4616:
3909:
4611:{\displaystyle {\begin{aligned}\mathbf {B} &={\frac {\omega ^{2}}{4\pi \varepsilon _{0}c^{3}}}({\hat {\mathbf {r} }}\times \mathbf {p} ){\frac {e^{i\omega (r/c-t)}}{r}}={\frac {\omega ^{2}\mu _{0}p_{0}}{4\pi c}}({\hat {\mathbf {r} }}\times {\hat {\mathbf {z} }}){\frac {e^{i\omega (r/c-t)}}{r}}=-{\frac {\omega ^{2}\mu _{0}p_{0}}{4\pi c}}\sin(\theta ){\frac {e^{i\omega (r/c-t)}}{r}}\mathbf {\hat {\phi }} \\\mathbf {E} &=c\mathbf {B} \times {\hat {\mathbf {r} }}=-{\frac {\omega ^{2}\mu _{0}p_{0}}{4\pi }}\sin(\theta )\left({\hat {\phi }}\times \mathbf {\hat {r}} \right){\frac {e^{i\omega (r/c-t)}}{r}}=-{\frac {\omega ^{2}\mu _{0}p_{0}}{4\pi }}\sin(\theta ){\frac {e^{i\omega (r/c-t)}}{r}}{\hat {\theta }}.\end{aligned}}}
3878:
3391:
3873:{\displaystyle {\begin{aligned}\mathbf {E} &={\frac {1}{4\pi \varepsilon _{0}}}\left\{{\frac {\omega ^{2}}{c^{2}r}}\left({\hat {\mathbf {r} }}\times \mathbf {p} \right)\times {\hat {\mathbf {r} }}+\left({\frac {1}{r^{3}}}-{\frac {i\omega }{cr^{2}}}\right)\left(3{\hat {\mathbf {r} }}\left-\mathbf {p} \right)\right\}e^{\frac {i\omega r}{c}}e^{-i\omega t}\\\mathbf {B} &={\frac {\omega ^{2}}{4\pi \varepsilon _{0}c^{3}}}({\hat {\mathbf {r} }}\times \mathbf {p} )\left(1-{\frac {c}{i\omega r}}\right){\frac {e^{i\omega r/c}}{r}}e^{-i\omega t}.\end{aligned}}}
675:
614:
703:
688:
1542:
266:
258:
202:
274:
38:
3211:
633:
2960:
1352:
2966:
field of a real magnetic dipole which is continuous everywhere. The delta function represents the strong field pointing in the opposite direction between the point charges, which is often omitted since one is rarely interested in the field at the dipole's position. For further discussions about the internal field of dipoles, see or
2402:
4773:
2780:
313:
has a magnetic field of exactly the same form as the electric field of an electric point dipole. A very small current-carrying loop is approximately a magnetic point dipole; the magnetic dipole moment of such a loop is the product of the current flowing in the loop and the (vector) area of the loop.
151:
points from the negative charge towards the positive charge, and has a magnitude equal to the strength of each charge times the separation between the charges. (To be precise: for the definition of the dipole moment, one should always consider the "dipole limit", where, for example, the distance of
221:
below) and may be labeled "north" and "south". In terms of the Earth's magnetic field, they are respectively "north-seeking" and "south-seeking" poles: if the magnet were freely suspended in the Earth's magnetic field, the north-seeking pole would point towards the north and the south-seeking pole
2965:
This is of the same form of the expression for the magnetic field of a point magnetic dipole, ignoring the delta function. In a real electric dipole, however, the charges are physically separate and the electric field diverges or converges at the point charges. This is different to the magnetic
1537:{\displaystyle \left\langle {\mathfrak {p}}\right\rangle =\left\langle \,{\mathfrak {I}}^{-1}\,S\,|{\mathfrak {p}}|\,{\mathfrak {I}}^{-1}\,S\,\right\rangle =\left\langle \,S\,|{\mathfrak {I}}\,{\mathfrak {p}}\,{\mathfrak {I}}^{-1}|\,S\,\right\rangle =-\left\langle {\mathfrak {p}}\right\rangle }
317:
Any configuration of charges or currents has a 'dipole moment', which describes the dipole whose field is the best approximation, at large distances, to that of the given configuration. This is simply one term in the multipole expansion when the total charge ("monopole moment") is 0—as it
2253:
3376:
2723:
2603:
1250:
1910:
671:) which is also a bent molecule, the bond dipole moments are not zero even though the O−O bonds are between similar atoms. This agrees with the Lewis structures for the resonance forms of ozone which show a positive charge on the central oxygen atom.
2269:
285:
consists of two equal and opposite point charges: in the literal sense, two poles. Its field at large distances (i.e., distances large in comparison to the separation of the poles) depends almost entirely on the dipole moment as defined above. A
997:
2955:{\displaystyle \mathbf {E} =-\nabla \Phi ={\frac {1}{4\pi \epsilon _{0}}}\ {\frac {3(\mathbf {p} \cdot {\hat {\mathbf {r} }}){\hat {\mathbf {r} }}-\mathbf {p} }{r^{3}}}-\delta ^{3}(\mathbf {r} ){\frac {\mathbf {p} }{3\epsilon _{0}}}.}
4630:
1114:
2075:
895:
119:
found in any electromagnetic system. A simple example of this system is a pair of charges of equal magnitude but opposite sign separated by some typically small distance. (A permanent electric dipole is called an
3098:
3047:
2094:
4876:
1344:
1747:
756:. However, due to the equilateral triangular distribution of the fluoride ions centered on and in the same plane as the boron cation, the symmetry of the molecule results in its dipole moment being zero.
1625:
3255:
1706:
213:
A permanent magnet, such as a bar magnet, owes its magnetism to the intrinsic magnetic dipole moment of the electron. The two ends of a bar magnet are referred to as poles (not to be confused with
2630:
2512:
3914:
3396:
1756:. This gives a non-vanishing dipole (by definition proportional to a non-vanishing first-order Stark shift) only if some of the wavefunctions belonging to the degenerate energies have opposite
1043:-state) atom can have only a zero permanent dipole. This fact follows quantum mechanically from the inversion symmetry of atoms. All 3 components of the dipole operator are antisymmetric under
3199:
3153:
4778:
is not distributed isotropically, but concentrated around the directions lying perpendicular to the dipole moment, as a result of the non-spherical electric and magnetic waves. In fact, the
3224:
In addition to dipoles in electrostatics, it is also common to consider an electric or magnetic dipole that is oscillating in time. It is an extension, or a more physical next-step, to
290:
is the limit obtained by letting the separation tend to 0 while keeping the dipole moment fixed. The field of a point dipole has a particularly simple form, and the order-1 term in the
1180:
489:, creating a temporary dipole. These dipoles are smaller in magnitude than permanent dipoles, but still play a large role in chemistry and biochemistry due to their prevalence. See
1793:
1661:
741:
isomer, the dipole moment is zero because the two C−Cl bonds are on opposite sides of the C=C and cancel (and the two bond moments for the much less polar C−H bonds also cancel).
1760:; i.e., have different behavior under inversion. This is a rare occurrence, but happens for the excited H-atom, where 2s and 2p states are "accidentally" degenerate (see article
467: : One atom attracts electrons more than another, becoming more negative, while the other atom becomes more positive. A molecule with a permanent dipole moment is called a
2397:{\displaystyle \mathbf {B} (\mathbf {m} ,\mathbf {r} )={\frac {\mu _{0}}{4\pi }}\ {\frac {3(\mathbf {m} \cdot {\hat {\mathbf {r} }}){\hat {\mathbf {r} }}-\mathbf {m} }{r^{3}}}}
1029:
209:
of a horizontally oriented electrical dipole of infinitesimal size. Strong colors indicate highest and lowest potential (where the opposing charges of the dipole are located).
1569:
1165:
1141:
1283:
4768:{\displaystyle \langle \mathbf {S} \rangle =\left({\frac {\mu _{0}p_{0}^{2}\omega ^{4}}{32\pi ^{2}c}}\right){\frac {\sin ^{2}(\theta )}{r^{2}}}\mathbf {\hat {r}} }
906:
322:
is for the magnetic case, since there are no magnetic monopoles. The dipole term is the dominant one at large distances: Its field falls off in proportion to
4907:
1053:
420:
have such dipole moments due to non-uniform distributions of positive and negative charges on the various atoms. Such is the case with polar compounds like
2011:
2984:
is defined as the direction of the force on a positive charge, electric field lines point away from a positive charge and toward a negative charge.
674:
4927:
3903: ≫ 1, the far-field takes the simpler form of a radiating "spherical" wave, but with angular dependence embedded in the cross-product:
3113:
The resulting torque will tend to align the dipole with the applied field, which in the case of an electric dipole, yields a potential energy of
1346:. Since the product of the wavefunction (in the ket) and its complex conjugate (in the bra) is always symmetric under inversion and its inverse,
824:
186:
identical to that generated by a very small current loop. However, an electron's magnetic dipole moment is not due to a current loop, but to an
5195:
5131:
2248:{\displaystyle B(\rho ,z)={\frac {\mu _{0}m}{4\pi \left(z^{2}+\rho ^{2}\right)^{\frac {3}{2}}}}{\sqrt {1+{\frac {3z^{2}}{z^{2}+\rho ^{2}}}}}}
3065:
3014:
652:. As a vector sum it depends on the relative orientation of the bonds, so that from the dipole moment information can be deduced about the
147:
Dipoles, whether electric or magnetic, can be characterized by their dipole moment, a vector quantity. For the simple electric dipole, the
4803:
1292:
900:
Notice that this definition is valid only for neutral atoms or molecules, i.e. total charge equal to zero. In the ionized case, we have
3214:
Modulus of the
Poynting vector for an oscillating electric dipole (exact solution). The two charges are shown as two small black dots.
1761:
187:
5234:
5156:
5106:
5074:
1714:
737:
isomer the two polar C−Cl bonds are on the same side of the C=C double bond and the molecular dipole moment is 1.90 D. In the
5027:
1578:
5011:
4921:
3371:{\displaystyle \mathbf {p} (\mathbf {r} ,t)=\mathbf {p} (\mathbf {r} )e^{-i\omega t}=p_{0}{\hat {\mathbf {z} }}e^{-i\omega t}.}
1980:
1752:
In the case of open-shell atoms with degenerate energy levels, one could define a dipole moment by the aid of the first-order
195:
443:
was the first scientist to study molecular dipoles extensively, and, as a consequence, dipole moments are measured in the non-
41:
The magnetic field of a sphere with a north magnetic pole at the top and a south magnetic pole at the bottom. By comparison,
5256:
2718:{\displaystyle \Phi (\mathbf {r} )={\frac {1}{4\pi \epsilon _{0}}}\,{\frac {\mathbf {p} \cdot {\hat {\mathbf {r} }}}{r^{2}}}}
2598:{\displaystyle \mathbf {A} (\mathbf {r} )={\frac {\mu _{0}}{4\pi }}{\frac {\mathbf {m} \times {\hat {\mathbf {r} }}}{r^{2}}}}
1666:
4962:
4952:
4881:
Notice that the dependence of the power on the fourth power of the frequency of the radiation is in accordance with the
309:(although the accurate description of such effects falls outside of classical electromagnetism). A theoretical magnetic
3165:
3119:
4957:
535:). The size of the induced dipole moment is equal to the product of the strength of the external field and the dipole
411:
2744:
1245:{\displaystyle \left\langle {\mathfrak {p}}\right\rangle =\left\langle \,S\,|{\mathfrak {p}}|\,S\,\right\rangle ,}
5277:
5272:
5046:
42:
2762:) is a dipole, as it is assumed here, this term is the only non-vanishing term in the multipole expansion of Φ(
3053:
1905:{\displaystyle B(m,r,\lambda )={\frac {\mu _{0}}{4\pi }}{\frac {m}{r^{3}}}{\sqrt {1+3\sin ^{2}(\lambda )}}\,,}
719:
234:, the north pole of a bar magnet points north. However, that means that Earth's geomagnetic north pole is the
90:
5051:
4947:
2617:
1171:
490:
31:
1634:
3104:
2733:
241:
The only known mechanisms for the creation of magnetic dipoles are by current loops or quantum-mechanical
164:
148:
140:
112:
66:
1708:. Since the only quantity that is equal to minus itself is the zero, the expectation value vanishes,
1005:
4932:
4897:
1550:
1146:
1122:
1044:
508:
472:
179:
168:
5252:
1258:
4917:
4882:
4797:
The total time-average power radiated by the field can then be derived from the
Poynting vector as
2751:
547:
291:
5210:
4779:
3382:
730:
653:
649:
5172:
4991:
Magnetic colatitude is 0 along the dipole's axis and 90° in the plane perpendicular to its axis.
1547:
it follows that the expectation value changes sign under inversion. We used here the fact that
523:(remember that a molecule has a charge distribution) is caused by an electric field external to
2420:
is the vector from the position of the dipole to the position where the field is being measured
613:
499:
These can occur when one molecule with a permanent dipole repels another molecule's electrons,
73:
5244:
5191:
5152:
5127:
5102:
5070:
4937:
3232:
1628:
749:
745:
663:
implies that the two C=O bond dipole moments cancel so that the molecule must be linear. For H
606:
464:
421:
407:
298:
246:
214:
2500:
1757:
1572:
992:{\displaystyle {\mathfrak {p}}=\sum _{i=1}^{N}\,q_{i}\,(\mathbf {r} _{i}-\mathbf {r} _{c}),}
718:
An example in organic chemistry of the role of geometry in determining dipole moment is the
645:
594:
425:
222:
would point towards the south. The dipole moment of the bar magnet points from its magnetic
132:
5231:
3210:
1289:-state, non-degenerate, wavefunction, which is symmetric or antisymmetric under inversion:
527:. This field may, for instance, originate from an ion or polar molecule in the vicinity of
5248:
5238:
4972:
4967:
4942:
4622:
2968:
785:
702:
564:
433:
429:
128:
116:
104:
3381:
In vacuum, the exact field produced by this oscillating dipole can be derived using the
1764:
for the origin of this degeneracy) and have opposite parity (2s is even and 2p is odd).
1109:{\displaystyle {\mathfrak {I}}\;{\mathfrak {p}}\;{\mathfrak {I}}^{-1}=-{\mathfrak {p}},}
814: th nucleus. The dipole observable (physical quantity) has the quantum mechanical
5095:
3225:
3219:
2992:
2988:
2981:
2767:
1950:
687:
626:
558:
536:
302:
242:
206:
183:
265:
135:
system. A simple example is a single loop of wire with constant current through it. A
5266:
807:
753:
784:. For instance, this collection may be a molecule consisting of electrons, all with
257:
4888:
A circular polarized dipole is described as a superposition of two linear dipoles.
1984:
1968:
1923:
1753:
2070:{\displaystyle \lambda =\arcsin \left({\frac {z}{\sqrt {z^{2}+\rho ^{2}}}}\right)}
201:
171:), with a magnitude equal to the current in the loop times the area of the loop.
588:
440:
273:
37:
5173:"The Electric Dipole Moment Vector -- Direction, Magnitude, Meaning, et cetera"
667:
O the O−H bond moments do not cancel because the molecule is bent. For ozone (O
625:
Potassium bromide (KBr) has one of the highest dipole moments because it is an
632:
359:
227:
223:
136:
277:
Field lines of a point dipole of any type, electric, magnetic, acoustic, etc.
600:
532:
301:
in nature, there are magnetic dipoles in the form of the quantum-mechanical
261:
Electric field lines of two opposing charges separated by a finite distance.
890:{\displaystyle {\mathfrak {p}}=\sum _{i=1}^{N}\,q_{i}\,\mathbf {r} _{i}\,.}
30:
This article is about the electromagnetic phenomenon. For other uses, see
4912:
4885:, and the underlying effects why the sky consists of mainly blue colour.
3231:
In particular, consider a harmonically oscillating electric dipole, with
2771:
576:
486:
482:
417:
306:
175:
160:
to infinity in such a way that the product remains a positive constant.)
121:
1774:
Magnet § Two models for magnets: magnetic poles and atomic currents
531:
or may be macroscopic (e.g., a molecule between the plates of a charged
428:
is shared unequally between atoms. Therefore, a molecule's dipole is an
1170:
The permanent dipole moment of an atom in a non-degenerate state (see
582:
231:
58:
17:
2487:
the dipole term in the multipole expansion of an arbitrary field, and
1174:) is given as the expectation (average) value of the dipole operator,
463:
These occur when two atoms in a molecule have substantially different
4902:
3093:{\displaystyle {\boldsymbol {\tau }}=\mathbf {m} \times \mathbf {B} }
3042:{\displaystyle {\boldsymbol {\tau }}=\mathbf {p} \times \mathbf {E} }
3000:
1960:
1946:
1773:
96:
79:
432:
with an inherent electric field that should not be confused with a
4871:{\displaystyle P={\frac {\mu _{0}\omega ^{4}p_{0}^{2}}{12\pi c}}.}
4787:
3209:
2996:
1964:
1339:{\displaystyle {\mathfrak {I}}\,|\,S\,\rangle =\pm |\,S\,\rangle }
570:
551:
449:
264:
200:
36:
644:
The overall dipole moment of a molecule may be approximated as a
5213:, Introduction to Electrodynamics, Prentice Hall, 1999, page 447
2491:
the field of any dipole-like configuration at large distances.
238:
pole (south-seeking pole) of its dipole moment and vice versa.
485:
happen to be more concentrated in one place than another in a
1742:{\displaystyle \left\langle {\mathfrak {p}}\right\rangle =0.}
546:
Dipole moment values can be obtained from measurement of the
673:
444:
5226:
2969:
Magnetic moment § Internal magnetic field of a dipole
1620:{\displaystyle {\mathfrak {I}}^{-1}={\mathfrak {I}}^{*}\,}
1031:
is the center of mass of the molecule/group of particles.
752:
greater than the traditionally cited threshold of 1.7 for
269:
Magnetic field lines of a ring current of finite diameter.
182:
have magnetic dipole moments, as an electron generates a
1991:
Conversion to cylindrical coordinates is achieved using
190:
property of the electron. The electron may also have an
640:
O has a net dipole. The two bond dipoles do not cancel.
115:
deals with the separation of the positive and negative
1701:{\displaystyle {\mathfrak {I}}^{**}={\mathfrak {I}}\,}
194:
dipole moment though such has yet to be observed (see
156:
to 0 while simultaneously, the charge strength should
4806:
4633:
3912:
3394:
3258:
3168:
3122:
3068:
3017:
2783:
2633:
2624:
due to an electric dipole at the origin is given by:
2515:
2272:
2097:
2014:
1796:
1717:
1669:
1637:
1581:
1553:
1355:
1295:
1261:
1183:
1149:
1125:
1056:
1008:
909:
827:
744:
Another example of the role of molecular geometry is
550:. Some typical gas phase values given with the unit
4973:
Magnetic moment#Internal magnetic field of a dipole
1937:
is the magnetic latitude (equal to 90° −
1931:
is the distance from the center, measured in metres
748:, which has three polar bonds with a difference in
49:magnetic pole near its north geographic pole and a
5094:
4870:
4767:
4610:
3872:
3370:
3193:
3147:
3092:
3041:
2954:
2717:
2597:
2396:
2247:
2069:
1904:
1741:
1700:
1655:
1619:
1563:
1536:
1338:
1277:
1244:
1159:
1135:
1108:
1023:
991:
889:
4759:
4427:
4289:
3194:{\displaystyle U=-\mathbf {m} \cdot \mathbf {B} }
3148:{\displaystyle U=-\mathbf {p} \cdot \mathbf {E} }
621:has a zero dipole as the two bond dipoles cancel.
678:Resonance Lewis structures of the ozone molecule
503:a dipole moment in that molecule. A molecule is
456:For molecules there are three types of dipoles:
1663:may be moved from bra to ket and then becomes
3159:The energy of a magnetic dipole is similarly
8:
5067:Modern Problems in Classical Electrodynamics
4642:
4634:
2999:arise on each side of the dipole creating a
2750:This term appears as the second term in the
1333:
1314:
1272:
629:that exists as a molecule in the gas phase.
249:has never been experimentally demonstrated.
163:For the magnetic (dipole) current loop, the
139:is an example of a magnet with a permanent
4908:Dipole model of the Earth's magnetic field
2754:of an arbitrary electrostatic potential Φ(
1922:is the strength of the field, measured in
1072:
1064:
167:points through the loop (according to the
4845:
4840:
4830:
4820:
4813:
4805:
4754:
4753:
4745:
4722:
4715:
4699:
4684:
4674:
4669:
4659:
4652:
4637:
4632:
4590:
4589:
4565:
4552:
4546:
4514:
4504:
4494:
4487:
4457:
4444:
4438:
4422:
4421:
4407:
4406:
4369:
4359:
4349:
4342:
4325:
4323:
4322:
4314:
4299:
4284:
4283:
4259:
4246:
4240:
4205:
4195:
4185:
4178:
4148:
4135:
4129:
4115:
4113:
4112:
4098:
4096:
4095:
4072:
4062:
4052:
4045:
4018:
4005:
3999:
3991:
3977:
3975:
3974:
3962:
3952:
3935:
3929:
3917:
3913:
3911:
3848:
3829:
3819:
3813:
3790:
3771:
3757:
3755:
3754:
3742:
3732:
3715:
3709:
3697:
3678:
3655:
3636:
3623:
3609:
3607:
3606:
3590:
3588:
3587:
3565:
3547:
3536:
3527:
3508:
3506:
3505:
3492:
3478:
3476:
3475:
3458:
3447:
3441:
3427:
3411:
3399:
3395:
3393:
3350:
3335:
3333:
3332:
3326:
3304:
3292:
3284:
3267:
3259:
3257:
3186:
3178:
3167:
3140:
3132:
3121:
3085:
3077:
3069:
3067:
3034:
3026:
3018:
3016:
2940:
2927:
2925:
2917:
2908:
2893:
2883:
2869:
2867:
2866:
2852:
2850:
2849:
2841:
2832:
2820:
2804:
2784:
2782:
2707:
2691:
2689:
2688:
2680:
2677:
2676:
2667:
2651:
2640:
2632:
2587:
2571:
2569:
2568:
2560:
2557:
2541:
2535:
2524:
2516:
2514:
2386:
2376:
2362:
2360:
2359:
2345:
2343:
2342:
2334:
2325:
2306:
2300:
2289:
2281:
2273:
2271:
2234:
2221:
2209:
2199:
2191:
2177:
2166:
2153:
2126:
2119:
2096:
2054:
2041:
2031:
2013:
1898:
1878:
1863:
1855:
1846:
1830:
1824:
1795:
1787:, of a dipole magnetic field is given by
1723:
1722:
1716:
1697:
1691:
1690:
1678:
1672:
1671:
1668:
1652:
1646:
1640:
1639:
1636:
1616:
1610:
1604:
1603:
1590:
1584:
1583:
1580:
1555:
1554:
1552:
1524:
1523:
1507:
1503:
1498:
1489:
1483:
1482:
1480:
1474:
1473:
1472:
1466:
1465:
1460:
1459:
1455:
1441:
1437:
1428:
1422:
1421:
1419:
1414:
1408:
1407:
1402:
1401:
1397:
1388:
1382:
1381:
1379:
1361:
1360:
1354:
1332:
1328:
1323:
1313:
1309:
1304:
1303:
1297:
1296:
1294:
1271:
1267:
1262:
1260:
1233:
1229:
1224:
1218:
1217:
1212:
1211:
1207:
1189:
1188:
1182:
1151:
1150:
1148:
1127:
1126:
1124:
1097:
1096:
1081:
1075:
1074:
1066:
1065:
1058:
1057:
1055:
1015:
1010:
1007:
977:
972:
962:
957:
952:
946:
941:
935:
924:
911:
910:
908:
883:
877:
872:
870:
864:
859:
853:
842:
829:
828:
826:
1945:is the magnetic colatitude, measured in
631:
612:
272:
256:
5004:
4984:
3070:
3019:
2263:The field itself is a vector quantity:
2084:is the perpendicular distance from the
507:when it carries an induced dipole. See
174:Similar to magnetic current loops, the
5030:, Henry George Liddell, Robert Scott,
5014:, Henry George Liddell, Robert Scott,
4790:angular distribution is precisely the
5149:CRC Handbook of Chemistry and Physics
1656:{\displaystyle {\mathfrak {I}}^{*}\,}
515:More generally, an induced dipole of
294:is precisely the point dipole field.
107:phenomenon which occurs in two ways:
7:
5088:
5086:
2770:from a dipole can be found from the
2608:with the same definitions as above.
436:, which generates a magnetic field.
5253:Energy Density of a Magnetic Dipole
5241:: a chapter from an online textbook
1724:
1692:
1673:
1641:
1605:
1585:
1556:
1525:
1484:
1475:
1467:
1423:
1409:
1383:
1362:
1298:
1219:
1190:
1152:
1128:
1098:
1076:
1067:
1059:
912:
830:
218:
4928:Magnetic dipole–dipole interaction
2798:
2795:
2634:
1959:is the dipole moment, measured in
760:Quantum-mechanical dipole operator
659:For example, the zero dipole of CO
305:associated with particles such as
53:magnetic pole near its South Pole.
25:
5188:Classical Electrodynamics, 3rd Ed
5124:Introduction to Quantum Mechanics
2475:is the permeability of free space
1768:Field of a static magnetic dipole
696:isomer, dipole moment 1.90 D
4756:
4638:
4424:
4326:
4315:
4300:
4116:
4099:
3992:
3978:
3918:
3772:
3758:
3698:
3637:
3624:
3610:
3591:
3509:
3493:
3479:
3400:
3336:
3293:
3285:
3268:
3260:
3187:
3179:
3141:
3133:
3086:
3078:
3035:
3027:
2928:
2918:
2884:
2870:
2853:
2842:
2785:
2692:
2681:
2641:
2572:
2561:
2525:
2517:
2377:
2363:
2346:
2335:
2290:
2282:
2274:
1571:, being a symmetry operator, is
1024:{\displaystyle \mathbf {r} _{c}}
1011:
973:
958:
873:
701:
686:
519:polarizable charge distribution
131:is the closed circulation of an
5101:(3rd ed.). Prentice Hall.
5097:Introduction to Electrodynamics
4922:Subtropical Indian Ocean Dipole
2456:is the unit vector parallel to
1564:{\displaystyle {\mathfrak {I}}}
1160:{\displaystyle {\mathfrak {I}}}
1136:{\displaystyle {\mathfrak {p}}}
481:These occur due to chance when
196:electron electric dipole moment
5257:Wolfram Demonstrations Project
4737:
4731:
4595:
4579:
4559:
4543:
4537:
4471:
4451:
4412:
4398:
4392:
4330:
4273:
4253:
4237:
4231:
4162:
4142:
4126:
4120:
4103:
4092:
4032:
4012:
3996:
3982:
3971:
3776:
3762:
3751:
3614:
3595:
3513:
3483:
3340:
3297:
3289:
3278:
3264:
2922:
2914:
2874:
2863:
2857:
2838:
2696:
2645:
2637:
2576:
2529:
2521:
2430:: the distance from the dipole
2367:
2356:
2350:
2331:
2294:
2278:
2113:
2101:
1893:
1887:
1818:
1800:
1499:
1461:
1415:
1403:
1324:
1305:
1278:{\displaystyle |\,S\,\rangle }
1263:
1225:
1213:
983:
953:
152:the generating charges should
1:
4953:Cylindrical multipole moments
4924:, two oceanographic phenomena
2987:When placed in a homogeneous
2612:Field from an electric dipole
2483:the field of a point dipole,
2466:is the (vector) dipole moment
1047:with respect to the nucleus,
5151:(65th ed.). CRC Press.
5122:Griffiths, David J. (1994).
5093:Griffiths, David J. (1999).
1143:is the dipole operator and
362:) term and higher powers of
297:Although there are no known
5190:. Wiley. pp. 148–150.
5069:. Oxford University Press.
4958:Spherical multipole moments
3110:(in ampere-square meters).
1167:is the inversion operator.
412:Dipole moments of molecules
5294:
3217:
2980:Since the direction of an
2745:permittivity of free space
1981:permeability of free space
1771:
711:isomer, dipole moment zero
405:
89:
86: 'twice' and
72:
29:
27:Electromagnetic phenomenon
5245:Electric Dipole Potential
5227:USGS Geomagnetism Program
5186:Jackson, John D. (1999).
5147:Weast, Robert C. (1984).
5065:Brau, Charles A. (2004).
5047:Oxford English Dictionary
4794: = 1 "p" wave.
2495:Magnetic vector potential
2426:is the absolute value of
1762:Laplace–Runge–Lenz vector
792:, and nuclei with charge
764:Consider a collection of
509:induced-dipole attraction
473:dipole–dipole attractions
3059:(in coulomb-meters), or
2506:of a magnetic dipole is
1783:The far-field strength,
178:particle and some other
5052:Oxford University Press
5032:A Greek-English Lexicon
5016:A Greek-English Lexicon
4948:Axial multipole moments
4786:) responsible for such
2618:electrostatic potential
1172:degenerate energy level
768:particles with charges
398:for the monopole term.
288:point (electric) dipole
245:since the existence of
207:electrostatic potential
32:dipole (disambiguation)
4903:Magnetic dipole models
4872:
4769:
4612:
3874:
3372:
3249:direction of the form
3215:
3195:
3149:
3105:magnetic dipole moment
3094:
3054:electric dipole moment
3043:
2956:
2758:). If the source of Φ(
2719:
2599:
2398:
2249:
2071:
1906:
1743:
1702:
1657:
1631:the Hermitian adjoint
1621:
1565:
1538:
1340:
1279:
1246:
1161:
1137:
1110:
1025:
993:
940:
891:
858:
679:
641:
622:
617:The linear molecule CO
278:
270:
262:
210:
165:magnetic dipole moment
149:electric dipole moment
141:magnetic dipole moment
54:
4873:
4770:
4613:
3875:
3373:
3213:
3196:
3150:
3095:
3044:
2995:, equal but opposite
2957:
2720:
2600:
2399:
2250:
2072:
1907:
1744:
1703:
1658:
1622:
1566:
1539:
1341:
1280:
1247:
1162:
1138:
1111:
1026:
994:
920:
892:
838:
775:and position vectors
677:
635:
616:
478:Instantaneous dipoles
439:The physical chemist
380:for higher terms, or
276:
268:
260:
204:
180:fundamental particles
40:
4933:Spin magnetic moment
4898:Polarization density
4804:
4631:
3910:
3392:
3256:
3238:and a dipole moment
3166:
3120:
3066:
3015:
2781:
2631:
2513:
2270:
2095:
2012:
1953:from the dipole axis
1794:
1715:
1667:
1635:
1579:
1551:
1353:
1293:
1259:
1181:
1147:
1123:
1054:
1006:
907:
825:
491:instantaneous dipole
205:Contour plot of the
169:right hand grip rule
103: 'axis') is an
4918:Indian Ocean Dipole
4883:Rayleigh scattering
4850:
4679:
2774:of this potential:
2752:multipole expansion
650:bond dipole moments
636:The bent molecule H
548:dielectric constant
292:multipole expansion
5237:2010-12-14 at the
5211:David J. Griffiths
4868:
4836:
4780:spherical harmonic
4765:
4665:
4621:The time-averaged
4608:
4606:
3870:
3868:
3383:retarded potential
3368:
3216:
3191:
3145:
3090:
3039:
2976:Torque on a dipole
2952:
2715:
2595:
2394:
2245:
2067:
1963:-square metres or
1902:
1739:
1698:
1653:
1617:
1561:
1534:
1336:
1275:
1242:
1157:
1133:
1106:
1039:A non-degenerate (
1021:
989:
887:
731:1,2-dichloroethene
680:
654:molecular geometry
642:
623:
299:magnetic monopoles
279:
271:
263:
247:magnetic monopoles
211:
55:
5255:by Franz Krafft.
5197:978-0-471-30932-1
5133:978-0-13-124405-4
5126:. Prentice Hall.
4963:Laplace expansion
4863:
4762:
4751:
4709:
4598:
4587:
4529:
4479:
4430:
4415:
4384:
4333:
4292:
4281:
4223:
4170:
4123:
4106:
4090:
4040:
3985:
3969:
3842:
3806:
3765:
3749:
3671:
3617:
3598:
3572:
3542:
3516:
3486:
3468:
3434:
3343:
3233:angular frequency
2947:
2899:
2877:
2860:
2831:
2827:
2713:
2699:
2674:
2593:
2579:
2555:
2392:
2370:
2353:
2324:
2320:
2243:
2241:
2189:
2185:
2061:
2060:
1896:
1861:
1844:
750:electronegativity
746:boron trifluoride
607:potassium bromide
465:electronegativity
460:Permanent dipoles
441:Peter J. W. Debye
422:hydrogen fluoride
408:Chemical polarity
402:Molecular dipoles
340:, as compared to
16:(Redirected from
5285:
5278:Potential theory
5273:Electromagnetism
5214:
5208:
5202:
5201:
5183:
5177:
5176:
5169:
5163:
5162:
5144:
5138:
5137:
5119:
5113:
5112:
5100:
5090:
5081:
5080:
5062:
5056:
5055:
5050:(2nd ed.).
5041:
5035:
5025:
5019:
5009:
4992:
4989:
4877:
4875:
4874:
4869:
4864:
4862:
4851:
4849:
4844:
4835:
4834:
4825:
4824:
4814:
4774:
4772:
4771:
4766:
4764:
4763:
4755:
4752:
4750:
4749:
4740:
4727:
4726:
4716:
4714:
4710:
4708:
4704:
4703:
4690:
4689:
4688:
4678:
4673:
4664:
4663:
4653:
4641:
4617:
4615:
4614:
4609:
4607:
4600:
4599:
4591:
4588:
4583:
4582:
4569:
4547:
4530:
4528:
4520:
4519:
4518:
4509:
4508:
4499:
4498:
4488:
4480:
4475:
4474:
4461:
4439:
4437:
4433:
4432:
4431:
4423:
4417:
4416:
4408:
4385:
4383:
4375:
4374:
4373:
4364:
4363:
4354:
4353:
4343:
4335:
4334:
4329:
4324:
4318:
4303:
4294:
4293:
4285:
4282:
4277:
4276:
4263:
4241:
4224:
4222:
4211:
4210:
4209:
4200:
4199:
4190:
4189:
4179:
4171:
4166:
4165:
4152:
4130:
4125:
4124:
4119:
4114:
4108:
4107:
4102:
4097:
4091:
4089:
4078:
4077:
4076:
4067:
4066:
4057:
4056:
4046:
4041:
4036:
4035:
4022:
4000:
3995:
3987:
3986:
3981:
3976:
3970:
3968:
3967:
3966:
3957:
3956:
3940:
3939:
3930:
3921:
3902:
3900:
3899:
3894:
3891:
3879:
3877:
3876:
3871:
3869:
3862:
3861:
3843:
3838:
3837:
3833:
3814:
3812:
3808:
3807:
3805:
3791:
3775:
3767:
3766:
3761:
3756:
3750:
3748:
3747:
3746:
3737:
3736:
3720:
3719:
3710:
3701:
3692:
3691:
3673:
3672:
3667:
3656:
3650:
3646:
3645:
3641:
3640:
3632:
3628:
3627:
3619:
3618:
3613:
3608:
3600:
3599:
3594:
3589:
3578:
3574:
3573:
3571:
3570:
3569:
3556:
3548:
3543:
3541:
3540:
3528:
3518:
3517:
3512:
3507:
3501:
3497:
3496:
3488:
3487:
3482:
3477:
3469:
3467:
3463:
3462:
3452:
3451:
3442:
3435:
3433:
3432:
3431:
3412:
3403:
3385:formulation as:
3377:
3375:
3374:
3369:
3364:
3363:
3345:
3344:
3339:
3334:
3331:
3330:
3318:
3317:
3296:
3288:
3271:
3263:
3206:Dipole radiation
3200:
3198:
3197:
3192:
3190:
3182:
3154:
3152:
3151:
3146:
3144:
3136:
3099:
3097:
3096:
3091:
3089:
3081:
3073:
3048:
3046:
3045:
3040:
3038:
3030:
3022:
3007:
2961:
2959:
2958:
2953:
2948:
2946:
2945:
2944:
2931:
2926:
2921:
2913:
2912:
2900:
2898:
2897:
2888:
2887:
2879:
2878:
2873:
2868:
2862:
2861:
2856:
2851:
2845:
2833:
2829:
2828:
2826:
2825:
2824:
2805:
2788:
2732:is the (vector)
2724:
2722:
2721:
2716:
2714:
2712:
2711:
2702:
2701:
2700:
2695:
2690:
2684:
2678:
2675:
2673:
2672:
2671:
2652:
2644:
2604:
2602:
2601:
2596:
2594:
2592:
2591:
2582:
2581:
2580:
2575:
2570:
2564:
2558:
2556:
2554:
2546:
2545:
2536:
2528:
2520:
2501:vector potential
2455:
2453:
2452:
2447:
2444:
2403:
2401:
2400:
2395:
2393:
2391:
2390:
2381:
2380:
2372:
2371:
2366:
2361:
2355:
2354:
2349:
2344:
2338:
2326:
2322:
2321:
2319:
2311:
2310:
2301:
2293:
2285:
2277:
2254:
2252:
2251:
2246:
2244:
2242:
2240:
2239:
2238:
2226:
2225:
2215:
2214:
2213:
2200:
2192:
2190:
2188:
2187:
2186:
2178:
2176:
2172:
2171:
2170:
2158:
2157:
2135:
2131:
2130:
2120:
2076:
2074:
2073:
2068:
2066:
2062:
2059:
2058:
2046:
2045:
2036:
2032:
2004:
1911:
1909:
1908:
1903:
1897:
1883:
1882:
1864:
1862:
1860:
1859:
1847:
1845:
1843:
1835:
1834:
1825:
1748:
1746:
1745:
1740:
1732:
1728:
1727:
1707:
1705:
1704:
1699:
1696:
1695:
1686:
1685:
1677:
1676:
1662:
1660:
1659:
1654:
1651:
1650:
1645:
1644:
1626:
1624:
1623:
1618:
1615:
1614:
1609:
1608:
1598:
1597:
1589:
1588:
1570:
1568:
1567:
1562:
1560:
1559:
1543:
1541:
1540:
1535:
1533:
1529:
1528:
1512:
1508:
1502:
1497:
1496:
1488:
1487:
1479:
1478:
1471:
1470:
1464:
1446:
1442:
1436:
1435:
1427:
1426:
1418:
1413:
1412:
1406:
1396:
1395:
1387:
1386:
1370:
1366:
1365:
1345:
1343:
1342:
1337:
1327:
1308:
1302:
1301:
1284:
1282:
1281:
1276:
1266:
1251:
1249:
1248:
1243:
1238:
1234:
1228:
1223:
1222:
1216:
1198:
1194:
1193:
1166:
1164:
1163:
1158:
1156:
1155:
1142:
1140:
1139:
1134:
1132:
1131:
1115:
1113:
1112:
1107:
1102:
1101:
1089:
1088:
1080:
1079:
1071:
1070:
1063:
1062:
1030:
1028:
1027:
1022:
1020:
1019:
1014:
998:
996:
995:
990:
982:
981:
976:
967:
966:
961:
951:
950:
939:
934:
916:
915:
896:
894:
893:
888:
882:
881:
876:
869:
868:
857:
852:
834:
833:
705:
690:
595:hydrogen cyanide
426:electron density
397:
395:
394:
389:
386:
379:
377:
376:
371:
368:
357:
355:
354:
349:
346:
339:
337:
336:
331:
328:
230:. In a magnetic
226:to its magnetic
133:electric current
117:electric charges
100:
93:
83:
76:
21:
5293:
5292:
5288:
5287:
5286:
5284:
5283:
5282:
5263:
5262:
5249:Stephen Wolfram
5239:Wayback Machine
5232:Fields of Force
5223:
5218:
5217:
5209:
5205:
5198:
5185:
5184:
5180:
5171:
5170:
5166:
5159:
5146:
5145:
5141:
5134:
5121:
5120:
5116:
5109:
5092:
5091:
5084:
5077:
5064:
5063:
5059:
5043:
5042:
5038:
5026:
5022:
5010:
5006:
5001:
4996:
4995:
4990:
4986:
4981:
4968:Molecular solid
4943:Solid harmonics
4894:
4852:
4826:
4816:
4815:
4802:
4801:
4741:
4718:
4717:
4695:
4691:
4680:
4655:
4654:
4648:
4629:
4628:
4623:Poynting vector
4605:
4604:
4548:
4521:
4510:
4500:
4490:
4489:
4440:
4405:
4401:
4376:
4365:
4355:
4345:
4344:
4304:
4296:
4295:
4242:
4212:
4201:
4191:
4181:
4180:
4131:
4079:
4068:
4058:
4048:
4047:
4001:
3958:
3948:
3941:
3931:
3922:
3908:
3907:
3895:
3892:
3887:
3886:
3884:
3867:
3866:
3844:
3815:
3795:
3783:
3779:
3738:
3728:
3721:
3711:
3702:
3694:
3693:
3674:
3657:
3651:
3605:
3601:
3583:
3579:
3561:
3557:
3549:
3532:
3526:
3522:
3474:
3470:
3454:
3453:
3443:
3440:
3436:
3423:
3416:
3404:
3390:
3389:
3346:
3322:
3300:
3254:
3253:
3244:
3222:
3208:
3164:
3163:
3118:
3117:
3064:
3063:
3013:
3012:
3003:
2978:
2936:
2932:
2904:
2889:
2834:
2816:
2809:
2779:
2778:
2742:
2703:
2679:
2663:
2656:
2629:
2628:
2614:
2583:
2559:
2547:
2537:
2511:
2510:
2497:
2474:
2448:
2445:
2440:
2439:
2437:
2382:
2327:
2312:
2302:
2268:
2267:
2261:
2230:
2217:
2216:
2205:
2201:
2162:
2149:
2148:
2144:
2143:
2136:
2122:
2121:
2093:
2092:
2050:
2037:
2027:
2010:
2009:
1992:
1978:
1874:
1851:
1836:
1826:
1792:
1791:
1781:
1776:
1770:
1718:
1713:
1712:
1670:
1665:
1664:
1638:
1633:
1632:
1602:
1582:
1577:
1576:
1549:
1548:
1519:
1481:
1454:
1450:
1420:
1380:
1378:
1374:
1356:
1351:
1350:
1291:
1290:
1257:
1256:
1206:
1202:
1184:
1179:
1178:
1145:
1144:
1121:
1120:
1073:
1052:
1051:
1037:
1009:
1004:
1003:
971:
956:
942:
905:
904:
871:
860:
823:
822:
816:dipole operator
804:
797:
783:
773:
762:
716:
715:
714:
713:
712:
706:
698:
697:
691:
670:
666:
662:
639:
620:
565:carbon monoxide
496:Induced dipoles
434:magnetic dipole
430:electric dipole
414:
404:
390:
387:
384:
383:
381:
372:
369:
366:
365:
363:
350:
347:
344:
343:
341:
332:
329:
326:
325:
323:
283:physical dipole
255:
129:magnetic dipole
113:electric dipole
105:electromagnetic
35:
28:
23:
22:
15:
12:
11:
5:
5291:
5289:
5281:
5280:
5275:
5265:
5264:
5261:
5260:
5242:
5229:
5222:
5221:External links
5219:
5216:
5215:
5203:
5196:
5178:
5164:
5157:
5139:
5132:
5114:
5107:
5082:
5075:
5057:
5044:"dipole, n.".
5036:
5020:
5003:
5002:
5000:
4997:
4994:
4993:
4983:
4982:
4980:
4977:
4976:
4975:
4970:
4965:
4960:
4955:
4950:
4945:
4940:
4935:
4930:
4925:
4915:
4910:
4905:
4900:
4893:
4890:
4879:
4878:
4867:
4861:
4858:
4855:
4848:
4843:
4839:
4833:
4829:
4823:
4819:
4812:
4809:
4782:function (sin
4776:
4775:
4761:
4758:
4748:
4744:
4739:
4736:
4733:
4730:
4725:
4721:
4713:
4707:
4702:
4698:
4694:
4687:
4683:
4677:
4672:
4668:
4662:
4658:
4651:
4647:
4644:
4640:
4636:
4619:
4618:
4603:
4597:
4594:
4586:
4581:
4578:
4575:
4572:
4568:
4564:
4561:
4558:
4555:
4551:
4545:
4542:
4539:
4536:
4533:
4527:
4524:
4517:
4513:
4507:
4503:
4497:
4493:
4486:
4483:
4478:
4473:
4470:
4467:
4464:
4460:
4456:
4453:
4450:
4447:
4443:
4436:
4429:
4426:
4420:
4414:
4411:
4404:
4400:
4397:
4394:
4391:
4388:
4382:
4379:
4372:
4368:
4362:
4358:
4352:
4348:
4341:
4338:
4332:
4328:
4321:
4317:
4313:
4310:
4307:
4305:
4302:
4298:
4297:
4291:
4288:
4280:
4275:
4272:
4269:
4266:
4262:
4258:
4255:
4252:
4249:
4245:
4239:
4236:
4233:
4230:
4227:
4221:
4218:
4215:
4208:
4204:
4198:
4194:
4188:
4184:
4177:
4174:
4169:
4164:
4161:
4158:
4155:
4151:
4147:
4144:
4141:
4138:
4134:
4128:
4122:
4118:
4111:
4105:
4101:
4094:
4088:
4085:
4082:
4075:
4071:
4065:
4061:
4055:
4051:
4044:
4039:
4034:
4031:
4028:
4025:
4021:
4017:
4014:
4011:
4008:
4004:
3998:
3994:
3990:
3984:
3980:
3973:
3965:
3961:
3955:
3951:
3947:
3944:
3938:
3934:
3928:
3925:
3923:
3920:
3916:
3915:
3881:
3880:
3865:
3860:
3857:
3854:
3851:
3847:
3841:
3836:
3832:
3828:
3825:
3822:
3818:
3811:
3804:
3801:
3798:
3794:
3789:
3786:
3782:
3778:
3774:
3770:
3764:
3760:
3753:
3745:
3741:
3735:
3731:
3727:
3724:
3718:
3714:
3708:
3705:
3703:
3700:
3696:
3695:
3690:
3687:
3684:
3681:
3677:
3670:
3666:
3663:
3660:
3654:
3649:
3644:
3639:
3635:
3631:
3626:
3622:
3616:
3612:
3604:
3597:
3593:
3586:
3582:
3577:
3568:
3564:
3560:
3555:
3552:
3546:
3539:
3535:
3531:
3525:
3521:
3515:
3511:
3504:
3500:
3495:
3491:
3485:
3481:
3473:
3466:
3461:
3457:
3450:
3446:
3439:
3430:
3426:
3422:
3419:
3415:
3410:
3407:
3405:
3402:
3398:
3397:
3379:
3378:
3367:
3362:
3359:
3356:
3353:
3349:
3342:
3338:
3329:
3325:
3321:
3316:
3313:
3310:
3307:
3303:
3299:
3295:
3291:
3287:
3283:
3280:
3277:
3274:
3270:
3266:
3262:
3242:
3226:spherical wave
3220:Dipole antenna
3207:
3204:
3203:
3202:
3189:
3185:
3181:
3177:
3174:
3171:
3157:
3156:
3143:
3139:
3135:
3131:
3128:
3125:
3101:
3100:
3088:
3084:
3080:
3076:
3072:
3050:
3049:
3037:
3033:
3029:
3025:
3021:
2993:magnetic field
2982:electric field
2977:
2974:
2963:
2962:
2951:
2943:
2939:
2935:
2930:
2924:
2920:
2916:
2911:
2907:
2903:
2896:
2892:
2886:
2882:
2876:
2872:
2865:
2859:
2855:
2848:
2844:
2840:
2837:
2823:
2819:
2815:
2812:
2808:
2803:
2800:
2797:
2794:
2791:
2787:
2768:electric field
2740:
2726:
2725:
2710:
2706:
2698:
2694:
2687:
2683:
2670:
2666:
2662:
2659:
2655:
2650:
2647:
2643:
2639:
2636:
2613:
2610:
2606:
2605:
2590:
2586:
2578:
2574:
2567:
2563:
2553:
2550:
2544:
2540:
2534:
2531:
2527:
2523:
2519:
2496:
2493:
2477:
2476:
2472:
2467:
2461:
2431:
2421:
2415:
2405:
2404:
2389:
2385:
2379:
2375:
2369:
2365:
2358:
2352:
2348:
2341:
2337:
2333:
2330:
2318:
2315:
2309:
2305:
2299:
2296:
2292:
2288:
2284:
2280:
2276:
2260:
2257:
2256:
2255:
2237:
2233:
2229:
2224:
2220:
2212:
2208:
2204:
2198:
2195:
2184:
2181:
2175:
2169:
2165:
2161:
2156:
2152:
2147:
2142:
2139:
2134:
2129:
2125:
2118:
2115:
2112:
2109:
2106:
2103:
2100:
2078:
2077:
2065:
2057:
2053:
2049:
2044:
2040:
2035:
2030:
2026:
2023:
2020:
2017:
1989:
1988:
1983:, measured in
1976:
1971:
1954:
1932:
1926:
1913:
1912:
1901:
1895:
1892:
1889:
1886:
1881:
1877:
1873:
1870:
1867:
1858:
1854:
1850:
1842:
1839:
1833:
1829:
1823:
1820:
1817:
1814:
1811:
1808:
1805:
1802:
1799:
1780:
1777:
1769:
1766:
1750:
1749:
1738:
1735:
1731:
1726:
1721:
1694:
1689:
1684:
1681:
1675:
1649:
1643:
1613:
1607:
1601:
1596:
1593:
1587:
1558:
1545:
1544:
1532:
1527:
1522:
1518:
1515:
1511:
1506:
1501:
1495:
1492:
1486:
1477:
1469:
1463:
1458:
1453:
1449:
1445:
1440:
1434:
1431:
1425:
1417:
1411:
1405:
1400:
1394:
1391:
1385:
1377:
1373:
1369:
1364:
1359:
1335:
1331:
1326:
1322:
1319:
1316:
1312:
1307:
1300:
1274:
1270:
1265:
1253:
1252:
1241:
1237:
1232:
1227:
1221:
1215:
1210:
1205:
1201:
1197:
1192:
1187:
1154:
1130:
1117:
1116:
1105:
1100:
1095:
1092:
1087:
1084:
1078:
1069:
1061:
1036:
1035:Atomic dipoles
1033:
1018:
1013:
1000:
999:
988:
985:
980:
975:
970:
965:
960:
955:
949:
945:
938:
933:
930:
927:
923:
919:
914:
898:
897:
886:
880:
875:
867:
863:
856:
851:
848:
845:
841:
837:
832:
802:
795:
779:
771:
761:
758:
707:
700:
699:
692:
685:
684:
683:
682:
681:
668:
664:
660:
637:
627:ionic compound
618:
611:
610:
609:: 10.41 D
604:
598:
592:
586:
580:
574:
568:
567:: 0.112 D
562:
559:carbon dioxide
537:polarizability
513:
512:
497:
494:
479:
476:
471:molecule. See
461:
453:in his honor.
403:
400:
358:for the next (
254:
253:Classification
251:
219:Classification
184:magnetic field
145:
144:
125:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
5290:
5279:
5276:
5274:
5271:
5270:
5268:
5258:
5254:
5250:
5246:
5243:
5240:
5236:
5233:
5230:
5228:
5225:
5224:
5220:
5212:
5207:
5204:
5199:
5193:
5189:
5182:
5179:
5174:
5168:
5165:
5160:
5158:0-8493-0465-2
5154:
5150:
5143:
5140:
5135:
5129:
5125:
5118:
5115:
5110:
5108:0-13-805326-X
5104:
5099:
5098:
5089:
5087:
5083:
5078:
5076:0-19-514665-4
5072:
5068:
5061:
5058:
5053:
5049:
5048:
5040:
5037:
5033:
5029:
5024:
5021:
5017:
5013:
5008:
5005:
4998:
4988:
4985:
4978:
4974:
4971:
4969:
4966:
4964:
4961:
4959:
4956:
4954:
4951:
4949:
4946:
4944:
4941:
4939:
4936:
4934:
4931:
4929:
4926:
4923:
4919:
4916:
4914:
4911:
4909:
4906:
4904:
4901:
4899:
4896:
4895:
4891:
4889:
4886:
4884:
4865:
4859:
4856:
4853:
4846:
4841:
4837:
4831:
4827:
4821:
4817:
4810:
4807:
4800:
4799:
4798:
4795:
4793:
4789:
4785:
4781:
4746:
4742:
4734:
4728:
4723:
4719:
4711:
4705:
4700:
4696:
4692:
4685:
4681:
4675:
4670:
4666:
4660:
4656:
4649:
4645:
4627:
4626:
4625:
4624:
4601:
4592:
4584:
4576:
4573:
4570:
4566:
4562:
4556:
4553:
4549:
4540:
4534:
4531:
4525:
4522:
4515:
4511:
4505:
4501:
4495:
4491:
4484:
4481:
4476:
4468:
4465:
4462:
4458:
4454:
4448:
4445:
4441:
4434:
4418:
4409:
4402:
4395:
4389:
4386:
4380:
4377:
4370:
4366:
4360:
4356:
4350:
4346:
4339:
4336:
4319:
4311:
4308:
4306:
4286:
4278:
4270:
4267:
4264:
4260:
4256:
4250:
4247:
4243:
4234:
4228:
4225:
4219:
4216:
4213:
4206:
4202:
4196:
4192:
4186:
4182:
4175:
4172:
4167:
4159:
4156:
4153:
4149:
4145:
4139:
4136:
4132:
4109:
4086:
4083:
4080:
4073:
4069:
4063:
4059:
4053:
4049:
4042:
4037:
4029:
4026:
4023:
4019:
4015:
4009:
4006:
4002:
3988:
3963:
3959:
3953:
3949:
3945:
3942:
3936:
3932:
3926:
3924:
3906:
3905:
3904:
3898:
3890:
3863:
3858:
3855:
3852:
3849:
3845:
3839:
3834:
3830:
3826:
3823:
3820:
3816:
3809:
3802:
3799:
3796:
3792:
3787:
3784:
3780:
3768:
3743:
3739:
3733:
3729:
3725:
3722:
3716:
3712:
3706:
3704:
3688:
3685:
3682:
3679:
3675:
3668:
3664:
3661:
3658:
3652:
3647:
3642:
3633:
3629:
3620:
3602:
3584:
3580:
3575:
3566:
3562:
3558:
3553:
3550:
3544:
3537:
3533:
3529:
3523:
3519:
3502:
3498:
3489:
3471:
3464:
3459:
3455:
3448:
3444:
3437:
3428:
3424:
3420:
3417:
3413:
3408:
3406:
3388:
3387:
3386:
3384:
3365:
3360:
3357:
3354:
3351:
3347:
3327:
3323:
3319:
3314:
3311:
3308:
3305:
3301:
3281:
3275:
3272:
3252:
3251:
3250:
3248:
3241:
3237:
3234:
3229:
3227:
3221:
3212:
3205:
3183:
3175:
3172:
3169:
3162:
3161:
3160:
3137:
3129:
3126:
3123:
3116:
3115:
3114:
3111:
3109:
3106:
3082:
3074:
3062:
3061:
3060:
3058:
3055:
3031:
3023:
3011:
3010:
3009:
3006:
3002:
2998:
2994:
2990:
2985:
2983:
2975:
2973:
2971:
2970:
2949:
2941:
2937:
2933:
2909:
2905:
2901:
2894:
2890:
2880:
2846:
2835:
2821:
2817:
2813:
2810:
2806:
2801:
2792:
2789:
2777:
2776:
2775:
2773:
2769:
2765:
2761:
2757:
2753:
2748:
2746:
2739:
2735:
2734:dipole moment
2731:
2708:
2704:
2685:
2668:
2664:
2660:
2657:
2653:
2648:
2627:
2626:
2625:
2623:
2619:
2611:
2609:
2588:
2584:
2565:
2551:
2548:
2542:
2538:
2532:
2509:
2508:
2507:
2505:
2502:
2494:
2492:
2490:
2489:approximately
2486:
2482:
2471:
2468:
2465:
2462:
2459:
2451:
2443:
2435:
2432:
2429:
2425:
2422:
2419:
2416:
2413:
2410:
2409:
2408:
2387:
2383:
2373:
2339:
2328:
2316:
2313:
2307:
2303:
2297:
2286:
2266:
2265:
2264:
2258:
2235:
2231:
2227:
2222:
2218:
2210:
2206:
2202:
2196:
2193:
2182:
2179:
2173:
2167:
2163:
2159:
2154:
2150:
2145:
2140:
2137:
2132:
2127:
2123:
2116:
2110:
2107:
2104:
2098:
2091:
2090:
2089:
2088:-axis. Then,
2087:
2083:
2063:
2055:
2051:
2047:
2042:
2038:
2033:
2028:
2024:
2021:
2018:
2015:
2008:
2007:
2006:
2003:
1999:
1995:
1986:
1982:
1975:
1972:
1970:
1966:
1962:
1958:
1955:
1952:
1948:
1944:
1940:
1936:
1933:
1930:
1927:
1925:
1921:
1918:
1917:
1916:
1899:
1890:
1884:
1879:
1875:
1871:
1868:
1865:
1856:
1852:
1848:
1840:
1837:
1831:
1827:
1821:
1815:
1812:
1809:
1806:
1803:
1797:
1790:
1789:
1788:
1786:
1778:
1775:
1767:
1765:
1763:
1759:
1755:
1736:
1733:
1729:
1719:
1711:
1710:
1709:
1687:
1682:
1679:
1647:
1630:
1629:by definition
1611:
1599:
1594:
1591:
1574:
1530:
1520:
1516:
1513:
1509:
1504:
1493:
1490:
1456:
1451:
1447:
1443:
1438:
1432:
1429:
1398:
1392:
1389:
1375:
1371:
1367:
1357:
1349:
1348:
1347:
1329:
1320:
1317:
1310:
1288:
1268:
1239:
1235:
1230:
1208:
1203:
1199:
1195:
1185:
1177:
1176:
1175:
1173:
1168:
1103:
1093:
1090:
1085:
1082:
1050:
1049:
1048:
1046:
1042:
1034:
1032:
1016:
986:
978:
968:
963:
947:
943:
936:
931:
928:
925:
921:
917:
903:
902:
901:
884:
878:
865:
861:
854:
849:
846:
843:
839:
835:
821:
820:
819:
817:
813:
809:
808:atomic number
805:
798:
791:
787:
782:
778:
774:
767:
759:
757:
755:
754:ionic bonding
751:
747:
742:
740:
736:
732:
728:
726:
722:
710:
704:
695:
689:
676:
672:
657:
655:
651:
647:
634:
630:
628:
615:
608:
605:
603:: 4.27 D
602:
599:
597:: 2.98 D
596:
593:
591:: 1.85 D
590:
587:
585:: 1.42 D
584:
581:
579:: 1.17 D
578:
575:
573:: 0.53 D
572:
569:
566:
563:
560:
557:
556:
555:
553:
549:
544:
542:
538:
534:
530:
526:
522:
518:
510:
506:
502:
498:
495:
492:
488:
484:
480:
477:
474:
470:
466:
462:
459:
458:
457:
454:
452:
451:
446:
442:
437:
435:
431:
427:
423:
419:
413:
409:
401:
399:
393:
375:
361:
353:
335:
321:
315:
312:
308:
304:
300:
295:
293:
289:
284:
275:
267:
259:
252:
250:
248:
244:
239:
237:
233:
229:
225:
220:
216:
208:
203:
199:
197:
193:
189:
185:
181:
177:
172:
170:
166:
161:
159:
155:
150:
142:
138:
134:
130:
126:
123:
118:
114:
110:
109:
108:
106:
102:
99:
92:
88:
85:
82:
75:
71:
68:
67:Ancient Greek
64:
60:
52:
48:
44:
39:
33:
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5206:
5187:
5181:
5167:
5148:
5142:
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5060:
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5039:
5034:, on Perseus
5031:
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5018:, on Perseus
5015:
5007:
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4887:
4880:
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4783:
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2979:
2967:
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2759:
2755:
2749:
2737:
2729:
2727:
2621:
2620:at position
2615:
2607:
2503:
2498:
2488:
2484:
2480:
2478:
2469:
2463:
2457:
2449:
2441:
2433:
2427:
2423:
2417:
2414:is the field
2411:
2406:
2262:
2085:
2081:
2079:
2001:
1997:
1993:
1990:
1973:
1956:
1942:
1938:
1934:
1928:
1919:
1914:
1784:
1782:
1754:Stark effect
1751:
1546:
1286:
1254:
1169:
1118:
1040:
1038:
1001:
899:
815:
811:
800:
793:
789:
780:
776:
769:
765:
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738:
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724:
720:
717:
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643:
624:
545:
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528:
524:
520:
516:
514:
504:
500:
468:
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448:
438:
424:(HF), where
415:
391:
373:
351:
333:
319:
316:
311:point dipole
310:
296:
287:
282:
280:
240:
235:
212:
191:
173:
162:
157:
153:
146:
97:
94:
87:
80:
77:
70:
62:
56:
50:
46:
3228:radiation.
2259:Vector form
589:water vapor
447:unit named
5267:Categories
4999:References
3245:along the
3218:See also:
1987:per metre.
1772:See also:
646:vector sum
406:See also:
360:quadrupole
228:north pole
137:bar magnet
65:(from
4857:π
4828:ω
4818:μ
4760:^
4735:θ
4729:
4697:π
4682:ω
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4643:⟩
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4596:^
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3503:×
3490:×
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3176:−
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3032:×
3020:τ
2938:ϵ
2906:δ
2902:−
2881:−
2875:^
2858:^
2847:⋅
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2799:Φ
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2232:ρ
2164:ρ
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2105:ρ
2052:ρ
2025:
2016:λ
1891:λ
1885:
1841:π
1828:μ
1816:λ
1779:Magnitude
1683:∗
1680:∗
1648:∗
1612:∗
1592:−
1517:−
1491:−
1430:−
1390:−
1334:⟩
1321:±
1315:⟩
1273:⟩
1094:−
1083:−
1045:inversion
969:−
922:∑
840:∑
733:. In the
601:cyanamide
533:capacitor
505:polarized
483:electrons
418:molecules
307:electrons
215:monopoles
188:intrinsic
5235:Archived
4938:Monopole
4913:Electret
4892:See also
4788:toroidal
2989:electric
2772:gradient
2479:This is
1941:) where
1730:⟩
1720:⟨
1531:⟩
1521:⟨
1510:⟩
1452:⟨
1444:⟩
1376:⟨
1368:⟩
1358:⟨
1236:⟩
1204:⟨
1196:⟩
1186:⟨
799:, where
577:phosgene
501:inducing
487:molecule
192:electric
176:electron
154:converge
122:electret
5054:. 1989.
3901:
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3052:for an
2766:). The
2743:is the
2485:exactly
2481:exactly
2454:
2438:
1985:henries
1979:is the
1951:degrees
1947:radians
1573:unitary
810:of the
806:is the
727:isomers
583:ammonia
396:
382:
378:
364:
356:
342:
338:
324:
232:compass
158:diverge
59:physics
18:Dipolar
5194:
5155:
5130:
5105:
5073:
3103:for a
3005:τ
3001:torque
2997:forces
2830:
2736:, and
2728:where
2407:where
2323:
2080:where
2022:arcsin
1965:joules
1961:ampere
1924:teslas
1915:where
1758:parity
1285:is an
1255:where
1119:where
1002:where
786:charge
320:always
217:, see
63:dipole
45:has a
5028:πόλος
4979:Notes
1969:tesla
739:trans
725:trans
709:Trans
571:ozone
554:are:
552:debye
469:polar
450:debye
416:Many
236:south
224:south
98:pólos
91:πόλος
69:
51:north
47:south
43:Earth
5251:and
5192:ISBN
5153:ISBN
5128:ISBN
5103:ISBN
5071:ISBN
4920:and
3883:For
2616:The
2499:The
2005:and
1967:per
1627:and
723:and
410:and
303:spin
243:spin
61:, a
5247:by
5012:δίς
4720:sin
4532:sin
4387:sin
4226:sin
3008:}:
2991:or
1949:or
1876:sin
735:cis
729:of
721:cis
694:Cis
648:of
561:: 0
539:of
517:any
198:).
111:An
81:dís
74:δίς
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5269::
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1996:=
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1575::
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1939:θ
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1600:=
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1500:|
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1200:=
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1017:c
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987:,
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979:c
974:r
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