- Right-hand rule
:"For the related yet different principle relating to electromagnetic coils, see
right hand grip rule".In mathematicsand physics, the right-hand rule is a common mnemonicfor understanding notation conventions for vectors in 3 dimensions. It was invented for use in electromagnetism by British physicist John Ambrose Flemingin the late 1800s. [cite book
last = Fleming
first = John Ambrose
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
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.
* 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
last = Wilson
first = Adam
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
accessdate = 2008-08-11] 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.
In 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.
The first form of the rule is used to determine the direction of the
cross productof 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 products, and use the second form.)
angular velocityof a rotating object and the rotational velocityof any point on the object
torque, the force that causes it, and the position of the point of application of the force
magnetic field, the position of the point where it is determined, and the electric current(or change in electric flux) that causes it
magnetic fieldin a coil of wire and the electric currentin the wire
* The force of a
magnetic fieldon a charged particle, the magnetic field itself, and the velocityof the object
vorticityat any point in the field of flow of a fluid
induced currentfrom motion in a magnetic field (known as Fleming's right hand rule) Fleming's left hand ruleis a rule for finding the direction of the thruston a conductor carrying a current in a magnetic field.
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 materials. Normally, for an electromagnetic wave, the electricand magneticfields, and the direction of propagation of the wave obey the right-hand rule. However, left-handed materials have special properties - the negative 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.
Right hand grip rule
Fleming's left hand rule
* [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]
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