The force that the electromagnetic field exerts on electrically charged particles, called the electromagnetic force, is one of the four fundamental forces. The other fundamental forces are the strong nuclear force (which holds atomic nuclei together), the weak nuclear force (which causes certain forms of radioactive decay), and the gravitational force. All other forces are ultimately derived from these fundamental forces. As it turns out, the electromagnetic force is the one responsible for practically all the phenomena one enc ...

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Electromagnetism, Electromagnetism - Electric and magnetic fields, Electromagnetism - The electromagnetic force, Electromagnetism - Origins of electromagnetic theory, Electromagnetism - Failures of classical electromagnetism, Electromagnetism - SI electricity units

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The electromagnetic field exerts the following force (often called the Lorentz force) on charged particles: where all boldfaced quantities are vectors: F is the force that a charge q experiences, E is the electric field at q's location, v is q's velocity, B is the strength of the magnetic field at q's position. This description of the force between charged particles, unlike Coulomb's force law, does not break down under relativity and in fact, the magnetic force is seen as part of the relativistic int ...

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Classical electromagnetism, Classical electromagnetism - Lorentz force, Classical electromagnetism - The Electric Field E, Classical electromagnetism - Electromagnetic waves, Classical electromagnetism - General Field Equations, Classical electromagnetism - Also See

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The scientist William Gilbert proposed, in his De Magnete (1600), that electricity and magnetism, while both capable of causing attraction and repulsion of objects, were distinct effects. Mariners had noticed that lightning strikes had the ability to disturb a compass needle, but the link between lightning and electricity was not confirmed until Franklin's proposed experiments (performed initially by others) in 1752. One of the first to discover and publish a link between man-made electric current and magnetism was Romagnosi, who in 1 ...

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Electromagnetism, Electromagnetism - Electric and magnetic fields, Electromagnetism - The electromagnetic force, Electromagnetism - Origins of electromagnetic theory, Electromagnetism - Failures of classical electromagnetism, Electromagnetism - SI electricity units

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The electromagnetic tensor is commonly written as a matrix: where E is the electric field B the magnetic field and c the speed of light. When using natural units, the speed of light is taken to equal 1. From the matrix form of the field tensor, it becomes clear that the electromagnetic tensor satisfies the following properties (Mathematical note: In this article, the abstract index notation will be used.): antisymmetry: (hence the name bivector). zero ...

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Electromagnetic tensor, Electromagnetic tensor - Details, Electromagnetic tensor - Derivation, Electromagnetic tensor - Significance of the Field Tensor, Electromagnetic tensor - The field tensor and relativity, Electromagnetic tensor - Role in Quantum Electrodynamics and Field Theory

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Some of the simplest physical fields are vector force fields. Historically, the first time fields were taken seriously was with Faraday's lines of force when describing the electric field. Then the gravitational field was described in the same way. Classical field theory - Newtonian gravitation. A classical field theory describing gravity was Newtonian gravitation which descr ...

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Classical field theory, Classical field theory - Non-relativistic field theory, Classical field theory - Newtonian gravitation, Classical field theory - Electric field, Classical field theory - Relativistic field theory, Classical field theory - Lagrangian dynamics, Classical field theory - Electromagnetism, Classical field theory - General relativity

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Modern formulations of classical field theories generally require Lorentz covariance as Lorentz covariance is now recognised as a fundamental aspect of nature. A field theory tends to be expressed mathematically by using Lagrangians. This is a function that, when subjected to an action principle, gives rise to the field equations and a conservation law for the theory. Classical field theory - Lagrangian dynamics. Main article: Lagrangian We have the field tensor (which could be a ...

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Classical field theory, Classical field theory - Non-relativistic field theory, Classical field theory - Newtonian gravitation, Classical field theory - Electric field, Classical field theory - Relativistic field theory, Classical field theory - Lagrangian dynamics, Classical field theory - Electromagnetism, Classical field theory - General relativity

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Modern formulations of classical field theories generally require Lorentz covariance as this is now recognised as a fundamental aspect of nature. A field theory tends to be expressed mathematically by using Lagrangians. This is a function that, when subjected to an action principle, gives rise to the field equations and a conservation law for the theory. Classical field theory - Lagrangian dynamics. Main article: Lagrangian We have the field tensor (which could be a tensor of any ...

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Classical field theory, Classical field theory - Non-relativistic field theory, Classical field theory - Newtonian gravitation, Classical field theory - Electric field, Classical field theory - Relativistic field theory, Classical field theory - Lagrangian dynamics, Classical field theory - Electromagnetism, Classical field theory - General relativity

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Charges are not the only sources of electric fields. According to Faraday's law of induction, where indicates the curl of the electric field, and represents the vector rate of decrease of magnetic flux density with time. This means that a magnetic field changing in time produces a curled electric field, possibly also changing in time. The situation in which electric or magnetic fields change in time is no longer electrostatics, but rather electrodynamics or electromagnetics. In this case, Coulomb's law no ...

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Electric field, Electric field - Definition and derivation for electrostatics, Electric field - Properties in electrostatics, Electric field - Parallels between electrostatics and gravity, Electric field - Time-varying fields

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As in flat spacetime, the electromagnetic field tensor is antisymmetric, with only two algebraically independent scalar invariants, Using these, we can classify the possible electromagnetic fields as follows: If I < 0 but J = 0, we have an electrostatic field, which means that some observers will measure a static electric field, and no magnetic field. If I > 0See also:

Electrovacuum solution, Electrovacuum solution - Mathematical definition, Electrovacuum solution - Invariants, Electrovacuum solution - Einstein tensor, Electrovacuum solution - Eigenvalues, Electrovacuum solution - Rainich conditions, Electrovacuum solution - Test fields, Electrovacuum solution - Examples

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There is not a complete correspondence between electromagnetism and gravitomagnetism, since unlike magnetic poles, which attract in the case of different magnetic polarities (or equidirectional electric fluids) and repel in the case of similar polarities (and opposite-directional fluids), the gravitomagnetic force makes different gravitomagnetic polarities (or equidirectional fluids of mass) to repel an ...

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Gravitomagnetism, Gravitomagnetism - Gravitomagnetism vs. electromagnetism, Gravitomagnetism - Higher-order effects, Gravitomagnetism - Gravitomagnetic field of Earth, Gravitomagnetism - Fringe physics

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There is not a complete correspondence between electromagnetism and gravitoelectromagnetism, since unlike magnetic poles, which attract in the case of different magnetic polarities (or equidirectional electric fluids) and repel in the case of similar polarities (and opposite-directional fluids), the gravitomagnetic force makes different gravitomagnetic polarities (or equidirectional fluids of mas ...

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Gravitoelectromagnetism, Gravitoelectromagnetism - Gravitoelectromagnetism vs. electromagnetism, Gravitoelectromagnetism - Higher-order effects, Gravitoelectromagnetism - Gravitoelectromagnetic field of Earth, Gravitoelectromagnetism - Fringe physics

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Sometimes one can assume that the field energy of any electromagnetic field is so small that its gravitational effects can be neglected. Then, to obtain an approximate electrovacuum solution, we need only solve the Maxwell equations on a given vacuum solution. In this case, the electromagnetic field is often called a test field, in analogy with the term test particle (denoting a small object whose mass is too small to contribute appreciably to the ambient gravitational field). Here, it is useful to know that any Killing vectors which may be present will (in the case of a vacuum solution) automat ...

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Electrovacuum solution, Electrovacuum solution - Mathematical definition, Electrovacuum solution - Invariants, Electrovacuum solution - Einstein tensor, Electrovacuum solution - Eigenvalues, Electrovacuum solution - Rainich conditions, Electrovacuum solution - Test fields, Electrovacuum solution - Examples

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Some of the higher-order gravitomagnetic effects can begin to reproduce effects reminiscent of the interactions of more conventional polarised charges. For instance, if two wheels are spun on a common axis, the mutual gravitational attraction between the two wheels arguably ought to be greater if they spin in opposite directions than in the same direction. This can be expressed as an attractive or repulsive gravitomagnetic component. Gravitomagnetic arguments also predict that a flexible or fluid toroidal mass undergoing minor axis ro ...

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Gravitomagnetism, Gravitomagnetism - Gravitomagnetism vs. electromagnetism, Gravitomagnetism - Higher-order effects, Gravitomagnetism - Gravitomagnetic field of Earth, Gravitomagnetism - Fringe physics

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Some of the higher-order gravitoelectromagnetic effects can begin to reproduce effects reminiscent of the interactions of more conventional polarised charges. For instance, if two wheels are spun on a common axis, the mutual gravitational attraction between the two wheels arguably ought to be greater if they spin in opposite directions than in the same direction. This can be expressed as an attractive or repulsive gravitomagnetic component. Gravitoelectromagnetic arguments also predict that a flexible or fluid toroidal mass undergoing ...

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Gravitoelectromagnetism, Gravitoelectromagnetism - Gravitoelectromagnetism vs. electromagnetism, Gravitoelectromagnetism - Higher-order effects, Gravitoelectromagnetism - Gravitoelectromagnetic field of Earth, Gravitoelectromagnetism - Fringe physics

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Maxwell interpreted the displacement current as a real motion of charges, even in a vacuum, where he supposed that it corresponded to motion of dipole charges in the ether. Although this interpretation has been abandoned, Maxwell's correction to Ampere's law remains valid (a changing electric field produces a magnetic field). With the addition of the displacement current, Maxwell concluded that light was a form of electromagnetism (see El ...

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Displacement current, Displacement current - Explanation, Displacement current - Mathematical Necessity, Displacement current - Interpretation, Displacement current - More recent developments

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Magnetism - Electromagnets. Electromagnets are useful in cases where a magnet must be switched on or off; for instance, large cranes to lift junked automobiles. For the case of electric current moving through a wire, the resulting field is directed according to the "right hand rule." If the right hand is used as a model, and the thumb of the right hand points along the wire from positive towards the negative side ("conventional current", the reverse of the direction of actual movement of electrons), then t ...

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Magnetism, Magnetism - Magnetic materials, Magnetism - Physics of magnetism, Magnetism - Charged particle in a magnetic field, Magnetism - Magnetic dipoles, Magnetism - Magnetic monopoles, Magnetism - Atomic magnetic dipoles, Magnetism - Types of magnets, Magnetism - Electromagnets, Magnetism - Permanent Magnets, Magnetism - SI magnetism units, Magnetism - Other magnetism units

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Magnetism - Electromagnets. Electromagnets are useful in cases where a magnet must be switched on or off; for instance, large cranes to lift junked automobiles. For the case of electric current moving through a wire, the resulting field is directed according to the "right hand rule." If the right hand is used as a model, and the thumb of the right hand points along the wire from positive towards the negative side ("conventional current", the reverse of the direction of actual movement of electrons), then t ...

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Magnetism, Magnetism - Magnetic materials, Magnetism - Physics of magnetism, Magnetism - Charged particle in a magnetic field, Magnetism - Magnetic dipoles ., Magnetism - Magnetic monopoles ., Magnetism - Atomic magnetic dipoles, Magnetism - Types of magnets, Magnetism - Electromagnets, Magnetism - Permanent Magnets, Magnetism - SI magnetism units, Magnetism - Other magnetism units, Magnetism - Footnotes

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Normally, magnetic fields are seen as dipoles, having a "South pole" and a "North pole"; terms dating back to the use of magnets as compasses, interacting with the Earth's magnetic field to indicate North and South on the globe. A magnetic field contains energy, and physical systems stabilize into the configuration with the lowest energy. Therefore, when placed in a magnetic field, a magnetic dipole tends to align itself in opposed polarity to that field, thereby canceling the net field strength as much as possible and lowering ...

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Magnetism, Magnetism - Magnetic materials, Magnetism - Physics of magnetism, Magnetism - Charged particle in a magnetic field, Magnetism - Magnetic dipoles, Magnetism - Magnetic monopoles, Magnetism - Atomic magnetic dipoles, Magnetism - Types of magnets, Magnetism - Electromagnets, Magnetism - Permanent Magnets, Magnetism - SI magnetism units, Magnetism - Other magnetism units

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Lagrangian - Quantum Electrodynamic Lagrangian. The Lagrangian density for QED is where ψ is a spinor, is its Dirac adjoint, Fμν is the electromagnetic tensor, D is the gauge covariant derivative, and is Feynman notation for γσDσ. Lagrangian - Dirac Lagrangian. The Lagrangian density for a Dirac field is . See also:

Lagrangian, Lagrangian - An example from classical mechanics, Lagrangian - Lagrangians and Lagrangian densities in field theory, Lagrangian - Electromagnetic Lagrangian, Lagrangian - Lagrangians in Quantum Field Theory, Lagrangian - Quantum Electrodynamic Lagrangian, Lagrangian - Dirac Lagrangian, Lagrangian - Quantum Chromodynamic Lagrangian, Lagrangian - Mathematical formalism

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Generally, in Lagrangian mechanics, the Lagrangian is equal to L = T − V where T is kinetic energy and V is potential energy. Given an electrically charged particle with mass m and charge q, with velocity v in an electromagnetic field with scalar potential φ and vector potential A, the particle's kinetic energy is and the particle's potential energy is where c is the speed of light. Th ...

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Lagrangian, Lagrangian - An example from classical mechanics, Lagrangian - Lagrangians and Lagrangian densities in field theory, Lagrangian - Electromagnetic Lagrangian, Lagrangian - Lagrangians in Quantum Field Theory, Lagrangian - Quantum Electrodynamic Lagrangian, Lagrangian - Dirac Lagrangian, Lagrangian - Quantum Chromodynamic Lagrangian, Lagrangian - Mathematical formalism

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Free space conveys that the region is absolutely devoid of matter and has no external fields or forces other than those considered in the problem at hand. In reality, no such state exists except as an idealization. Even in the "vacuum" of outer space, there are small quantities of matter (mostly hydrogen), and noise sources. The density of the interplanetary medium and interstellar medium is to a large degree low, and so for many applications (especially when there are weak external fiel ...

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Free space, Free space - Theory and mathematics, Free space - Ideal states and real world applications, Free space - Electromagnetic field propagation, Free space - Patents, Free space - External articles and references

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