718:: 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.
403:
127:
374:
580:
746:
539:
858:
730:
692:: 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
606:
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
81:
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
558:
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
385:
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
520:
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
122:
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.
869:
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:
820:
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
912:
712:
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.
1046:
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
98:, 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
944:. 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.)
368:
394:, 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."
320:
287:
248:
219:
190:
161:
948:
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
686:
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.
90:
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.
595:-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
932:
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.
1334:
1526:
1282:
607:
fasten the screw, while pointing away from the hole and turning in the new direction (i.e. counterclockwise) will unfasten the screw.
525:
to give repeated changes of handedness. (If the axes do not have a positive or negative direction, then handedness has no meaning.)
876:
1365:
1069:
1204:
844:, resulting in a magnetic field. When wrapping the right hand around the solenoid with the fingers in the direction of the
862:
1038:
Unlike most mathematical concepts, the meaning of a right-handed coordinate system cannot be expressed in terms of any
1428:
1244:
99:
1521:
1327:
329:
564:
1226:
Magnets and electric currents. An elementary treatise for the use of electrical artisans and science teachers
833:
when viewing the tip of the thumb) is a result of this convention and not an underlying physical phenomenon.
999:
966:
A magnetic field, the position of the point where it is determined, and the electric current (or change in
551:
813:
513:
coordinates, the above description of the axes is the same, except using the left hand; and the ¼ turn is
1490:
1018:
55:
1536:
1320:
51:
1511:
1449:
1352:
1454:
1099:
918:
The direction of the cross product may be found by application of the right-hand rule as follows:
482:-axis in the positive direction (third coordinate vector), then the fingers curl from the positive
793:
591:
is a curved line formed by a point rotating around a center while the center moves up or down the
1531:
1059:
757:
59:
296:
263:
224:
195:
166:
137:
1541:
1021:
can be chosen to follow the right-hand rule. Right-handed coordinate systems are often used in
91:
522:
82:
second or y-axis, then the third or z-axis can point along either right thumb or left thumb.
24:
19:
This article is about three-dimensional vector geometry. For the maze-solving technique, see
1229:. Harvard University. London, E. & F.N. Spon, limited; New York, Spon & Chamberlain.
1392:
1159:
845:
789:
679:
382:
111:
103:
8:
1418:
1277:
1043:
784:
of a body, a magnetic field, or a fluid, or vice versa, when it is necessary to define a
560:
402:
1163:
980:
The force of a magnetic field on a charged particle, the magnetic field itself, and the
792:
in the magnetic field that the current created. Ampère was inspired by fellow physicist
1516:
1382:
1224:
1149:
1064:
788:
to understand how rotation occurs. It reveals a connection between the current and the
1194:
1423:
1290:
1200:
1175:
1074:
697:
620:
43:
1293:
126:
1464:
1167:
1084:
1047:
1039:
949:
837:
826:
797:
773:
559:
body is moving in the direction of the axis arrow. If the thumb is pointing north,
555:
71:
67:
1196:
Vector calculus, linear algebra, and differential forms : a unified approach
1137:
1120:
1089:
995:
960:
801:
785:
616:
1171:
1307:
974:
568:
490:-axis (second coordinate vector). When viewed at a position along the positive
75:
373:
1505:
1360:
1179:
967:
715:
689:
387:
290:
119:
63:
20:
1136:
Chappell, James M.; Iqbal, Azhar; Hartnett, John G.; Abbott, Derek (2016).
1094:
777:
547:
391:
256:
107:
963:
that causes it, and the position of the point of application of the force.
623:
vector of a surface to the boundary curve of the surface. Given a surface
579:
381:
The right-hand rule in physics was introduced in the late 19th century by
1459:
1444:
925:
The middle finger points in the direction of the magnetic field vector B.
115:
31:
1026:
1022:
745:
538:
95:
1298:
988:
830:
1312:
478:
coordinates, if the thumb of a person's right hand points along the
1344:
1154:
981:
841:
781:
47:
922:
The index finger points in the direction of the velocity vector v.
857:
1485:
1413:
1377:
941:
825:
lines around the conductor. The direction of the magnetic field (
663:
and the fingers curl along the orientation of the bounding curve
35:
796:, who observed that needles swirled when in the proximity of an
390:, the direction of which is represented by the direction of the
1480:
1408:
956:
861:
Illustration of the right-hand rule on the ninth series of the
848:, the thumb points in the direction of the magnetic north pole.
729:
1387:
1308:
Christian Moser : right-hand-rule : wpftutorial.net
1079:
907:{\displaystyle \mathbf {F} =q\mathbf {v} \times \mathbf {B} }
603:
588:
546:
In mathematics, a rotating body is commonly represented by a
323:
16:
Mnemonic for understanding orientation of vectors in 3D space
1135:
822:
800:-carrying wire and concluded that electricity could create
70:, as well as to establish the direction of the force on a
928:
The thumb points in the direction of the cross product F.
704:
end, loop around outside the helix, and re-enter at the −
657:
provided that the right thumb points in the direction of
114:
recognized that treating these components separately, as
1288:
192: is a vector perpendicular to the plane spanned by
1199:. Internet Archive. Ithaca, NY : Matrix Editions.
977:
in a coil of wire and the electric current in the wire.
610:
1283:
Right and Left Hand Rules - Interactive Java
Tutorial
879:
542:
Conventional direction of the axis of a rotating body
332:
299:
266:
227:
198:
169:
140:
486:-axis (first coordinate vector) toward the positive
812:This rule is used in two different applications of
1138:"The Vector Algebra War: A Historical Perspective"
906:
362:
314:
281:
242:
213:
184:
155:
413:For right-handed coordinates, use the right hand.
1503:
991:at any point in the field of the flow of a fluid
722:
678:When electricity flows (with direction given by
635:(a choice of "upward direction" with respect to
415:For left-handed coordinates, use the left hand.
1328:
1245:"PHYS345 Introduction to the Right Hand Rule"
1033:
567:). This causes the Sun, Moon, and stars to
363:{\displaystyle {\vec {a}}\times {\vec {b}}}
1335:
1321:
998:from motion in a magnetic field (known as
940:The right-hand rule has widespread use in
571:westward according to the left-hand rule.
1153:
1278:Feynman's lecture on the right-hand rule
1262:IIT Foundation Series: Physics – Class 8
1118:
856:
744:
728:
578:
537:
401:
372:
125:
1285:National High Magnetic Field Laboratory
1222:
1192:
1504:
1242:
1238:
1236:
1223:Fleming, J. A. (John Ambrose) (1902).
1193:Hubbard, John H. (John Hamal) (2009).
760:right-hand grip rule, also called the
408:right-handed coordinates on the right.
62:and to determine the direction of the
1342:
1316:
1289:
749:Finding direction of magnetic field (
574:
554:. The length of the vector gives the
406:Left-handed coordinates on the left,
1218:
1216:
1042:. Rather, the definition depends on
611:Curve orientation and normal vectors
494:-axis, the ¼ turn from the positive
102:yields a quaternion comprising both
94:, recognized for his development of
1233:
1070:Fleming's left-hand rule for motors
780:) must be defined to represent the
741:flows in the direction of the thumb
672:
13:
733:Prediction of direction of field (
629:with a specified normal direction
563:according to the right-hand rule (
533:
250: with the direction given by
14:
1553:
1527:Vectors (mathematics and physics)
1271:
1213:
852:
831:clockwise rotation of coordinates
130:Right-hand rule for cross product
1119:Hamilton, William Rowan (1853).
900:
892:
881:
935:
1429:List of biochemistry mnemonics
1255:
1186:
1129:
1112:
807:
619:, it is necessary to relate a
397:
354:
339:
306:
273:
234:
205:
176:
147:
1:
1105:
723:Ampère's right-hand grip rule
696:direction. Since there is no
583:Left- and right-handed screws
134:The cross product of vectors
700:, the field lines exit the +
528:
23:. For the traffic rule, see
7:
1491:List of chemistry mnemonics
1172:10.1109/access.2016.2538262
1053:
1019:Cartesian coordinate system
326:points in the direction of
10:
1558:
1125:. unknown library. Dublin.
737:), given that the current
315:{\displaystyle {\vec {b}}}
282:{\displaystyle {\vec {a}}}
243:{\displaystyle {\vec {b}}}
214:{\displaystyle {\vec {a}}}
185:{\displaystyle {\vec {b}}}
156:{\displaystyle {\vec {a}}}
85:
72:current-carrying conductor
18:
1473:
1450:Mnemonics in trigonometry
1437:
1401:
1351:
1251:. University of Delaware.
1000:Fleming's right-hand rule
863:Swiss 200-francs banknote
377:Fleming's right hand rule
50:, utilized to define the
1264:, Pearson, 2009, p. 312.
1100:Reflection (mathematics)
1034:Meta-mathematical issues
753:) for an electrical coil
1243:Watson, George (1998).
1122:Lectures on quaternions
1060:Chirality (mathematics)
60:three-dimensional space
1522:Orientation (geometry)
914:(vector cross product)
908:
866:
814:Ampère's circuital law
772:is used either when a
754:
742:
641:), the boundary curve
584:
543:
409:
378:
364:
316:
283:
260:of your right hand on
244:
215:
186:
157:
131:
100:two vector quaternions
92:William Rowan Hamilton
909:
860:
794:Hans Christian Ørsted
762:right-hand screw rule
748:
732:
582:
541:
451:Second finger or palm
423:Two fingers and thumb
405:
376:
365:
317:
284:
245:
216:
187:
158:
129:
25:Priority to the right
1393:Thermodynamic square
877:
846:conventional current
829:rotation instead of
790:magnetic field lines
680:conventional current
330:
297:
264:
225:
196:
167:
138:
112:Josiah Willard Gibbs
1164:2016IEEEA...4.1997C
1040:mathematical axioms
684:long straight wire,
655:positively oriented
454:Fingers curled 90°
416:
252:the right-hand rule
1383:Planetary mnemonic
1291:Weisstein, Eric W.
1065:Curl (mathematics)
1017:unit vectors in a
904:
867:
755:
743:
585:
575:Helixes and screws
550:along the axis of
544:
448:(or second vector)
412:
410:
379:
360:
312:
279:
240:
211:
182:
153:
132:
1537:Science mnemonics
1499:
1498:
1424:Taxonomy mnemonic
1294:"Right-hand rule"
1206:978-0-9715766-5-0
1075:Improper rotation
970:) that causes it.
840:passes through a
698:magnetic monopole
653:is defined to be
602:The threads of a
569:appear to revolve
556:speed of rotation
504:counter-clockwise
472:
471:
462:(or third vector)
440:Fingers extended
434:(or first vector)
357:
342:
309:
276:
254:: If you put the
237:
208:
179:
150:
1549:
1512:Electromagnetism
1337:
1330:
1323:
1314:
1313:
1304:
1303:
1265:
1259:
1253:
1252:
1240:
1231:
1230:
1220:
1211:
1210:
1190:
1184:
1183:
1157:
1133:
1127:
1126:
1116:
950:angular velocity
913:
911:
910:
905:
903:
895:
884:
838:electric current
827:counterclockwise
798:electric current
673:Electromagnetism
668:
662:
652:
646:
640:
634:
628:
498:to the positive
417:
411:
369:
367:
366:
361:
359:
358:
350:
344:
343:
335:
321:
319:
318:
313:
311:
310:
302:
288:
286:
285:
280:
278:
277:
269:
249:
247:
246:
241:
239:
238:
230:
220:
218:
217:
212:
210:
209:
201:
191:
189:
188:
183:
181:
180:
172:
162:
160:
159:
154:
152:
151:
143:
1557:
1556:
1552:
1551:
1550:
1548:
1547:
1546:
1502:
1501:
1500:
1495:
1469:
1433:
1397:
1371:Right-hand rule
1347:
1341:
1274:
1269:
1268:
1260:
1256:
1241:
1234:
1221:
1214:
1207:
1191:
1187:
1134:
1130:
1117:
1113:
1108:
1090:Poynting vector
1056:
1036:
996:induced current
938:
899:
891:
880:
878:
875:
874:
855:
810:
802:magnetic fields
786:rotation vector
770:corkscrew-rule;
766:coffee-mug rule
725:
675:
664:
658:
648:
642:
636:
630:
624:
617:vector calculus
613:
577:
565:prograde motion
536:
534:A rotating body
531:
523:can be composed
426:Curled fingers
414:
407:
400:
349:
348:
334:
333:
331:
328:
327:
301:
300:
298:
295:
294:
268:
267:
265:
262:
261:
229:
228:
226:
223:
222:
200:
199:
197:
194:
193:
171:
170:
168:
165:
164:
142:
141:
139:
136:
135:
88:
40:right-hand rule
28:
17:
12:
11:
5:
1555:
1545:
1544:
1539:
1534:
1532:Rules of thumb
1529:
1524:
1519:
1514:
1497:
1496:
1494:
1493:
1488:
1483:
1477:
1475:
1471:
1470:
1468:
1467:
1462:
1457:
1452:
1447:
1441:
1439:
1435:
1434:
1432:
1431:
1426:
1421:
1416:
1411:
1405:
1403:
1399:
1398:
1396:
1395:
1390:
1385:
1380:
1375:
1374:
1373:
1368:
1366:Left-hand rule
1357:
1355:
1349:
1348:
1340:
1339:
1332:
1325:
1317:
1311:
1310:
1305:
1286:
1280:
1273:
1272:External links
1270:
1267:
1266:
1254:
1232:
1212:
1205:
1185:
1128:
1110:
1109:
1107:
1104:
1103:
1102:
1097:
1092:
1087:
1082:
1077:
1072:
1067:
1062:
1055:
1052:
1035:
1032:
1031:
1030:
1003:
992:
985:
984:of the object.
978:
975:magnetic field
971:
964:
953:
937:
934:
930:
929:
926:
923:
916:
915:
902:
898:
894:
890:
887:
883:
854:
853:Cross products
851:
850:
849:
834:
809:
806:
724:
721:
720:
719:
713:
687:
674:
671:
612:
609:
576:
573:
535:
532:
530:
527:
470:
469:
466:
463:
456:
455:
452:
449:
442:
441:
438:
437:First or index
435:
428:
427:
424:
421:
399:
396:
356:
353:
347:
341:
338:
308:
305:
289: and the
275:
272:
236:
233:
207:
204:
178:
175:
149:
146:
87:
84:
76:magnetic field
15:
9:
6:
4:
3:
2:
1554:
1543:
1542:Hand gestures
1540:
1538:
1535:
1533:
1530:
1528:
1525:
1523:
1520:
1518:
1515:
1513:
1510:
1509:
1507:
1492:
1489:
1487:
1484:
1482:
1479:
1478:
1476:
1472:
1466:
1463:
1461:
1458:
1456:
1453:
1451:
1448:
1446:
1443:
1442:
1440:
1436:
1430:
1427:
1425:
1422:
1420:
1417:
1415:
1412:
1410:
1407:
1406:
1404:
1400:
1394:
1391:
1389:
1386:
1384:
1381:
1379:
1376:
1372:
1369:
1367:
1364:
1363:
1362:
1359:
1358:
1356:
1354:
1350:
1346:
1338:
1333:
1331:
1326:
1324:
1319:
1318:
1315:
1309:
1306:
1301:
1300:
1295:
1292:
1287:
1284:
1281:
1279:
1276:
1275:
1263:
1258:
1250:
1246:
1239:
1237:
1228:
1227:
1219:
1217:
1208:
1202:
1198:
1197:
1189:
1181:
1177:
1173:
1169:
1165:
1161:
1156:
1151:
1148:: 1997–2004.
1147:
1143:
1139:
1132:
1124:
1123:
1115:
1111:
1101:
1098:
1096:
1093:
1091:
1088:
1086:
1085:Oersted's law
1083:
1081:
1078:
1076:
1073:
1071:
1068:
1066:
1063:
1061:
1058:
1057:
1051:
1049:
1045:
1041:
1028:
1024:
1020:
1016:
1012:
1008:
1004:
1001:
997:
993:
990:
986:
983:
979:
976:
972:
969:
968:electric flux
965:
962:
958:
954:
951:
947:
946:
945:
943:
933:
927:
924:
921:
920:
919:
896:
888:
885:
873:
872:
871:
864:
859:
847:
843:
839:
835:
832:
828:
824:
819:
818:
817:
815:
805:
803:
799:
795:
791:
787:
783:
779:
776:(such as the
775:
771:
767:
763:
759:
752:
747:
740:
736:
731:
727:
717:
716:Lorentz force
714:
711:
707:
703:
699:
695:
691:
690:Electromagnet
688:
685:
681:
677:
676:
670:
667:
661:
656:
651:
645:
639:
633:
627:
622:
618:
608:
605:
600:
598:
594:
590:
581:
572:
570:
566:
562:
561:Earth rotates
557:
553:
549:
540:
526:
524:
518:
516:
512:
507:
505:
501:
497:
493:
489:
485:
481:
477:
467:
464:
461:
458:
457:
453:
450:
447:
444:
443:
439:
436:
433:
430:
429:
425:
422:
419:
418:
404:
395:
393:
389:
388:magnetic flux
384:
375:
371:
351:
345:
336:
325:
303:
292:
291:middle finger
270:
259:
258:
253:
231:
202:
173:
144:
128:
124:
121:
117:
113:
109:
105:
101:
97:
93:
83:
79:
77:
73:
69:
65:
64:cross product
61:
57:
53:
49:
45:
41:
37:
33:
26:
22:
21:Wall follower
1370:
1297:
1261:
1257:
1248:
1225:
1195:
1188:
1145:
1141:
1131:
1121:
1114:
1095:Pseudovector
1037:
1014:
1010:
1006:
939:
936:Applications
931:
917:
868:
811:
778:Euler vector
769:
765:
761:
756:
750:
738:
734:
726:
709:
705:
701:
693:
683:
665:
659:
654:
649:
643:
637:
631:
625:
614:
601:
596:
592:
586:
548:pseudovector
545:
519:
514:
510:
508:
503:
499:
495:
491:
487:
483:
479:
476:right-handed
475:
473:
459:
445:
431:
383:John Fleming
380:
255:
251:
133:
110:components.
89:
80:
39:
29:
1460:Piphilology
1438:Mathematics
1409:CHON/CHNOPS
1142:IEEE Access
808:Application
511:left-handed
420:Axis/vector
398:Coordinates
322:, then the
96:quaternions
52:orientation
32:mathematics
1506:Categories
1155:1509.00501
1106:References
1048:weak force
1027:kinematics
1023:rigid body
708:end. The +
392:forefinger
44:convention
1517:Mechanics
1345:mnemonics
1299:MathWorld
1180:2169-3536
989:vorticity
897:×
529:Rotations
515:clockwise
355:→
346:×
340:→
307:→
274:→
235:→
206:→
177:→
148:→
1343:Science
1249:udel.edu
1054:See also
982:velocity
842:solenoid
782:rotation
758:Ampère's
552:rotation
502:axis is
48:mnemonic
1486:SCORPAN
1419:Four Fs
1414:ESCAPPM
1402:Biology
1378:OBAFGKM
1353:Physics
1160:Bibcode
952:vector.
942:physics
768:or the
682:) in a
647:around
599:-axis.
86:History
68:vectors
66:of two
36:physics
1481:Clorpt
1455:PEMDAS
1203:
1178:
1044:chiral
959:, the
957:torque
774:vector
621:normal
468:Thumb
108:vector
104:scalar
46:and a
38:, the
1474:Other
1465:Xyzzy
1388:SUVAT
1150:arXiv
1080:ISO 2
961:force
604:screw
589:helix
465:Thumb
324:thumb
257:index
120:cross
74:in a
42:is a
1445:FOIL
1201:ISBN
1176:ISSN
1025:and
1013:and
1005:The
994:The
987:The
823:flux
509:For
474:For
221:and
163:and
118:and
106:and
56:axes
34:and
1361:FBI
1168:doi
836:An
615:In
293:on
116:dot
78:.
58:in
54:of
30:In
1508::
1296:.
1247:.
1235:^
1215:^
1174:.
1166:.
1158:.
1144:.
1140:.
1050:.
1009:,
1002:).
973:A
955:A
816::
804:.
764:,
669:.
660:n̂
632:n̂
587:A
517:.
506:.
500:y-
496:x-
370:.
1336:e
1329:t
1322:v
1302:.
1209:.
1182:.
1170::
1162::
1152::
1146:4
1029:.
1015:z
1011:y
1007:x
901:B
893:v
889:q
886:=
882:F
865:.
751:B
739:I
735:B
710:z
706:z
702:z
694:z
666:C
650:S
644:C
638:S
626:S
597:z
593:z
492:z
488:y
484:x
480:z
460:z
446:y
432:x
352:b
337:a
304:b
271:a
232:b
203:a
174:b
145:a
27:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
