a type of function which takes as input a pair of tangent vectors and at a point of a surface (or higher dimensional differentiable manifold) and produces a real number scalar in a way that generalizes many of the familiar properties of the dot product of vectors in Euclidean space.

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Minkowski space

In mathematical physics, Minkowski space (or Minkowski spacetime) is a combining of three-dimensional Euclidean space and time into a four-dimensional manifold where the spacetime interval between any two events is independent of the inertial frame of reference in which they are recorded.

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Moving magnet and conductor problem

The moving magnet and conductor problem is a famous thought experiment, originating in the 19th century, concerning the intersection of classical electromagnetism and special relativity.

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Nabla symbol

∇ The nabla symbol The nabla is a triangular symbol like an inverted Greek delta:Indeed, it is called anadelta (ανάδελτα) in Modern Greek.

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Nonclassical light

Nonclassical light is light that cannot be described using classical electromagnetism; its characteristics are described by the quantized electromagnetic field and quantum mechanics.

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Nonlinear optics

Nonlinear optics (NLO) is the branch of optics that describes the behavior of light in nonlinear media, that is, media in which the dielectric polarization P responds nonlinearly to the electric field E of the light.

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Normal (geometry)

In geometry, a normal is an object such as a line or vector that is perpendicular to a given object.

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Numerical partial differential equations

Numerical partial differential equations is the branch of numerical analysis that studies the numerical solution of partial differential equations (PDEs).

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Ohm's law

Ohm's law states that the current through a conductor between two points is directly proportional to the voltage across the two points.

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Oliver Heaviside

Oliver Heaviside FRS (18 May 1850 – 3 February 1925) was an English self-taught electrical engineer, mathematician, and physicist who adapted complex numbers to the study of electrical circuits, invented mathematical techniques for the solution of differential equations (equivalent to Laplace transforms), reformulated Maxwell's field equations in terms of electric and magnetic forces and energy flux, and independently co-formulated vector analysis.

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Optics

Optics is the branch of physics which involves the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it.

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Overdetermined system

In mathematics, a system of equations is considered overdetermined if there are more equations than unknowns.

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Partial differential equation

In mathematics, a partial differential equation (PDE) is a differential equation that contains unknown multivariable functions and their partial derivatives.

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Particle physics

Particle physics (also high energy physics) is the branch of physics that studies the nature of the particles that constitute matter and radiation.

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Perfectly matched layer

A perfectly matched layer (PML) is an artificial absorbing layer for wave equations, commonly used to truncate computational regions in numerical methods to simulate problems with open boundaries, especially in the FDTD and FE methods.

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Periodic boundary conditions

Periodic boundary conditions (PBCs) are a set of boundary conditions which are often chosen for approximating a large (infinite) system by using a small part called a unit cell.

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Permeability (electromagnetism)

In electromagnetism, permeability is the measure of the ability of a material to support the formation of a magnetic field within itself.

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Permittivity

In electromagnetism, absolute permittivity, often simply called permittivity, usually denoted by the Greek letter ε (epsilon), is the measure of resistance that is encountered when forming an electric field in a particular medium.

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Phase (waves)

Phase is the position of a point in time (an instant) on a waveform cycle.

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Phase velocity

The phase velocity of a wave is the rate at which the phase of the wave propagates in space.

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Photoelectric effect

The photoelectric effect is the emission of electrons or other free carriers when light shines on a material.

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Photon

The photon is a type of elementary particle, the quantum of the electromagnetic field including electromagnetic radiation such as light, and the force carrier for the electromagnetic force (even when static via virtual particles).

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Physical constant

A physical constant, sometimes fundamental physical constant or universal constant, is a physical quantity that is generally believed to be both universal in nature and have constant value in time.

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Physical law

A physical law or scientific law is a theoretical statement "inferred from particular facts, applicable to a defined group or class of phenomena, and expressible by the statement that a particular phenomenon always occurs if certain conditions be present." Physical laws are typically conclusions based on repeated scientific experiments and observations over many years and which have become accepted universally within the scientific community.

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Planck constant

The Planck constant (denoted, also called Planck's constant) is a physical constant that is the quantum of action, central in quantum mechanics.

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Planck units

In particle physics and physical cosmology, Planck units are a set of units of measurement defined exclusively in terms of five universal physical constants, in such a manner that these five physical constants take on the numerical value of 1 when expressed in terms of these units.

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Planck's law

Planck's law describes the spectral density of electromagnetic radiation emitted by a black body in thermal equilibrium at a given temperature T. The law is named after Max Planck, who proposed it in 1900.

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Poincaré group

The Poincaré group, named after Henri Poincaré (1906), was first defined by Minkowski (1908) as the group of Minkowski spacetime isometries.

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Polarization density

In classical electromagnetism, polarization density (or electric polarization, or simply polarization) is the vector field that expresses the density of permanent or induced electric dipole moments in a dielectric material.

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Position (vector)

In geometry, a position or position vector, also known as location vector or radius vector, is a Euclidean vector that represents the position of a point P in space in relation to an arbitrary reference origin O. Usually denoted x, r, or s, it corresponds to the straight-line from O to P. The term "position vector" is used mostly in the fields of differential geometry, mechanics and occasionally vector calculus.

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Prentice Hall

Prentice Hall is a major educational publisher owned by Pearson plc.

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Proposed redefinition of SI base units

The International Committee for Weights and Measures (CIPM) has proposed revised definitions of the SI base units, for consideration at the 26th General Conference on Weights and Measures (CGPM).

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Pseudovector

In physics and mathematics, a pseudovector (or axial vector) is a quantity that transforms like a vector under a proper rotation, but in three dimensions gains an additional sign flip under an improper rotation such as a reflection.

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Quantum cryptography

Quantum cryptography is the science of exploiting quantum mechanical properties to perform cryptographic tasks.

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Quantum electrodynamics

In particle physics, quantum electrodynamics (QED) is the relativistic quantum field theory of electrodynamics.

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Quantum entanglement

Quantum entanglement is a physical phenomenon which occurs when pairs or groups of particles are generated, interact, or share spatial proximity in ways such that the quantum state of each particle cannot be described independently of the state of the other(s), even when the particles are separated by a large distance—instead, a quantum state must be described for the system as a whole.

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Quantum field theory

In theoretical physics, quantum field theory (QFT) is the theoretical framework for constructing quantum mechanical models of subatomic particles in particle physics and quasiparticles in condensed matter physics.

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Quantum mechanics

Quantum mechanics (QM; also known as quantum physics, quantum theory, the wave mechanical model, or matrix mechanics), including quantum field theory, is a fundamental theory in physics which describes nature at the smallest scales of energy levels of atoms and subatomic particles.

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Quantum optics

Quantum optics (QO) is a field of research that uses semi-classical and quantum-mechanical physics to investigate phenomena involving light and its interactions with matter at submicroscopic levels.

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Quaternion

In mathematics, the quaternions are a number system that extends the complex numbers.

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Radio wave

Radio waves are a type of electromagnetic radiation with wavelengths in the electromagnetic spectrum longer than infrared light.

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Relative permittivity

The relative permittivity of a material is its (absolute) permittivity expressed as a ratio relative to the permittivity of vacuum.

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Resonator

A resonator is a device or system that exhibits resonance or resonant behavior, that is, it naturally oscillates at some frequencies, called its resonant frequencies, with greater amplitude than at others.

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Riemann–Silberstein vector

In mathematical physics, in particular electromagnetism, the Riemann–Silberstein vector, named after Bernhard Riemann and Ludwik Silberstein, (or sometimes ambiguously called the "electromagnetic field") is a complex vector that combines the electric field E and the magnetic field B.

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Rudolf Kohlrausch

Rudolf Hermann Arndt Kohlrausch (November 6, 1809 in Göttingen – March 8, 1858 in Erlangen) was a German physicist.

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Scalar (physics)

A scalar or scalar quantity in physics is a physical quantity that can be described by a single element of a number field such as a real number, often accompanied by units of measurement.

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Science and Hypothesis

Science and Hypothesis (La Science et l'Hypothèse) is a book by French mathematician Henri Poincaré, first published in 1902.

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Sine wave

A sine wave or sinusoid is a mathematical curve that describes a smooth periodic oscillation.

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Single-photon avalanche diode

A single-photon avalanche diode (SPAD) is a solid-state photodetector in which a photon-generated carrier (via the internal photoelectric effect) can trigger a short-duration but relatively large avalanche current.

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Solenoidal vector field

In vector calculus a solenoidal vector field (also known as an incompressible vector field, a divergence-free vector field, or a '''transverse vector field''') is a vector field v with divergence zero at all points in the field.

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Spacetime

In physics, spacetime is any mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum.

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Spacetime algebra

In mathematical physics, spacetime algebra (STA) is a name for the Clifford algebra Cl1,3(R), or equivalently the geometric algebra, which can be particularly closely associated with the geometry of special relativity and relativistic spacetime.

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Special relativity

In physics, special relativity (SR, also known as the special theory of relativity or STR) is the generally accepted and experimentally well-confirmed physical theory regarding the relationship between space and time.

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Speed of light

The speed of light in vacuum, commonly denoted, is a universal physical constant important in many areas of physics.

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Spin ice

A spin ice is a magnetic substance that does not have a single minimal-energy state.

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Stokes' theorem

In vector calculus, and more generally differential geometry, Stokes' theorem (also called the generalized Stokes theorem or the Stokes–Cartan theorem) is a statement about the integration of differential forms on manifolds, which both simplifies and generalizes several theorems from vector calculus.

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Surface (topology)

In topology and differential geometry, a surface is a two-dimensional manifold, and, as such, may be an "abstract surface" not embedded in any Euclidean space.

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Surface integral

In mathematics, a surface integral is a generalization of multiple integrals to integration over surfaces.

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Tensor

In mathematics, tensors are geometric objects that describe linear relations between geometric vectors, scalars, and other tensors.

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Tensor calculus

In mathematics, tensor calculus or tensor analysis is an extension of vector calculus to tensor fields (tensors that may vary over a manifold, e.g. in spacetime).

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The Maxwellians

The Maxwellians is a book by Bruce J. Hunt, published in 1991 by Cornell University Press.

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Theoretical physics

Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena.

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Topological insulator

A topological insulator is a material with non-trivial symmetry-protected topological order that behaves as an insulator in its interior but whose surface contains conducting states, meaning that electrons can only move along the surface of the material.

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Two-photon physics

Two-photon physics, also called gamma–gamma physics, is a branch of particle physics that describes the interactions between two photons.

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Vacuum permeability

The physical constant μ0, (pronounced "mu naught" or "mu zero"), commonly called the vacuum permeability, permeability of free space, permeability of vacuum, or magnetic constant, is an ideal, (baseline) physical constant, which is the value of magnetic permeability in a classical vacuum.

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Vacuum permittivity

The physical constant (pronounced as "epsilon nought"), commonly called the vacuum permittivity, permittivity of free space or electric constant, is an ideal, (baseline) physical constant, which is the value of the absolute dielectric permittivity of classical vacuum.

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Vector area

In 3-dimensional geometry, for a finite planar surface of scalar area and unit normal, the vector area is defined as the unit normal scaled by the area: For an orientable surface composed of a set of flat facet areas, the vector area of the surface is given by where is the unit normal vector to the area.

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Vector calculus

Vector calculus, or vector analysis, is a branch of mathematics concerned with differentiation and integration of vector fields, primarily in 3-dimensional Euclidean space \mathbb^3.

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Vector field

In vector calculus and physics, a vector field is an assignment of a vector to each point in a subset of space.

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Vector potential

In vector calculus, a vector potential is a vector field whose curl is a given vector field.

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Virtual particle

In physics, a virtual particle is a transient fluctuation that exhibits some of the characteristics of an ordinary particle, but whose existence is limited by the uncertainty principle.

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Volume element

In mathematics, a volume element provides a means for integrating a function with respect to volume in various coordinate systems such as spherical coordinates and cylindrical coordinates.

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Volume integral

In mathematics—in particular, in multivariable calculus—a volume integral refers to an integral over a 3-dimensional domain, that is, it is a special case of multiple integrals.

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Vorticity

In continuum mechanics, the vorticity is a pseudovector field that describes the local spinning motion of a continuum near some point (the tendency of something to rotate), as would be seen by an observer located at that point and traveling along with the flow.

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Walter Lewin

Walter Hendrik Gustav Lewin (born January 29, 1936) is a Dutch astrophysicist and former professor of physics at the Massachusetts Institute of Technology.

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Wave equation

The wave equation is an important second-order linear partial differential equation for the description of waves—as they occur in classical physics—such as mechanical waves (e.g. water waves, sound waves and seismic waves) or light waves.

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Waveguide

A waveguide is a structure that guides waves, such as electromagnetic waves or sound, with minimal loss of energy by restricting expansion to one dimension or two.

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Wheeler–Feynman absorber theory

The Wheeler–Feynman absorber theory (also called the Wheeler–Feynman time-symmetric theory), named after its originators, the physicists Richard Feynman and John Archibald Wheeler, is an interpretation of electrodynamics derived from the assumption that the solutions of the electromagnetic field equations must be invariant under time-reversal transformation, as are the field equations themselves.

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Wilhelm Eduard Weber

Wilhelm Eduard Weber (24 October 1804 – 23 June 1891) was a German physicist and, together with Carl Friedrich Gauss, inventor of the first electromagnetic telegraph.

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Wireless

Wireless communication, or sometimes simply wireless, is the transfer of information or power between two or more points that are not connected by an electrical conductor.

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Work (physics)

In physics, a force is said to do work if, when acting, there is a displacement of the point of application in the direction of the force.

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X-ray

X-rays make up X-radiation, a form of electromagnetic radiation.

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References

[1] https://en.wikipedia.org/wiki/Maxwell's_equations

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