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Lorenz Gauge
In electromagnetism, the Lorenz gauge condition or Lorenz gauge, for Ludvig Lorenz, is a partial gauge fixing of the electromagnetic vector potential by requiring \partial_\mu A^\mu = 0. The name is frequently confused with Hendrik Lorentz, who has given his name to many concepts in this field. The condition is Lorentz invariant. The condition does not completely determine the gauge: one can still make a gauge transformation A^\mu \to A^\mu + \partial^\mu f, where \partial^\mu is the four-gradient and f is a harmonic scalar function (that is, a scalar function satisfying \partial_\mu\partial^\mu f = 0, the equation of a massless scalar field). The Lorenz condition is used to eliminate the redundant spin-0 component in the representation theory of the Lorentz group. It is equally used for massive spin-1 fields where the concept of gauge transformations does not apply at all. Description In electromagnetism, the Lorenz condition is generally used in calculations of time-dependent ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electromagnetism
In physics, electromagnetism is an interaction that occurs between particles with electric charge. It is the second-strongest of the four fundamental interactions, after the strong force, and it is the dominant force in the interactions of atoms and molecules. Electromagnetism can be thought of as a combination of electricity and magnetism, two distinct but closely intertwined phenomena. In essence, electric forces occur between any two charged particles, causing an attraction between particles with opposite charges and repulsion between particles with the same charge, while magnetism is an interaction that occurs exclusively between ''moving'' charged particles. These two effects combine to create electromagnetic fields in the vicinity of charge particles, which can exert influence on other particles via the Lorentz force. At high energy, the weak force and electromagnetic force are unified as a single electroweak force. The electromagnetic force is responsible for ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
American Journal Of Physics
The ''American Journal of Physics'' is a monthly, peer-reviewed scientific journal published by the American Association of Physics Teachers and the American Institute of Physics. The editor-in-chief is Beth Parks of Colgate University."Current Frequency: Monthly, 2002; and Former Frequency varies, 1940-2001" Confirmation of Editor, ISSN, CODEN, and other relevant information. Aims and scope The focus of this journal is undergraduate and graduate level physics. The intended audience is college and university physics teachers and students. Coverage includes current research in physics, instructional laboratory equipment, laboratory demonstrations, teaching methodologies, lists of resources, and book reviews. In addition, historical, philosophical and cultural aspects of physics are also covered. According to the 2021 Journal Citation Reports from Clarivate, this journal has a 2020 impact factor of 1.022. History The former title of this journal was ''American Physics Teache ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Symmetry
Symmetry (from grc, συμμετρία "agreement in dimensions, due proportion, arrangement") in everyday language refers to a sense of harmonious and beautiful proportion and balance. In mathematics, "symmetry" has a more precise definition, and is usually used to refer to an object that is invariant under some transformations; including translation, reflection, rotation or scaling. Although these two meanings of "symmetry" can sometimes be told apart, they are intricately related, and hence are discussed together in this article. Mathematical symmetry may be observed with respect to the passage of time; as a spatial relationship; through geometric transformations; through other kinds of functional transformations; and as an aspect of abstract objects, including theoretic models, language, and music. This article describes symmetry from three perspectives: in mathematics, including geometry, the most familiar type of symmetry for many people; in science and n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electric Field
An electric field (sometimes E-field) is the physical field that surrounds electrically charged particles and exerts force on all other charged particles in the field, either attracting or repelling them. It also refers to the physical field for a system of charged particles. Electric fields originate from electric charges and time-varying electric currents. Electric fields and magnetic fields are both manifestations of the electromagnetic field, one of the four fundamental interactions (also called forces) of nature. Electric fields are important in many areas of physics, and are exploited in electrical technology. In atomic physics and chemistry, for instance, the electric field is the attractive force holding the atomic nucleus and electrons together in atoms. It is also the force responsible for chemical bonding between atoms that result in molecules. The electric field is defined as a vector field that associates to each point in space the electrostatic (Coulomb) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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. It is a three-dimensional form of the wave equation. The homogeneous form of the equation, written in terms of either the electric field or the magnetic field , takes the form: \begin \left(v_^2\nabla^2 - \frac \right) \mathbf &= \mathbf \\ \left(v_^2\nabla^2 - \frac \right) \mathbf &= \mathbf \end where v_ = \frac is the speed of light (i.e. phase velocity) in a medium with permeability , and permittivity , and is the Laplace operator. In a vacuum, , a fundamental physical constant. The electromagnetic wave equation derives from Maxwell's equations. In most older literature, is called the ''magnetic flux density'' or ''magnetic induction''. The following equations\begin \nabla \cdot \mathbf &= 0\\ \nabla \cdot \mathbf &= 0 \endpredicate that any electromagnetic wave must be a transverse wave, w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
James Clerk Maxwell
James Clerk Maxwell (13 June 1831 – 5 November 1879) was a Scottish mathematician and scientist responsible for the classical theory of electromagnetic radiation, which was the first theory to describe electricity, magnetism and light as different manifestations of the same phenomenon. Maxwell's equations for electromagnetism have been called the " second great unification in physics" where the first one had been realised by Isaac Newton. With the publication of " A Dynamical Theory of the Electromagnetic Field" in 1865, Maxwell demonstrated that electric and magnetic fields travel through space as waves moving at the speed of light. He proposed that light is an undulation in the same medium that is the cause of electric and magnetic phenomena. (This article accompanied an 8 December 1864 presentation by Maxwell to the Royal Society. His statement that "light and magnetism are affections of the same substance" is at page 499.) The unification of light and electri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
D'Alembertian
In special relativity, electromagnetism and wave theory, the d'Alembert operator (denoted by a box: \Box), also called the d'Alembertian, wave operator, box operator or sometimes quabla operator (''cf''. nabla symbol) is the Laplace operator of Minkowski space. The operator is named after French mathematician and physicist Jean le Rond d'Alembert. In Minkowski space, in standard coordinates , it has the form : \begin \Box & = \partial^\mu \partial_\mu = \eta^ \partial_\nu \partial_\mu = \frac \frac - \frac - \frac - \frac \\ & = \frac - \nabla^2 = \frac - \Delta ~~. \end Here \nabla^2 := \Delta is the 3-dimensional Laplacian and is the inverse Minkowski metric with :\eta_ = 1, \eta_ = \eta_ = \eta_ = -1, \eta_ = 0 for \mu \neq \nu. Note that the and summation indices range from 0 to 3: see Einstein notation. We have assumed units such that the speed of light = 1. (Some authors alternatively use the negative metric signature of , with \eta_ = -1,\; \eta_ = \eta_ = \e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coulomb Gauge
In the physics of gauge theories, gauge fixing (also called choosing a gauge) denotes a mathematical procedure for coping with redundant degrees of freedom in field variables. By definition, a gauge theory represents each physically distinct configuration of the system as an equivalence class of detailed local field configurations. Any two detailed configurations in the same equivalence class are related by a gauge transformation, equivalent to a shear along unphysical axes in configuration space. Most of the quantitative physical predictions of a gauge theory can only be obtained under a coherent prescription for suppressing or ignoring these unphysical degrees of freedom. Although the unphysical axes in the space of detailed configurations are a fundamental property of the physical model, there is no special set of directions "perpendicular" to them. Hence there is an enormous amount of freedom involved in taking a "cross section" representing each physical configuration ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maxwell's Equations
Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits. The equations provide a mathematical model for electric, optical, and radio technologies, such as power generation, electric motors, wireless communication, lenses, radar etc. They describe how electric field, electric and magnetic fields are generated by electric charge, charges, electric current, currents, and changes of the fields.''Electric'' and ''magnetic'' fields, according to the theory of relativity, are the components of a single electromagnetic field. The equations are named after the physicist and mathematician James Clerk Maxwell, who, in 1861 and 1862, published an early form of the equations that included the Lorentz force law. Maxwell first used the equations to propose that light is an electromagnetic phenomenon. The modern f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gaussian Units
Gaussian units constitute a metric system of physical units. This system is the most common of the several electromagnetic unit systems based on cgs (centimetre–gram–second) units. It is also called the Gaussian unit system, Gaussian-cgs units, or often just cgs units. The term "cgs units" is ambiguous and therefore to be avoided if possible: there are several variants of cgs with conflicting definitions of electromagnetic quantities and units. SI units predominate in most fields, and continue to increase in popularity at the expense of Gaussian units. Alternative unit systems also exist. Conversions between quantities in Gaussian and SI units are direct unit conversions, because the quantities themselves are defined differently in each system. This means that the equations expressing physical laws of electromagnetism—such as Maxwell's—will change depending on the system of units employed. As an example, quantities that are dimensionless in one system may have dimension ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electric Potential
The electric potential (also called the ''electric field potential'', potential drop, the electrostatic potential) is defined as the amount of work energy needed to move a unit of electric charge from a reference point to the specific point in an electric field. More precisely, it is the energy per unit charge for a test charge that is so small that the disturbance of the field under consideration is negligible. Furthermore, the motion across the field is supposed to proceed with negligible acceleration, so as to avoid the test charge acquiring kinetic energy or producing radiation. By definition, the electric potential at the reference point is zero units. Typically, the reference point is earth or a point at infinity, although any point can be used. In classical electrostatics, the electrostatic field is a vector quantity expressed as the gradient of the electrostatic potential, which is a scalar quantity denoted by or occasionally , equal to the electric potential ener ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Magnetic Vector Potential
In classical electromagnetism, magnetic vector potential (often called A) is the vector quantity defined so that its curl is equal to the magnetic field: \nabla \times \mathbf = \mathbf. Together with the electric potential ''φ'', the magnetic vector potential can be used to specify the electric field E as well. Therefore, many equations of electromagnetism can be written either in terms of the fields E and B, or equivalently in terms of the potentials ''φ'' and A. In more advanced theories such as quantum mechanics, most equations use potentials rather than fields. Magnetic vector potential was first introduced by Franz Ernst Neumann and Wilhelm Eduard Weber in 1845 and in 1846, respectively. Lord Kelvin also introduced vector potential in 1847, along with the formula relating it to the magnetic field. Magnetic vector potential The magnetic vector potential A is a vector field, defined along with the electric potential ''ϕ'' (a scalar field) by the equations: \math ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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