729:: If an electric charge moves across a magnetic field, it experiences a force according to the Lorentz force, with the direction given by the right-hand rule. If the index finger represents the direction of flow of charge (i.e. the current) and the middle finger represents the direction of the magnetic field in space, the direction of the force on the charge is represented by the thumb. Because the charge is moving, the force causes the particle path to bend. The bending force is computed by the vector cross-product. This means that the bending force increases with the velocity of the particle and the strength of the magnetic field. The force is maximum when the particle direction and magnetic fields are perpendicular, is less at any other angle, and is zero when the particle moves parallel to the field.
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703:: The magnetic field around a wire is relatively weak. If the wire is coiled into a helix, all the field lines inside the helix point in the same direction and each successive coil reinforces the others. The advance of the helix, the non-circular part of the current, and the field lines all point in the positive
617:
are helical and therefore screws can be right- or left-handed. To properly fasten or unfasten a screw, one applies the above rules: if a screw is right-handed, pointing one's right thumb in the direction of the hole and turning in the direction of the right hand's curled fingers (i.e. clockwise) will
92:
The various right- and left-hand rules arise from the fact that the three axes of three-dimensional space have two possible orientations. This can be seen by holding your hands together with palms up and fingers curled. If the curl of the fingers represents a movement from the first or x-axis to the
569:
and the direction of the axis gives the direction of rotation according to the right-hand rule: right fingers curled in the direction of rotation and the right thumb pointing in the positive direction of the axis. This allows some simple calculations using the vector cross-product. No part of the
396:
in his book
Magnets and Electric Currents. Fleming described the orientation of the induced electromotive force by referencing the motion of the conductor and the direction of the magnetic field in the following depiction: “If a conductor, represented by the middle finger, be moved in a field of
531:
Interchanging the labels of any two axes reverses the handedness. Reversing the direction of one axis (or three axes) also reverses the handedness. Reversing two axes amounts to a 180° rotation around the remaining axis, also preserving the handedness. These operations
133:
product, simplifies vector formalism. Following a substantial debate, the mainstream shifted from
Hamilton's quaternionic system to Gibbs' three-vectors system. This transition led to the prevalent adoption of the right-hand rule in the contemporary contexts.
880:
The cross product of two vectors is often taken in physics and engineering. For example, as discussed above, the force exerted on a moving charged particle when moving in a magnetic field B is given by the magnetic term of
Lorentz force:
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An electric current passes through a straight wire. When the thumb is pointed in the direction of conventional current (from positive to negative), the curled fingers will then point in the direction of the magnetic
923:
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end where the lines exit is defined as the north pole. If the fingers of the right hand are curled in the direction of the circular component of the current, the right thumb points to the north pole.
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phenomena in the physical world, for example the culturally transmitted meaning of right and left hands, a majority human population with dominant right hand, or certain phenomena involving the
109:, a mathematical system for representing three-dimensional rotations, is often attributed with the introduction of this convention. In the context of quaternions, the Hamiltonian product of
955:. 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.)
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405:, the direction of this motion, being in the direction of the thumb, then the electromotive force set up in it will be indicated by the direction in which the middle finger points."
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For a rotating object, if the right-hand fingers follow the curve of a point on the object, then the thumb points along the axis of rotation in the direction of the
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it creates a cylindrical magnetic field around the wire according to the right-hand rule. The conventional direction of a magnetic line is given by a compass needle.
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The right-hand rule dates back to the 19th century when it was implemented as a way for identifying the positive direction of coordinate axes in three dimensions.
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606:-axis. Helices are either right or left handed with curled fingers giving the direction of rotation and thumb giving the direction of advance along the
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For example, for a positively charged particle moving to the north, in a region where the magnetic field points west, the resultant force points up.
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fasten the screw, while pointing away from the hole and turning in the new direction (i.e. counterclockwise) will unfasten the screw.
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to give repeated changes of handedness. (If the axes do not have a positive or negative direction, then handedness has no meaning.)
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Unlike most mathematical concepts, the meaning of a right-handed coordinate system cannot be expressed in terms of any
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Magnets and electric currents. An elementary treatise for the use of electrical artisans and science teachers
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when viewing the tip of the thumb) is a result of this convention and not an underlying physical phenomenon.
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A magnetic field, the position of the point where it is determined, and the electric current (or change in
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coordinates, the above description of the axes is the same, except using the left hand; and the ¼ turn is
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The direction of the cross product may be found by application of the right-hand rule as follows:
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is a curved line formed by a point rotating around a center while the center moves up or down the
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can be chosen to follow the right-hand rule. Right-handed coordinate systems are often used in
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second or y-axis, then the third or z-axis can point along either right thumb or left thumb.
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This article is about three-dimensional vector geometry. For the maze-solving technique, see
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1240:. Harvard University. London, E. & F.N. Spon, limited; New York, Spon & Chamberlain.
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of a body, a magnetic field, or a fluid, or vice versa, when it is necessary to define a
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The force of a magnetic field on a charged particle, the magnetic field itself, and the
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in the magnetic field that the current created. Ampère was inspired by fellow physicist
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to understand how rotation occurs. It reveals a connection between the current and the
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body is moving in the direction of the axis arrow. If the thumb is pointing north,
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Vector calculus, linear algebra, and differential forms : a unified approach
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Chappell, James M.; Iqbal, Azhar; Hartnett, John G.; Abbott, Derek (2016).
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that causes it, and the position of the point of application of the force.
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vector of a surface to the boundary curve of the surface. Given a surface
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The right-hand rule in physics was introduced in the late 19th century by
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The middle finger points in the direction of the magnetic field vector B.
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The index finger points in the direction of the velocity vector v.
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lines around the conductor. The direction of the magnetic field (
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and the fingers curl along the orientation of the bounding curve
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Illustration of the right-hand rule on the ninth series of the
859:, the thumb points in the direction of the magnetic north pole.
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Christian Moser : right-hand-rule : wpftutorial.net
918:{\displaystyle \mathbf {F} =q\mathbf {v} \times \mathbf {B} }
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In mathematics, a rotating body is commonly represented by a
27:
Mnemonic for understanding orientation of vectors in 3D space
811:-carrying wire and concluded that electricity could create
81:, as well as to establish the direction of the force on a
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The thumb points in the direction of the cross product F.
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end, loop around outside the helix, and re-enter at the −
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provided that the right thumb points in the direction of
125:
recognized that treating these components separately, as
203: is a vector perpendicular to the plane spanned by
1210:. Internet Archive. Ithaca, NY : Matrix Editions.
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in a coil of wire and the electric current in the wire.
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Right and Left Hand Rules - Interactive Java
Tutorial
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Conventional direction of the axis of a rotating body
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424:For right-handed coordinates, use the right hand.
1002:at any point in the field of the flow of a fluid
689:When electricity flows (with direction given by
646:(a choice of "upward direction" with respect to
426:For left-handed coordinates, use the left hand.
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1256:"PHYS345 Introduction to the Right Hand Rule"
8:
578:). This causes the Sun, Moon, and stars to
374:{\displaystyle {\vec {a}}\times {\vec {b}}}
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1234:Fleming, J. A. (John Ambrose) (1902).
1204:Hubbard, John H. (John Hamal) (2009).
771:right-hand grip rule, also called the
419:right-handed coordinates on the right.
73:and to determine the direction of the
760:Finding direction of magnetic field (
565:. The length of the vector gives the
417:Left-handed coordinates on the left,
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1053:. Rather, the definition depends on
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622:Curve orientation and normal vectors
505:-axis, the ¼ turn from the positive
113:yields a quaternion comprising both
105:, recognized for his development of
1081:Fleming's left-hand rule for motors
791:) must be defined to represent the
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744:Prediction of direction of field (
640:with a specified normal direction
574:according to the right-hand rule (
261: with the direction given by
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1538:Vectors (mathematics and physics)
842:clockwise rotation of coordinates
141:Right-hand rule for cross product
1130:Hamilton, William Rowan (1853).
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1440:List of biochemistry mnemonics
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707:direction. Since there is no
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711:, the field lines exit the +
34:. For the traffic rule, see
1502:List of chemistry mnemonics
1183:10.1109/access.2016.2538262
1030:Cartesian coordinate system
337:points in the direction of
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1136:. unknown library. Dublin.
748:), given that the current
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225:{\displaystyle {\vec {a}}}
196:{\displaystyle {\vec {b}}}
167:{\displaystyle {\vec {a}}}
83:current-carrying conductor
29:
1461:Mnemonics in trigonometry
1262:. University of Delaware.
1011:Fleming's right-hand rule
874:Swiss 200-francs banknote
388:Fleming's right hand rule
61:, utilized to define the
1275:, Pearson, 2009, p. 312.
1111:Reflection (mathematics)
1045:Meta-mathematical issues
764:) for an electrical coil
1254:Watson, George (1998).
1133:Lectures on quaternions
1071:Chirality (mathematics)
71:three-dimensional space
1533:Orientation (geometry)
925:(vector cross product)
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1086:Improper rotation
981:) that causes it.
851:passes through a
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664:is defined to be
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1471:Piphilology
1449:Mathematics
1420:CHON/CHNOPS
1153:IEEE Access
819:Application
522:left-handed
431:Axis/vector
409:Coordinates
333:, then the
107:quaternions
63:orientation
43:mathematics
1517:Categories
1166:1509.00501
1117:References
1059:weak force
1038:kinematics
1034:rigid body
719:end. The +
403:forefinger
55:convention
1528:Mechanics
1356:mnemonics
1310:MathWorld
1191:2169-3536
1000:vorticity
908:×
540:Rotations
526:clockwise
366:→
357:×
351:→
318:→
285:→
246:→
217:→
188:→
159:→
1354:Science
1260:udel.edu
1065:See also
993:velocity
853:solenoid
793:rotation
769:Ampère's
563:rotation
513:axis is
59:mnemonic
1497:SCORPAN
1430:Four Fs
1425:ESCAPPM
1413:Biology
1389:OBAFGKM
1364:Physics
1171:Bibcode
963:vector.
953:physics
779:or the
693:) in a
658:around
610:-axis.
97:History
79:vectors
77:of two
47:physics
1492:Clorpt
1466:PEMDAS
1214:
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1055:chiral
970:, the
968:torque
785:vector
632:normal
479:Thumb
119:vector
115:scalar
57:and a
49:, the
1485:Other
1476:Xyzzy
1399:SUVAT
1161:arXiv
1091:ISO 2
972:force
615:screw
600:helix
476:Thumb
335:thumb
268:index
131:cross
85:in a
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1456:FOIL
1212:ISBN
1187:ISSN
1036:and
1024:and
1016:The
1005:The
998:The
834:flux
520:For
485:For
232:and
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67:axes
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