- Right-hand rule
:"For the related yet different principle relating to electromagnetic coils, see

".Inright hand grip rule mathematics andphysics , the**right-hand rule**is a commonmnemonic for understanding notation conventions for vectors in 3 dimensions. It was invented for use in electromagnetism by British physicistJohn Ambrose Fleming in the late 1800s. [*cite book*] [

last = Fleming

first = John Ambrose

authorlink =

coauthors =

title = Magnets and Electric Currents, 2nd Edition

publisher = E.& F. N. Spon

date = 1902

location = London

pages = p.173-174

url = http://books.google.com/books?id=ASUYAAAAYAAJ&pg=PA173

doi =

id =

isbn =*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*]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.

There are variations on the mnemonic depending on context, but all variations are related to the one idea of choosing a convention.

**Direction associated with an ordered pair of directions**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.:$vec\{a\}\; imes\; vec\{b\}\; =\; vec\{c\}$

* 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".

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. [

*[*]*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**Direction associated with a rotation**A different form of the right-hand rule is used in situations where a vector must be assigned to the "

rotation " of a body, a magnetic field or a fluid. [*cite web*] 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 rule is applicable.

last = Wilson

first = Adam

authorlink =

coauthors =

title = Hand Rules

work = Course outline, EE2683 Electric Circuits and Machines

publisher = Faculty of Engineering, Univ. of New Brunswick

date = 2008

url = http://www.ece.unb.ca/Courses/EE2683/AW/hand_rules.pdf

format =

doi =

accessdate = 2008-08-11In this form, the fingers of the right hand are curled to match the curvature and direction of the motion or the magnetic field. The thumb indicates the direction of the vector.

**Applications**The first form of the rule is used to determine the direction of the

cross product of two vectors. This leads to widespread use inphysics , 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 tocross product s, and use the second form.)* The

angular velocity of a rotating object and therotational velocity of any point on the object

* Atorque , the force that causes it, and the position of the point of application of the force

* Amagnetic field , the position of the point where it is determined, and theelectric current (or change inelectric flux ) that causes it

* Amagnetic field in a coil of wire and theelectric current in the wire

* The force of amagnetic field on a charged particle, the magnetic field itself, and thevelocity of the object

* Thevorticity at any point in the field of flow of a fluid

* Theinduced current from motion in a magnetic field (known asFleming's right hand rule )Fleming's left hand rule is a rule for finding the direction of thethrust on a conductor carrying a current in a magnetic field.**Left handedness**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.

An example of this situation is for

left-handed material s. Normally, for anelectromagnetic wave , theelectric andmagnetic fields, and the direction of propagation of the wave obey the right-hand rule. However, left-handed materials have special properties - thenegative refractive index . It makes the direction of propagation point in the opposite direction.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.**ymmetry****ee also**

*Chirality (mathematics)

*Cross product

*Right hand grip rule

*Curl (mathematics)

*Pseudovector

*Improper rotation

*Reflection (mathematics)

*Fleming's left hand rule

*Vorticity **External links*** [

*http://www.magnet.fsu.edu/education/tutorials/java/handrules/index.html Right and Left Hand Rules - Interactive Java Tutorial*] National High Magnetic Field Laboratory

* [*http://physics.syr.edu/courses/video/RightHandRule/index2.html A demonstration of the right-hand rule at physics.syr.edu*]

* [*http://mathworld.wolfram.com/Right-HandRule.html Definition at mathworld.wolfram.com*]

* [*http://xkcd.com/199/ Comic depicting other alternatives to the right-hand rule*]**Footnotes**

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2010.*