Editing Magnetic field (section)

=== The B-field ===
{{Multiple image|header=Finding the magnetic force
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|image1=FuerzaCentripetaLorentzP.svg | alt1 = |caption1=A charged particle that is moving with velocity '''v''' in a magnetic field '''B''' will feel a magnetic force '''F'''. Since the magnetic force always pulls sideways to the direction of motion, the particle moves in a circle.
|image2=Mano-2.svg| alt2 = |caption2=Since these three vectors are related to each other by a [[cross product]], the direction of this force can be found using the [[right hand rule]].
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!Alternative names for '''B'''<ref name=Electromagnetics>E. J. Rothwell and M. J. Cloud (2010) [https://books.google.com/books?id=7AHLBQAAQBAJ&pg=PA23 ''Electromagnetics'']. Taylor & Francis. p. 23. {{ISBN|1420058266}}.</ref>
|-
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* Magnetic flux density<ref name=":1"/>{{rp|p=138}}
* Magnetic induction<ref name=Stratton />
* Magnetic field (ambiguous)
|}

The magnetic field vector {{math|'''B'''}} at any point can be defined as the vector that, when used in the [[Lorentz force law]], correctly predicts the force on a charged particle at that point:<ref name="purcell2ed" /><ref name="Griffiths3ed">{{cite book | title=Introduction to Electrodynamics | first=David J. | last=Griffiths | author-link = David J. Griffiths | year=1999 | edition=3rd|isbn=0-13-805326-X | publisher=Pearson}}</ref>{{rp|p=204}}

{{Equation box 1
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|title='''Lorentz force law'''  (''[[Euclidean vector|vector]] form, [[International System of Units|SI units]]'')
|equation=<math>\mathbf{F} = q\mathbf{E} + q(\mathbf{v} \times \mathbf{B})</math>
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Here {{math|'''F'''}} is the force on the particle, {{math|''q''}} is the particle's [[electric charge]], {{math|'''E'''}} is the external electric field, {{math|'''v'''}}, is the particle's [[velocity]], and × denotes the [[cross product]]. The direction of force on the charge can be determined by a [[mnemonic]] known as the ''right-hand rule'' (see the figure).<ref group="note">An alternative mnemonic to the right hand rule is [[Fleming's left-hand rule for motors|Fleming's left-hand rule]].</ref> Using the right hand, pointing the thumb in the direction of the current, and the fingers in the direction of the magnetic field, the resulting force on the charge points outwards from the palm. The force on a negatively charged particle is in the opposite direction. If both the speed and the charge are reversed then the direction of the force remains the same. For that reason a magnetic field measurement (by itself) cannot distinguish whether there is a positive charge moving to the right or a negative charge moving to the left. (Both of these cases produce the same current.) On the other hand, a magnetic field combined with an electric field ''can'' distinguish between these, see [[#Hall effect|Hall effect]] below.

The first term in the Lorentz equation is from the theory of [[electrostatics]], and says that a particle of charge {{math|''q''}} in an electric field {{math|'''E'''}} experiences an electric force:
<math display="block">\mathbf{F}_{\text{electric}} = q \mathbf{E}.</math>

The second term is the magnetic force:<ref name="Griffiths3ed" />
<math display="block">\mathbf{F}_{\text{magnetic}} = q(\mathbf{v} \times \mathbf{B}).</math>

Using the definition of the cross product, the magnetic force can also be written as a [[Scalar (physics)|scalar]] equation:<ref name="purcell2ed"/>{{rp|p=357}}
<math display="block">F_{\text{magnetic}} = q v B \sin(\theta)</math>
where {{math|''F''<sub>magnetic</sub>}}, {{mvar|v}}, and {{mvar|B}} are the [[Norm (mathematics)|scalar magnitude]] of their respective vectors, and {{mvar|θ}} is the angle between the velocity of the particle and the magnetic field. The vector {{math|'''B'''}} is ''defined'' as the vector field necessary to make the Lorentz force law correctly describe the motion of a charged particle. In other words,<ref name="purcell2ed">{{cite book|last=Purcell | first = E. | title=Electricity and Magnetism | url=https://archive.org/details/electricitymagne00purc_621|url-access=limited|year=2011|edition=2nd | publisher=Cambridge University Press|isbn=978-1107013605}}</ref>{{rp|pages=[https://archive.org/details/electricitymagne00purc_621/page/n192 173]–4}}

{{blockquote|[T]he command, "Measure the direction and magnitude of the vector {{math|'''B'''}} at such and such a place," calls for the following operations: Take a particle of known charge {{math|''q''}}. Measure the force on {{math|''q''}} at rest, to determine {{math|'''E'''}}. Then measure the force on the particle when its velocity is {{math|'''v'''}}; repeat with {{math|'''v'''}} in some other direction. Now find a {{math|'''B'''}} that makes the Lorentz force law fit all these results—that is the magnetic field at the place in question.}}

The {{math|'''B'''}} field can also be defined by the torque on a magnetic dipole, {{math|'''m'''}}.<ref name="jackson3ed">{{cite book | last1=Jackson | first1=John David | author-link = John David Jackson (physicist) | title=Classical electrodynamics | date=1998 | publisher=Wiley | location=New York | isbn=0-471-30932-X | edition=3rd}}</ref>{{rp|p=174}}

{{Equation box 1
|indent=:
|title='''Magnetic torque'''  (''[[Euclidean vector|vector]] form, [[International System of Units|SI units]]'')
|equation=<math>\boldsymbol{\tau} = \mathbf{m} \times \mathbf{B}</math>
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The [[SI]] unit of {{math|'''B'''}} is [[tesla (unit)|tesla]] (symbol: T).<ref group="note">The SI unit of {{math|Φ<sub>''B''</sub>}} ([[magnetic flux]]) is the [[Weber (unit)|weber]] (symbol: Wb), related to the [[tesla (unit)|tesla]] by 1&nbsp;Wb/m<sup>2</sup> = 1&nbsp;T. The SI unit tesla is equal to ([[newton (unit)|newton]]·[[second]])/([[coulomb (unit)|coulomb]]·[[metre]]). This can be seen from the magnetic part of the Lorentz force law.</ref> The [[Gaussian units|Gaussian-cgs unit]] of {{math|'''B'''}} is the [[gauss (unit)|gauss]] (symbol: G). (The conversion is 1&nbsp;T ≘ 10000&nbsp;G.<ref name=BIPMTab9>{{cite web |url=https://www.bipm.org/en/publications/si-brochure/table9.html |title=Non-SI units accepted for use with the SI, and units based on fundamental constants (contd.) |website=SI Brochure: The International System of Units (SI) [8th edition, 2006; updated in 2014] |publisher=Bureau International des Poids et Mesures |access-date=19 April 2018 |archive-date=8 June 2019 |archive-url=https://web.archive.org/web/20190608123210/https://www.bipm.org/en/publications/si-brochure/table9.html |url-status=dead }}</ref><ref name=KLang/>) One nanotesla corresponds to 1 gamma (symbol: γ).<ref name=KLang>{{cite book |title=A Companion to Astronomy and Astrophysics|url=https://books.google.com/books?id=aUjkKuaVIloC&pg=PA176 |last=Lang|first=Kenneth R.|publisher=Springer |access-date=19 April 2018|date=2006|page=176|isbn=9780387333670 }}</ref>