Maxwell's 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 and magnetic fields are generated by charges, currents, and changes of the fields.[note 1] 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.
An important consequence of Maxwell's equations is that they demonstrate how fluctuating electric and magnetic fields propagate at a constant speed (c) in a vacuum. Known as electromagnetic radiation, these waves may occur at various wavelengths to produce a spectrum of radiation from radio waves to gamma rays.
The equations have two major variants. The microscopic equations have universal applicability but are unwieldy for common calculations. They relate the electric and magnetic fields to total charge and total current, including the complicated charges and currents in materials at the atomic scale. The macroscopic equations define two new auxiliary fields that describe the large-scale behaviour of matter without having to consider atomic scale charges and quantum phenomena like spins. However, their use requires experimentally determined parameters for a phenomenological description of the electromagnetic response of materials.
The term "Maxwell's equations" is often also used for equivalent alternative formulations. Versions of Maxwell's equations based on the electric and magnetic scalar potentials are preferred for explicitly solving the equations as a boundary value problem, analytical mechanics, or for use in quantum mechanics. The covariant formulation (on spacetime rather than space and time separately) makes the compatibility of Maxwell's equations with special relativity manifest. Maxwell's equations in curved spacetime, commonly used in high energy and gravitational physics, are compatible with general relativity.[note 2] In fact, Albert Einstein developed special and general relativity to accommodate the invariant speed of light, a consequence of Maxwell's equations, with the principle that only relative movement has physical consequences.
The publication of the equations marked the unification of a theory for previously separately described phenomena: magnetism, electricity, light and associated radiation. Since the mid-20th century, it has been understood that Maxwell's equations do not give an exact description of electromagnetic phenomena, but are instead a classical limit of the more precise theory of quantum electrodynamics.
https://en.wikipedia.org/wiki/Maxwell%27s_equations
In classical electromagnetism, Ampère's circuital law (not to be confused with Ampère's force law that André-Marie Ampère discovered in 1823)[1] relates the integrated magnetic field around a closed loop to the electric current passing through the loop. James Clerk Maxwell (not Ampère) derived it using hydrodynamicsin his 1861 published paper "On Physical Lines of Force"[2] 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,[3][4][5] which is one of Maxwell's equations which form the basis of classical electromagnetism.
https://en.wikipedia.org/wiki/Ampère%27s_circuital_law
In physics and electromagnetism, Gauss's law, also known as Gauss's flux theorem, (or sometimes simply called Gauss's theorem) is a law relating the distribution of electric charge to the resulting electric field. In its integral form, it states that the flux of the electric field out of an arbitrary closed surface is proportional to the electric charge enclosed by the surface, irrespective of how that charge is distributed. Even though the law alone is insufficient to determine the electric field across a surface enclosing any charge distribution, this may be possible in cases where symmetry mandates uniformity of the field. Where no such symmetry exists, Gauss's law can be used in its differential form, which states that the divergence of the electric field is proportional to the local density of charge.
The law was first[1] formulated by Joseph-Louis Lagrange in 1773,[2] followed by Carl Friedrich Gauss in 1835,[3] both in the context of the attraction of ellipsoids. It is one of Maxwell's four equations, which forms the basis of classical electrodynamics.[note 1] Gauss's law can be used to derive Coulomb's law,[4] and vice versa.
https://en.wikipedia.org/wiki/Gauss%27s_law
Faraday's law of induction (briefly, Faraday's law) 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 known as electromagnetic induction. It is the fundamental operating principle of transformers, inductors, and many types of electrical motors, generators and solenoids.[2][3]
The Maxwell–Faraday equation (listed as one of Maxwell's equations) describes the fact that a spatially varying (and also possibly time-varying, depending on how a magnetic field varies in time) electric field always accompanies a time-varying magnetic field, while Faraday's law states that there is EMF (electromotive force, defined as electromagnetic work done on a unit charge when it has traveled one round of a conductive loop) on the conductive loop when the magnetic flux through the surface enclosed by the loop varies in time.
Faraday's law had been discovered and one aspect of it (transformer EMF) was formulated as the Maxwell–Faraday equation later. The equation of Faraday's law can be derived by the Maxwell–Faraday equation (describing transformer EMF) and the Lorentz force (describing motional EMF). The integral form of the Maxwell–Faraday equation describes only the transformer EMF, while the equation of Faraday's law describes both the transformer EMF and the motional EMF.
https://en.wikipedia.org/wiki/Faraday%27s_law_of_induction
https://en.wikipedia.org/wiki/Tensor
https://en.wikipedia.org/wiki/Tension_(physics)
https://en.wikipedia.org/wiki/Voltage
https://en.wikipedia.org/wiki/Torque
https://en.wikipedia.org/wiki/Angular_acceleration
https://en.wikipedia.org/wiki/Molecular_vibration
https://en.wikipedia.org/wiki/Rotation
https://en.wikipedia.org/wiki/Symmetry_(geometry)
https://en.wikipedia.org/wiki/Instant_centre_of_rotation
https://en.wikipedia.org/wiki/Specific_rotation
https://en.wikipedia.org/wiki/Improper_rotation
https://en.wikipedia.org/wiki/Dispersion_(optics)
https://en.wikipedia.org/wiki/Euclidean_plane_isometry#Translation%2C_rotation%2C_and_orthogonal_subgroups
https://en.wikipedia.org/wiki/Permittivity
https://en.wikipedia.org/wiki/Permeability_(electromagnetism)
https://en.wikipedia.org/wiki/Euler–Heisenberg_Lagrangian
https://en.wikipedia.org/wiki/Fresnel_equations
https://en.wikipedia.org/wiki/Riemann–Silberstein_vector
https://en.wikipedia.org/wiki/Heinrich_Hertz
https://en.wikipedia.org/wiki/Bernhard_Riemann
https://en.wikipedia.org/wiki/Molecular_geometry
https://en.wikipedia.org/wiki/Conjugated_system
https://en.wikipedia.org/wiki/Translation
https://en.wikipedia.org/wiki/Rotation
https://en.wikipedia.org/wiki/Vibration
https://en.wikipedia.org/wiki/Energy
https://en.wikipedia.org/wiki/Friction
https://en.wikipedia.org/wiki/Force
https://en.wikipedia.org/wiki/Torque
https://en.wikipedia.org/wiki/String
https://en.wikipedia.org/wiki/Vertical
https://en.wikipedia.org/wiki/Pressure
https://en.wikipedia.org/wiki/Rate
https://en.wikipedia.org/wiki/Material_Property
https://en.wikipedia.org/wiki/Ratio
https://en.wikipedia.org/wiki/Probability
https://en.wikipedia.org/wiki/Exponent
https://en.wikipedia.org/wiki/Zero
https://en.wikipedia.org/wiki/Zero_spin
https://en.wikipedia.org/wiki/Zero_dipole
https://en.wikipedia.org/wiki/diatom
https://en.wikipedia.org/wiki/Spiral
https://en.wikipedia.org/wiki/Circle
https://en.wikipedia.org/wiki/Triangle
https://en.wikipedia.org/wiki/Line
https://en.wikipedia.org/wiki/Point
https://en.wikipedia.org/wiki/Particle
https://en.wikipedia.org/wiki/Square
https://en.wikipedia.org/wiki/Dimension
https://en.wikipedia.org/wiki/Chemical_bond
https://en.wikipedia.org/wiki/Chiral
https://en.wikipedia.org/wiki/Stereochemistry
https://en.wikipedia.org/wiki/Isomer
https://en.wikipedia.org/wiki/Iso
https://en.wikipedia.org/wiki/Supramolecular_chemistry
https://en.wikipedia.org/wiki/Symmetry
https://en.wikipedia.org/wiki/Nuclear_cascade
https://en.wikipedia.org/wiki/Nuclear
https://en.wikipedia.org/wiki/Infrared
https://en.wikipedia.org/wiki/Microwave
https://en.wikipedia.org/wiki/Observable_universe
https://en.wikipedia.org/wiki/Neutrino
https://en.wikipedia.org/wiki/Neutron
https://en.wikipedia.org/wiki/Mirror
https://en.wikipedia.org/wiki/Matter
https://en.wikipedia.org/wiki/Dark_matter
https://en.wikipedia.org/wiki/Spring
https://en.wikipedia.org/wiki/Merry_go_round
https://en.wikipedia.org/wiki/Carousel
https://en.wikipedia.org/wiki/Spin
https://en.wikipedia.org/wiki/Temperature
https://en.wikipedia.org/wiki/see_saw
https://en.wikipedia.org/wiki/Swing
https://en.wikipedia.org/wiki/stepdown_scale_process
https://en.wikipedia.org/wiki/Transform
https://en.wikipedia.org/wiki/Matrix
https://en.wikipedia.org/wiki/Shear
https://en.wikipedia.org/wiki/Compression
https://en.wikipedia.org/wiki/Rheology
https://en.wikipedia.org/wiki/Discrimination
https://en.wikipedia.org/wiki/Reaction
https://en.wikipedia.org/wiki/Distinction
https://en.wikipedia.org/wiki/Differentiation
https://en.wikipedia.org/wiki/De-Integration
https://en.wikipedia.org/wiki/Integration
https://en.wikipedia.org/wiki/Mathematics
https://en.wikipedia.org/wiki/Observable_universe
https://en.wikipedia.org/wiki/Astronomy
https://en.wikipedia.org/wiki/Capacity
https://en.wikipedia.org/wiki/Limit
https://en.wikipedia.org/wiki/Perturbations
https://en.wikipedia.org/wiki/Loop
https://en.wikipedia.org/wiki/Curve
https://en.wikipedia.org/wiki/Parabola
https://en.wikipedia.org/wiki/Tractrix
Voltage, electric potential difference, electric pressure or electric tension is the difference in electric potential between two points, which (in a static electric field) is defined as the work needed per unit of charge to move a test charge between the two points. In the International System of Units, the derived unit for voltage (potential difference) is named volt.[1]: 166 In SI units, work per unit charge is expressed as joules per coulomb, where 1 volt = 1 joule (of work) per 1 coulomb (of charge). The old SI definition for volt used power and current; starting in 1990, the quantum Hall and Josephson effect were used, and recently (2019) fundamental physical constants have been introduced for the definition of all SI units and derived units.[1]: 177f, 197f Voltage or electric potential difference is denoted symbolically by ∆V, simplified V,[2] or U,[3] for instance in the context of Ohm's or Kirchhoff's circuit laws.
Electric potential differences between points can be caused physically by electric charge build up or imbalance (e.g. well known "static" and electronic capacitor) also by electric current through a magnetic field, and by time-varying magnetic fields (e.g. dynamo or generator), or some combination of these three.[4][5]Additionally on a macroscopic scale potential difference can be caused by electrochemical processes (cells and batteries) and pressure induced piezoelectric effect and heat induced emf across metal-metal junctions. These latter processes at microscopic level have the physical origins previously mentioned. A voltmetercan be used to measure the voltage (or potential difference) between two points in a system; often a common reference potential such as the ground of the system is used as one of the points. A voltage may represent either a source of energy (electromotive force) or lost, used, or stored energy (potential drop).
https://en.wikipedia.org/wiki/Voltage
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