Lorentz force

In physics, specifically in electromagnetism, the Lorentz force (or electromagnetic force) is the combination of electric and magnetic force on a point charge due to electromagnetic fields. A particle of charge $q$ moving with a velocity $v$ in an electric field $E$ and a magnetic field $B$ experiences a force (in SI units^[1]^[2]) of

\mathbf {F} =q\left(\mathbf {E} +\mathbf {v} \times \mathbf {B} \right).

It says that the electromagnetic force on a charge

q

is a combination of (1) a force in the direction of the electric field

E

(proportional to the magnitude of the field and the quantity of charge), and (2) a force at right angles to both the magnetic field

B

and the velocity

v

of the charge (proportional to the magnitude of the field, the charge, and the velocity).

Variations on this basic formula describe the magnetic force on a current-carrying wire (sometimes called Laplace force), the electromotive force in a wire loop moving through a magnetic field (an aspect of Faraday's law of induction), and the force on a moving charged particle.^[3]

Historians suggest that the law is implicit in a paper by James Clerk Maxwell, published in 1865.^[4] Hendrik Lorentz arrived at a complete derivation in 1895,^[5] identifying the contribution of the electric force a few years after Oliver Heaviside correctly identified the contribution of the magnetic force.^[6]

^ In SI units, $B$ is measured in teslas (symbol: T). In Gaussian-cgs units, $B$ is measured in gauss (symbol: G). See e.g. "Geomagnetism Frequently Asked Questions". National Geophysical Data Center. Retrieved 21 October 2013.)
^ The $H$ -field is measured in amperes per metre (A/m) in SI units, and in oersteds (Oe) in cgs units. "International system of units (SI)". NIST reference on constants, units, and uncertainty. National Institute of Standards and Technology. 12 April 2010. Retrieved 9 May 2012.
^ Huray, Paul G. (2009-11-16). Maxwell's Equations. John Wiley & Sons. ISBN 978-0-470-54276-7.
^ Cite error: The named reference Huray was invoked but never defined (see the help page).
^ Cite error: The named reference Dahl was invoked but never defined (see the help page).
^ Cite error: The named reference Nahin was invoked but never defined (see the help page).

[units-1] In SI units, $B$ is measured in teslas (symbol: T). In Gaussian-cgs units, $B$ is measured in gauss (symbol: G). See e.g. "Geomagnetism Frequently Asked Questions". National Geophysical Data Center. Retrieved 21 October 2013.)

[units2-2] The $H$ -field is measured in amperes per metre (A/m) in SI units, and in oersteds (Oe) in cgs units. "International system of units (SI)". NIST reference on constants, units, and uncertainty. National Institute of Standards and Technology. 12 April 2010. Retrieved 9 May 2012.

[3] Huray, Paul G. (2009-11-16). Maxwell's Equations. John Wiley & Sons. ISBN 978-0-470-54276-7.

[Huray-4] Cite error: The named reference Huray was invoked but never defined (see the help page).

[Dahl-5] Cite error: The named reference Dahl was invoked but never defined (see the help page).

[Nahin-6] Cite error: The named reference Nahin was invoked but never defined (see the help page).

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