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| {{about|three-dimensional vector geometry|the maze-solving technique|Maze solving algorithm#Wall follower}}
| | This is a preview for the new '''MathML rendering mode''' (with SVG fallback), which is availble in production for registered users. |
| [[Image:Cartesian coordinate system handedness.svg|thumb|The left-handed orientation is shown on the left, and the right-handed on the right.]]
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| [[Image:Rechte-hand-regel.jpg|right|thumb|Use of right hand]]
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| In [[mathematics]] and [[physics]], the '''right-hand rule''' is a common [[mnemonic]] for understanding notation conventions for [[vector (geometry)|vectors]] in 3 dimensions. It was invented for use in electromagnetism by British physicist [[John Ambrose Fleming]] in the late 19th century.<ref>{{cite book
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| | last = Fleming
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| | first = John Ambrose
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| | authorlink =
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| | coauthors =
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| | title = Magnets and Electric Currents, 2nd Edition
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| | publisher = E.& F. N. Spon
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| | year = 1902
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| | location = London
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| | pages = 173–174
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| | url = http://books.google.com/books?id=ASUYAAAAYAAJ&pg=PA173
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| | doi =
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| | id =
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| | isbn = }}</ref><ref>{{cite web|title=Right and left hand rules|work=Tutorials, Magnet Lab U.|publisher=National High Magnetic Field Laboratory|url=http://www.magnet.fsu.edu/education/tutorials/java/handrules/index.html|accessdate=2008-04-30}}</ref>
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| When choosing three vectors that must be at right angles to each other, there are two distinct solutions, so when expressing this idea in mathematics, one must remove the ambiguity of which solution is meant.
| | If you would like use the '''MathML''' rendering mode, you need a wikipedia user account that can be registered here [[https://en.wikipedia.org/wiki/Special:UserLogin/signup]] |
| | * Only registered users will be able to execute this rendering mode. |
| | * Note: you need not enter a email address (nor any other private information). Please do not use a password that you use elsewhere. |
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| There are variations on the mnemonic depending on context, but all variations are related to the one idea of choosing a convention.
| | Registered users will be able to choose between the following three rendering modes: |
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| ==Direction associated with an ordered pair of directions==
| | '''MathML''' |
| One form of the right-hand rule is used in situations in which an ordered operation must be performed on two vectors ''a'' and ''b'' that has a result which is a vector ''c'' perpendicular to both ''a'' and ''b''. The most common example is the vector [[cross product]]. The right-hand rule imposes the following procedure for choosing one of the two directions.
| | :<math forcemathmode="mathml">E=mc^2</math> |
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| :<math> \vec{a} \times \vec{b} = \vec{c}</math> | | <!--'''PNG''' (currently default in production) |
| | :<math forcemathmode="png">E=mc^2</math> |
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| * With the thumb, index, and middle fingers at right angles to each other (with the index finger pointed straight), the middle finger points in the direction of ''c'' when the thumb represents ''a'' and the index finger represents ''b''.
| | '''source''' |
| | :<math forcemathmode="source">E=mc^2</math> --> |
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| Other (equivalent) finger assignments are possible. For example, the first (index) finger can represent ''a'', the first vector in the product; the second (middle) finger, ''b'', the second vector; and the thumb, ''c'', the product.<ref>[http://www.physics.udel.edu/~watson/phys345/Fall1998/class/1-right-hand-rule.html PHYS345 Introduction to the Right Hand Rule], George Watson, University of Delaware, 1998</ref>
| | <span style="color: red">Follow this [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering link] to change your Math rendering settings.</span> You can also add a [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering-skin Custom CSS] to force the MathML/SVG rendering or select different font families. See [https://www.mediawiki.org/wiki/Extension:Math#CSS_for_the_MathML_with_SVG_fallback_mode these examples]. |
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| ==Direction associated with a rotation== | | ==Demos== |
| [[Image:Manoderecha.svg|thumb|Prediction of direction of field (''B''), given that the current ''I'' flows in the direction of the thumb]]
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| [[File:Right-hand grip rule.svg|thumb|The right-hand rule [[screw thread#Handedness|as applied to motion produced with screw threads]]]]
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| A different form of the right-hand rule, sometimes called the ''right-hand grip rule'' or the ''corkscrew-rule'' or the ''right-hand thumb rule'', is used in situations where a vector must be assigned to the ''[[rotation]]'' of a body, a magnetic field or a fluid. Alternatively, when a rotation is specified by a vector, and it is necessary to understand the way in which the rotation occurs, the right-hand grip rule is applicable.
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| This version of the rule is used in two complementary applications of [[Ampère's circuital law]]:
| | Here are some [https://commons.wikimedia.org/w/index.php?title=Special:ListFiles/Frederic.wang demos]: |
| # An [[electric current]] passes through a [[solenoid]], resulting in a [[magnetic field]]. When you wrap your right hand around the solenoid with your fingers in the direction of the [[conventional current]], your thumb points in the direction of the magnetic north pole.
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| # An electric current passes through a straight wire. Here, the thumb points in the direction of the conventional current (from positive to negative), and the fingers point in the direction of the magnetic lines of [[flux]].
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| The principle is also used to determine the direction of the [[torque]] [[Euclidean vector|vector]]. If you grip the imaginary axis of rotation of the rotational force so that your fingers point in the direction of the force, then the extended thumb points in the direction of the torque vector.
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| The right-hand grip rule is a convention derived from the right-hand rule convention for vectors. When applying the rule to current in a straight wire for example, the direction of the magnetic field (counterclockwise instead of clockwise when viewed from the tip of the thumb) is a result of this convention and not an underlying physical phenomenon.
| | * accessibility: |
| | ** Safari + VoiceOver: [https://commons.wikimedia.org/wiki/File:VoiceOver-Mac-Safari.ogv video only], [[File:Voiceover-mathml-example-1.wav|thumb|Voiceover-mathml-example-1]], [[File:Voiceover-mathml-example-2.wav|thumb|Voiceover-mathml-example-2]], [[File:Voiceover-mathml-example-3.wav|thumb|Voiceover-mathml-example-3]], [[File:Voiceover-mathml-example-4.wav|thumb|Voiceover-mathml-example-4]], [[File:Voiceover-mathml-example-5.wav|thumb|Voiceover-mathml-example-5]], [[File:Voiceover-mathml-example-6.wav|thumb|Voiceover-mathml-example-6]], [[File:Voiceover-mathml-example-7.wav|thumb|Voiceover-mathml-example-7]] |
| | ** [https://commons.wikimedia.org/wiki/File:MathPlayer-Audio-Windows7-InternetExplorer.ogg Internet Explorer + MathPlayer (audio)] |
| | ** [https://commons.wikimedia.org/wiki/File:MathPlayer-SynchronizedHighlighting-WIndows7-InternetExplorer.png Internet Explorer + MathPlayer (synchronized highlighting)] |
| | ** [https://commons.wikimedia.org/wiki/File:MathPlayer-Braille-Windows7-InternetExplorer.png Internet Explorer + MathPlayer (braille)] |
| | ** NVDA+MathPlayer: [[File:Nvda-mathml-example-1.wav|thumb|Nvda-mathml-example-1]], [[File:Nvda-mathml-example-2.wav|thumb|Nvda-mathml-example-2]], [[File:Nvda-mathml-example-3.wav|thumb|Nvda-mathml-example-3]], [[File:Nvda-mathml-example-4.wav|thumb|Nvda-mathml-example-4]], [[File:Nvda-mathml-example-5.wav|thumb|Nvda-mathml-example-5]], [[File:Nvda-mathml-example-6.wav|thumb|Nvda-mathml-example-6]], [[File:Nvda-mathml-example-7.wav|thumb|Nvda-mathml-example-7]]. |
| | ** Orca: There is ongoing work, but no support at all at the moment [[File:Orca-mathml-example-1.wav|thumb|Orca-mathml-example-1]], [[File:Orca-mathml-example-2.wav|thumb|Orca-mathml-example-2]], [[File:Orca-mathml-example-3.wav|thumb|Orca-mathml-example-3]], [[File:Orca-mathml-example-4.wav|thumb|Orca-mathml-example-4]], [[File:Orca-mathml-example-5.wav|thumb|Orca-mathml-example-5]], [[File:Orca-mathml-example-6.wav|thumb|Orca-mathml-example-6]], [[File:Orca-mathml-example-7.wav|thumb|Orca-mathml-example-7]]. |
| | ** From our testing, ChromeVox and JAWS are not able to read the formulas generated by the MathML mode. |
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| ==Applications== | | ==Test pages == |
| The first form of the rule is used to determine the direction of the [[cross product]] of two vectors. This leads to widespread use in [[physics]], wherever the cross product occurs. A list of physical quantities whose directions are related by the right-hand rule is given below. (Some of these are related only indirectly to [[cross product]]s, and use the second form.)
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| * The [[angular velocity]] of a rotating object and the [[rotational velocity]] of any point on the object
| | To test the '''MathML''', '''PNG''', and '''source''' rendering modes, please go to one of the following test pages: |
| * A [[torque]], the [[force (physics)|force]] that causes it, and the position of the point of application of the force
| | *[[Displaystyle]] |
| * A [[magnetic field]], the position of the point where it is determined, and the [[electric current]] (or change in [[electric flux]]) that causes it | | *[[MathAxisAlignment]] |
| * A [[magnetic field]] in a coil of wire and the [[electric current]] in the wire | | *[[Styling]] |
| * The force of a [[magnetic field]] on a charged particle, the magnetic field itself, and the [[velocity]] of the object | | *[[Linebreaking]] |
| * The [[vorticity]] at any point in the field of flow of a fluid | | *[[Unique Ids]] |
| * The [[induced current]] from motion in a magnetic field (known as [[Fleming's left-hand rule for motors|Fleming's right-hand rule]]) | | *[[Help:Formula]] |
| * The x, y and z unit vectors in a [[Cartesian coordinate system]] can be chosen to follow the right-hand rule. Right-handed coordinate systems are often used in [[rigid body]] physics and [[kinematics]]. | |
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| [[Fleming's left-hand rule]] is a rule for finding the direction of the [[thrust]] on a conductor carrying a current in a magnetic field. | | *[[Inputtypes|Inputtypes (private Wikis only)]] |
| [[Image:LeftHandOutline.png|thumb|Fleming's left-hand rule]]
| | *[[Url2Image|Url2Image (private Wikis only)]] |
| | | ==Bug reporting== |
| ==Left-hand rule==
| | If you find any bugs, please report them at [https://bugzilla.wikimedia.org/enter_bug.cgi?product=MediaWiki%20extensions&component=Math&version=master&short_desc=Math-preview%20rendering%20problem Bugzilla], or write an email to math_bugs (at) ckurs (dot) de . |
| In certain situations, it may be useful to use the opposite convention, where one of the vectors is reversed and so creates a left-handed triad instead of a right-handed triad.
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| An example of this situation is for [[left-handed material]]s. Normally, for an [[electromagnetic wave]], the [[electric]] and [[magnetic]] fields, and the direction of [[Wave propagation|propagation]] of the wave obey the right-hand rule. However, left-handed materials have special properties, notably the [[negative refractive index]]. It makes the direction of propagation point in the opposite direction.
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| De Graaf's translation of Fleming's left-hand rule - which uses thrust, field and current - and the right-hand rule, is the FBI rule. The FBI rule changes thrust into F ([[Lorentz force]]), B (direction of the magnetic field) and I (current). The FBI rule is easily remembered by US citizens because of the commonly known abbreviation for the [[Federal Bureau of Investigation]].
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| ==Symmetry==
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| {| class=wikitable
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| ! Vector !! Right-hand !! Right-hand !! Right-hand !! Left-hand !! Left-hand !! Left-Hand
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| |-
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| | a, x or I || Thumb || Fingers or palm || First or Index || Thumb || Fingers or palm || First or index
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| |-
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| | b, y or B || First or index || Thumb || Fingers or palm || Fingers or palm || First or index || Thumb
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| |-
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| | c, z or F || Fingers or palm || First or index || Thumb || First or index || Thumb || Fingers or palm
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| |}
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| ==See also==
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| {{Commons category}}
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| *[[Chirality (mathematics)]] | |
| *[[Curl (mathematics)]]
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| *[[Pseudovector]]
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| *[[Improper rotation]]
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| *[[Reflection (mathematics)]]
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| *[[Fleming's left-hand rule for motors]]
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| *[[Vorticity]]
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| *[[ISO 2]]
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| ==Notes== | |
| {{reflist}}
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| ==External links==
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| * [http://www.magnet.fsu.edu/education/tutorials/java/handrules/index.html Right and Left Hand Rules - Interactive Java Tutorial] National High Magnetic Field Laboratory
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| *[http://physics.syr.edu/courses/video/RightHandRule/index2.html A demonstration of the right-hand rule at physics.syr.edu]
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| * {{MathWorld|Right-HandRule|Right-hand rule}}
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| {{DEFAULTSORT:Right-Hand Rule}}
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| [[Category:Electromagnetism]]
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| [[Category:Mechanics]]
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| [[Category:Orientation]]
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| [[Category:Vectors]]
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| [[Category:Rules of thumb]]
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| [[ar:قاعدة اليد اليمنى]]
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| [[bs:Pravilo desne ruke]]
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| [[ca:Regla de la mà dreta]]
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| [[cs:Pravidlo pravé ruky]]
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| [[da:Højrehåndsregel]]
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| [[de:Drei-Finger-Regel]]
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| [[es:Regla de la mano derecha]]
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| [[eu:Eskuin eskuaren araua]]
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| [[fa:قاعده راستگرد]]
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| [[fr:Règle de la main droite]]
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| [[hy:Ձախ ձեռքի կանոնը]]
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| [[hr:Pravilo desne ruke]]
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| [[id:Kaidah tangan kanan]]
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| [[it:Regola della mano destra]]
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| [[he:כלל יד ימין]]
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| [[lt:Dešiniosios rankos taisyklė]]
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| [[hu:Jobbkéz-szabály (geometria)]]
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| [[nl:Linker- en rechterhandregels]]
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| [[no:Høyrehåndsregelen]]
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| [[nn:Høgrehandsregelen]]
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| [[pl:Reguła prawej dłoni]]
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| [[pt:Regra da mão direita]]
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| [[ru:Правило буравчика]]
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| [[sl:Pravilo desne roke]]
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| [[sr:Правило десне руке]]
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| [[sh:Pravilo desne ruke]]
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| [[fi:Oikean käden sääntö]]
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| [[sv:Högerhandsregeln]]
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| [[tr:Sağ el kuralı]]
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| [[uk:Правило гвинта]]
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