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Encyclopedia > Lorentz force
Electromagnetism
Electricity · Magnetism
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Lorentz force.
Lorentz force.

In physics, the Lorentz force is the force exerted on a charged particle in an electromagnetic field. The particle will experience a force due to electric field of qE, and due to the magnetic field qv × B. Combined they give the Lorentz force equation (or law): Image File history File links Solenoid. ... Electromagnetism is the physics of the electromagnetic field: a field which exerts a force on particles that possess the property of electric charge, and is in turn affected by the presence and motion of those particles. ... Lightning strikes during a night-time thunderstorm. ... It has been suggested that this article or section be merged with magnet. ... Electrostatics (also known as Static Electricity) is the branch of physics that deals with the forces exerted by a static (i. ... Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interaction. ... Coulombs torsion balance In physics, Coulombs law is an inverse-square law indicating the magnitude and direction of electrostatic force that one stationary, electrically charged object of small dimensions (ideally, a point source) exerts on another. ... It has been suggested that optical field be merged into this article or section. ... In physics and mathematical analysis, Gausss law is the electrostatic application of the generalized Gausss theorem giving the equivalence relation between any flux, e. ... This article or section does not cite any references or sources. ... In physics, the electric dipole moment for a pair of opposite charges of magnitude q is defined as the magnitude of the charge times the distance between them and the defined direction is toward the positive charge. ... Magnetostatics is the study of static magnetic fields. ... In physics, Ampères Circuital law, discovered by André-Marie Ampère, relates the circulating magnetic field in a closed loop to the electric current passing through the loop. ... This template is misplaced. ... Magnetic flux, represented by the Greek letter Φ (phi), is a measure of quantity of magnetism, taking account of the strength and the extent of a magnetic field. ... The Biot-Savart law is a physical law with applications in both electromagnetics and fluid dynamics. ... A bar magnet. ... Classical electrodynamics (or classical electromagnetism) is a theory of electromagnetism that was developed over the course of the 19th century, most prominently by James Clerk Maxwell. ... Electric current is the flow (movement) of electric charge. ... Electromotive force (emf) is the amount of energy gained per unit charge that passes through a device in the opposite direction to the electric field existing across that device. ... Electromagnetic induction is the production of an electrical potential difference (or voltage) across a conductor situated in a changing magnetic flux. ... Faradays law of induction (more generally, the law of electromagnetic induction) states that the induced emf (electromotive force) in a closed loop equals the negative of the time rate of change of magnetic flux through the loop. ... Displacement current is a quantity related to a changing electric field. ... In electromagnetism, Maxwells equations are a set of equations first presented as a distinct group in the later half of the nineteenth century by James Clerk Maxwell. ... The electromagnetic field is a physical field that is produced by electrically charged objects and which affects the behaviour of charged objects in the vicinity of the field. ... Electromagnetic waves can be imagined as a self-propagating transverse oscillating wave of electric and magnetic fields. ... This article or section does not adequately cite its references or sources. ... Electrical conduction is the movement of electrically charged particles through a transmission medium (electrical conductor). ... Electrical resistance is a measure of the degree to which an electrical component opposes the passage of current. ... Capacitance is a measure of the amount of electric charge stored (or separated) for a given electric potential. ... Inductance (or electric inductance) is a measure of the amount of magnetic flux produced for a given electric current. ... Electrical impedance, or simply impedance, is a measure of opposition to a sinusoidal alternating electric current. ... A resonator is a device or part that vibrates (or oscillates) with waves. ... It has been suggested that this article or section be merged with Waveguide (optics). ... Image File history File links This is a lossless scalable vector image. ... Image File history File links This is a lossless scalable vector image. ... The first few hydrogen atom electron orbitals shown as cross-sections with color-coded probability density Physics (Greek: (phúsis), nature and (phusiké), knowledge of nature) is the branch of science concerned with the discovery and characterization of universal laws which govern matter, energy, space, and time. ... In physics, force is an influence that may cause an object to accelerate. ... Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interaction. ... The electromagnetic field is a physical field that is produced by electrically charged objects and which affects the behaviour of charged objects in the vicinity of the field. ... Hendrik Antoon Lorentz (July 18, 1853, Arnhem – February 4, 1928, Haarlem) was a Dutch physicist who shared the 1902 Nobel Prize in Physics with Pieter Zeeman for the discovery and elucidation of the Zeeman effect. ...

mathbf{F} = q (mathbf{E} + mathbf{v} times mathbf{B}),

where

F is the force (in newtons)
E is the electric field (in volts per meter)
B is the magnetic field (in webers per square meter, or equivalently, teslas)
q is the electric charge of the particle (in coulombs)
v is the instantaneous velocity of the particle (in meters per second)
and × is the cross product.

Thus a positively charged particle will be accelerated in the same linear orientation as the E field, but will curve perpendicularly to the B field according to the right-hand rule. In physics, force is an influence that may cause an object to accelerate. ... The newton (symbol: N) is the SI unit of force. ... It has been suggested that optical field be merged into this article or section. ... Josephson junction array chip developed by NIST as a standard volt. ... The metre, or meter (symbol: m) is the SI base unit of length. ... This template is misplaced. ... In physics, the weber (symbol: Wb) is the SI unit of magnetic flux. ... SI unit. ... Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interaction. ... The coulomb (symbol: C) is the SI unit of electric charge. ... In physics, velocity is defined as the rate of change of displacement or the rate of displacement. ... Look up second in Wiktionary, the free dictionary. ... For the crossed product in algebra and functional analysis, see crossed product. ... The left-handed orientation is shown on the left, and the right-handed on the right. ...

Contents

The Significance of the Lorentz Force

The Lorentz force is one of the original eight Maxwell's equations (equation D) and it is the solution to the differential form of Faraday's Law. Nowadays, Faraday's law is used instead of the Lorentz force in Maxwell's equations. Faraday's law and the Lorentz force both express the same physics. The discovery of the Lorentz force was before Lorentz's time. It can be seen at equation (77) in Maxwell's 1861 paper On Physical Lines of Force. 1 July 2007 (UTC)Bold text In electromagnetism, Maxwells equations are a set of equations first presented as a distinct group in the later half of the nineteenth century by James Clerk Maxwell. ... Faradays law of induction (more generally, the law of electromagnetic induction) states that the induced emf (electromotive force) in a closed loop equals the negative of the time rate of change of magnetic flux through the loop. ... In electromagnetism, Maxwells equations are a set of equations first presented as a distinct group in the later half of the nineteenth century by James Clerk Maxwell. ...


Lorentz force in special relativity

When particle speeds approach the speed of light, the Lorentz force equation must be modified according to special relativity: The special theory of relativity was proposed in 1905 by Albert Einstein in his article On the Electrodynamics of Moving Bodies. Some three centuries earlier, Galileos principle of relativity had stated that all uniform motion was relative, and that there was no absolute and well-defined state of rest...

{d left ( gamma m mathbf{v} right ) over dt } = mathbf{F} = q (mathbf{E} + mathbf{v} times mathbf{B}),

where

gamma  stackrel{mathrm{def}}{=} frac{1}{sqrt{1 - frac{|mathbf{v}|^2}{c^2}}}

is called the Lorentz factor and c is the speed of light in a vacuum. It has been suggested that Lorentz term be merged into this article or section. ... A line showing the speed of light on a scale model of Earth and the Moon The speed of light in a vacuum is an important physical constant denoted by the letter c for constant or the Latin word celeritas meaning swiftness.[1] It is the speed of all electromagnetic...


This relativistic form is identical to the conventional expression of the Lorentz force if the momentum form of Newton's law, F= dp/dt, is used, and the momentum p is assumed to be p = γmv.


The change of energy due to the electric and magnetic fields, in relativistic form, is simply

{d left ( gamma m c^2 right ) over dt } = q mathbf{E} cdot mathbf{v} .

The change in energy depends only on the electric field, and not on the magnetic field.


Covariant form of the Lorentz force

The Lorentz force equation can be written in covariant form in terms of the field strength tensor. In special relativity, in order to more clearly express the fact that Maxwells equations (in vacuum) take the same form in any inertial coordinate system, the vacuum Maxwells equations are written in terms of four-vectors and tensors in the manifestly covariant form (cgs units): , and where is... It has been suggested that this article or section be merged with Covariant. ...

frac{d p^alpha}{d tau} = q u_beta F^{alpha beta}
where
τ is c times the proper time of the particle,
q is the charge,
u is the 4-velocity of the particle, defined as:
u_beta = left(u_0, u_1, u_2, u_3 right) = gamma left(c, v_x, v_y, v_z right) ,and
F is the field strength tensor (or electromagnetic tensor) and is written in terms of fields as:
F^{alpha beta} = begin{bmatrix} 0 & -E_x/c & -E_y/c & -E_z/c  E_x/c & 0 & -B_z & B_y  E_y/c & B_z & 0 & -B_x  E_z/c & -B_y & B_x & 0 end{bmatrix}.

The fields are transformed to a frame moving with constant relative velocity by: In relativity, proper time is time measured by a single clock between events that occur at the same place as the clock. ... Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interaction. ... In physics, in particular in special relativity and general relativity, the four-velocity of an object is a four-vector (vector in four-dimensional spacetime) that replaces classical velocity (a three-dimensional vector). ... To meet Wikipedias quality standards, this article or section may require cleanup. ...

acute{F}^{mu nu} = {Lambda^{mu}}_{alpha} {Lambda^{nu}}_{beta} F^{alpha beta} ,

where {Lambda^{mu}}_{alpha} is a Lorentz transformation. A Lorentz transformation (LT) is a linear transformation that preserves the spacetime interval between any two events in Minkowski space, while leaving the origin fixed (=rotation of Minkowski space). ...


Derivation

The μ = 1 component (x-component) of the force is

gamma frac{d p^1}{d t} = frac{d p^1}{d tau} = q u_beta F^{1 beta} = qleft(-u^0 F^{10} + u^1 F^{11} + u^2 F^{12} + u^3 F^{13} right) .,

Here, τ is the proper time of the particle. Substituting the components of the electromagnetic tensor F yields In relativity, proper time is time measured by a single clock between events that occur at the same place as the clock. ...

gamma frac{d p^1}{d t} = q left(-u^0 left(frac{-E_x}{c} right) + u^2 (B_z) + u^3 (-B_y) right) ,

Writing the four-velocity in terms of the ordinary velocity yields In physics, in particular in special relativity and general relativity, the four-velocity of an object is a four-vector (vector in four-dimensional spacetime) that replaces classical velocity (a three-dimensional vector). ...

gamma frac{d p^1}{d t} = q gamma left(c left(frac{E_x}{c} right) + v_y B_z - v_z B_y right) ,
gamma frac{d p^1}{d t} = q gamma left( E_x + left(mathbf{v} times mathbf{B} right)_x right) .,

The calculation of the μ = 2 or μ = 3 is similar yielding

gamma frac{d mathbf{p} }{d t} = frac{d mathbf{p} }{d tau} = q gamma left(mathbf{E} + (mathbf{v} times mathbf{B})right) ,,

which is the Lorentz force law.


Applications

The Lorentz force is a principle exploited in many devices including:

The Lorentz force can also act on a current carrying conductor, in this case called Laplace Force, by the interaction of the conduction electrons with the atoms of the conductor material. This force is used in many devices including : A pair of Dee electrodes with loops of coolant pipes on their surface at the Lawrence Hall of Science. ... For the DC Comics Superhero also called Atom Smasher, see Albert Rothstein. ... A homopolar generator, also known as a unipolar generator, acyclic generator, or disk dynamo, is an electrical generator in which the magnetic field has the same polarity at every point, so that the armature passes through the magnetic field lines of force continually in the same direction. ... A cavity magnetron is a high-powered vacuum tube that generates coherent microwaves. ... An MPD thruster during test firing The Magnetoplasmadynamic (MPD) thruster (MPDT) is a form of electric propulsion (a subdivision of spacecraft propulsion) which uses the Lorentz force (a force resulting from the interaction between a magnetic field and an electric current) to generate thrust. ... Mass spectrometry is a technique for separating ions by their mass-to-charge (m/z) ratios. ... The Biot-Savart law is a physical law with applications in both electromagnetics and fluid dynamics. ...

// A railgun is a form of gun that converts electrical energy (rather than the more conventional chemical energy from an explosive propellant) into projectile kinetic energy. ... “Dynamo” redirects here. ... Rotating magnetic field as a sum of magnetic vectors from 3 phase coils An electric motor converts electrical energy into mechanical energy. ...

See also

Wikimedia Commons has media related to:
Lorentz force

Image File history File links Commons-logo. ... The Wikimedia Commons (also called Wikicommons) is a repository of free content images, sound and other multimedia files. ... Electromagnetism is the physics of the electromagnetic field: a field which exerts a force on particles that possess the property of electric charge, and is in turn affected by the presence and motion of those particles. ... To meet Wikipedias quality standards, this article or section may require cleanup. ... Hendrik Antoon Lorentz (July 18, 1853, Arnhem – February 4, 1928, Haarlem) was a Dutch physicist who shared the 1902 Nobel Prize in Physics with Pieter Zeeman for the discovery and elucidation of the Zeeman effect. ... In electromagnetism, Maxwells equations are a set of equations first presented as a distinct group in the later half of the nineteenth century by James Clerk Maxwell. ... In special relativity, in order to more clearly express the fact that Maxwells equations (in vacuum) take the same form in any inertial coordinate system, the vacuum Maxwells equations are written in terms of four-vectors and tensors in the manifestly covariant form (cgs units): , and where is... Conductor moving in a magnetic field. ... The Abraham-Lorentz force is the average force on an accelerating charged particle caused by the particle emitting electromagnetic radiation. ...

Reference

  • Serway and Jewett (2004). Physics for Scientists and Engineers with Modern Physics. Thomson Brooks/Cole. ISBN 0-534-40846-X. 
  • Feynman, Leighton and Sands (2006). The Feynman Lectures on Physics The Definitive Edition Volume II. Pearson Addison Wesley. ISBN 0-8053-9047-2. 

External links

  • Lorentz force (animation)

  Results from FactBites:
 
Spartanburg SC | GoUpstate.com | Spartanburg Herald-Journal (425 words)
In physics, the Lorentz force is the force exerted on a charged particle in an electromagnetic field.
The Lorentz force is one of the original eight Maxwell's equations (equation D) and it is the solution to the differential form of Faraday's Law.
The Lorentz force equation can be written in covariant form in terms of the field strength tensor.
  More results at FactBites »

 
 

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