2645:
5610:
8503:, so the magnetic moment of the electron is antiparallel to the spin. This can be understood with the following classical picture: if we imagine that the spin angular momentum is created by the electron mass spinning around some axis, the electric current that this rotation creates circulates in the opposite direction, because of the negative charge of the electron; such current loops produce a magnetic moment which is antiparallel to the spin. Hence, for a positron (the anti-particle of the electron) the magnetic moment is parallel to its spin.
47:
6504:
5333:
2340:
3507:
2192:
2419:
858:
6516:) is in the opposite direction to the magnetic moment (which points from the negative charge to the positive charge), while inside a current loop it is in the same direction (see the figure to the right). The limits of these fields must also be different as the sources shrink to zero size. This distinction only matters if the dipole limit is used to calculate fields inside a magnetic material.
5605:{\displaystyle {\begin{aligned}\mathbf {A} \left(\mathbf {r} ,t\right)&={\frac {\mu _{0}}{4\pi }}\int {\frac {\mathbf {j} \left(\mathbf {r} '\right)}{\left|\mathbf {r} -\mathbf {r} '\right|}}\,\mathrm {d} V',\\\psi \left(\mathbf {r} ,t\right)&={\frac {1}{4\pi }}\int {\frac {\rho \left(\mathbf {r} '\right)}{\left|\mathbf {r} -\mathbf {r} '\right|}}\,\mathrm {d} V',\end{aligned}}}
3086:
1310:
6294:
8287:
6494:
3708:
3257:
2953:
1134:
6119:
4165:
8164:
8529:. The quantum mechanical properties of the nucleons include the spin among others. Since the electromagnetic moments of the nucleus depend on the spin of the individual nucleons, one can look at these properties with measurements of nuclear moments, and more specifically the nuclear magnetic dipole moment.
3965:
1314:
Generically, the intrinsic energy includes the self-field energy of the system plus the energy of the internal workings of the system. For example, for a hydrogen atom in a 2p state in an external field, the self-field energy is negligible, so the internal energy is essentially the eigenenergy of the
8548:
of a nucleus of a given isotope is characterized by a well-defined magnetic dipole moment, the magnitude of which is a fixed number, often measured experimentally to a great precision. This number is very sensitive to the individual contributions from nucleons, and a measurement or prediction of its
2174:
The preferred classical explanation of a magnetic moment has changed over time. Before the 1930s, textbooks explained the moment using hypothetical magnetic point charges. Since then, most have defined it in terms of Ampèrian currents. In magnetic materials, the cause of the magnetic moment are the
972:
the object experiences in a given magnetic field. When the same magnetic field is applied, objects with larger magnetic moments experience larger torques. The strength (and direction) of this torque depends not only on the magnitude of the magnetic moment but also on its orientation relative to the
6993:
Viewing a magnetic dipole as current loop brings out the close connection between magnetic moment and angular momentum. Since the particles creating the current (by rotating around the loop) have charge and mass, both the magnetic moment and the angular momentum increase with the rate of rotation.
5108:
have been experimentally detected.) A magnetic dipole is the limit of either a current loop or a pair of poles as the dimensions of the source are reduced to zero while keeping the moment constant. As long as these limits only apply to fields far from the sources, they are equivalent. However, the
1762:
The magnetic moment is a quantity that describes the magnetic strength of an entire object. Sometimes, though, it is useful or necessary to know how much of the net magnetic moment of the object is produced by a particular portion of that magnet. Therefore, it is useful to define the magnetization
6326:
2215:
always come in pairs, their forces partially cancel each other because while one pole pulls, the other repels. This cancellation is greatest when the poles are close to each other i.e. when the bar magnet is short. The magnetic force produced by a bar magnet, at a given point in space, therefore
976:
The magnetic moment also expresses the magnetic force effect of a magnet. The magnetic field of a magnetic dipole is proportional to its magnetic dipole moment. The dipole component of an object's magnetic field is symmetric about the direction of its magnetic dipole moment, and decreases as the
1114:
This definition is based on how one could, in principle, measure the magnetic moment of an unknown sample. For a current loop, this definition leads to the magnitude of the magnetic dipole moment equaling the product of the current times the area of the loop. Further, this definition allows the
8152:
Due to the angular momentum, the dynamics of a magnetic dipole in a magnetic field differs from that of an electric dipole in an electric field. The field does exert a torque on the magnetic dipole tending to align it with the field. However, torque is proportional to rate of change of angular
8549:
value can reveal important information about the content of the nuclear wave function. There are several theoretical models that predict the value of the magnetic dipole moment and a number of experimental techniques aiming to carry out measurements in nuclei along the nuclear chart.
3556:
1551:
5796:
8316:
is the effective magnetic field (the external field plus any self-induced field). The first term describes precession of the moment about the effective field, while the second is a damping term related to dissipation of energy caused by interaction with the surroundings.
2365:
and repel each other similar to magnets, it was natural to hypothesize that all magnetic fields are due to electric current loops. In this model developed by Ampère, the elementary magnetic dipole that makes up all magnets is a sufficiently small amperian loop of current
5101:(represented by four poles that together form two equal and opposite dipoles). The magnitude of the magnetic field for each term decreases progressively faster with distance than the previous term, so that at large enough distances the first non-zero term will dominate.
4647:
3154:
2808:
This is valid for the moment due to any localized current distribution provided that the magnetic field is uniform. For non-uniform B the equation is also valid for the torque about the center of the magnetic dipole provided that the magnetic dipole is small enough.
2725:
must be used. Fortunately, the linear relationship between the magnetic dipole moment of a particle and its angular momentum still holds, although it is different for each particle. Further, care must be used to distinguish between the intrinsic angular momentum (or
1630:
1417:
2547:
7332:
4030:
6511:
The two models for a dipole (magnetic poles or current loop) give the same predictions for the magnetic field far from the source. However, inside the source region, they give different predictions. The magnetic field between poles (see the figure for
3837:
2946:
7663:
Contributions due to the sources of the first kind can be calculated from knowing the distribution of all the electric currents (or, alternatively, of all the electric charges and their velocities) inside the system, by using the formulas below.
6005:
3081:{\displaystyle {\begin{aligned}\mathbf {F} _{\text{loop}}&=\left(\mathbf {m} \times \nabla \right)\times \mathbf {B} \\&=\nabla \left(\mathbf {m} \cdot \mathbf {B} \right)-\left(\nabla \cdot \mathbf {B} \right)\mathbf {m} \end{aligned}}}
5888:
1305:{\displaystyle \mathbf {m} =-{\hat {\mathbf {x} }}{\frac {\partial U_{\text{int}}}{\partial B_{x}}}-{\hat {\mathbf {y} }}{\frac {\partial U_{\text{int}}}{\partial B_{y}}}-{\hat {\mathbf {z} }}{\frac {\partial U_{\text{int}}}{\partial B_{z}}}.}
8427:
7143:
5329:
Both of these potentials can be calculated for any arbitrary current distribution (for the amperian loop model) or magnetic charge distribution (for the magnetic charge model) provided that these are limited to a small enough region to give:
7228:
7848:
3149:
3379:
4264:
7956:
6289:{\displaystyle \mathbf {B} (\mathbf {r} )=\nabla \times {\mathbf {A} }={\frac {\mu _{0}}{4\pi }}\left({\frac {3\mathbf {r} (\mathbf {m} \cdot \mathbf {r} )}{|\mathbf {r} |^{5}}}-{\frac {\mathbf {m} }{|\mathbf {r} |^{3}}}\right).}
8282:{\displaystyle {\frac {1}{\gamma }}{\frac {\mathrm {d} \mathbf {m} }{\mathrm {d} t}}=\mathbf {m} \times \mathbf {H} _{\text{eff}}-{\frac {\lambda }{\gamma m}}\mathbf {m} \times {\frac {\mathrm {d} \mathbf {m} }{\mathrm {d} t}}}
4995:
1915:
5067:
8148:
1827:
2120:
1459:
6887:
5697:
5088:
The magnetic field of any magnet can be modeled by a series of terms for which each term is more complicated (having finer angular detail) than the one before it. The first three terms of that series are called the
5325:
4287:
2804:
3456:
1089:
6489:{\displaystyle {\mathbf {H} }({\mathbf {r} })=-\nabla \psi ={\frac {1}{4\pi }}\left({\frac {3\mathbf {r} (\mathbf {m} \cdot \mathbf {r} )}{|\mathbf {r} |^{5}}}-{\frac {\mathbf {m} }{|\mathbf {r} |^{3}}}\right).}
6698:
6519:
If a magnetic dipole is formed by taking a "north pole" and a "south pole", bringing them closer and closer together but keeping the product of magnetic pole charge and distance constant, the limiting field is
2457:
The magnetic dipole moment can be calculated for a localized (does not extend to infinity) current distribution assuming that we know all of the currents involved. Conventionally, the derivation starts from a
7553:
5693:
to give a series of terms that have larger of power of distances in the denominator. The first nonzero term, therefore, will dominate for large distances. The first non-zero term for the vector potential is:
2288:
1555:
7456:
6078:
2712:
When calculating the magnetic moments of materials or molecules on the microscopic level it is often convenient to use a third model for the magnetic moment that exploits the linear relationship between the
1984:
1344:
7501:
Even though atomic particles cannot be accurately described as orbiting (and spinning) charge distributions of uniform charge-to-mass ratio, this general trend can be observed in the atomic world so that:
3832:
1315:
2p state, which includes
Coulomb potential energy and the kinetic energy of the electron. The interaction-field energy between the internal dipoles and external fields is not part of this internal energy.
5247:
5338:
2958:
8758:, associated with the intrinsic spin of the particle and/or with the orbital motion of the particle in a system. Values of the intrinsic magnetic moments of some particles are given in the table below:
2469:
7248:
3760:
is a vector from the center of the magnetic dipole to the location where the magnetic field is measured. The inverse cube nature of this equation is more readily seen by expressing the location vector
2410:
is the area of the loop. The direction of the magnetic moment is in a direction normal to the area enclosed by the current consistent with the direction of the current using the right hand rule.
7053:
7372:
3703:{\displaystyle \mathbf {H} (\mathbf {r} )={\frac {1}{4\pi }}\left({\frac {3\mathbf {r} (\mathbf {m} \cdot \mathbf {r} )}{|\mathbf {r} |^{5}}}-{\frac {\mathbf {m} }{|\mathbf {r} |^{3}}}\right),}
2875:
7735:
For an atom, individual electron spins are added to get a total spin, and individual orbital angular momenta are added to get a total orbital angular momentum. These two then are added using
2404:
2244:
7768:
5924:
7671:
of each elementary particle's intrinsic magnetic moment, a fixed number, often measured experimentally to a great precision. For example, any electron's magnetic moment is measured to be
5823:
2703:
2615:
2030:
8360:
7087:
7162:
7773:
3252:{\displaystyle \mathbf {F} _{\text{loop}}=\mathbf {F} _{\text{dipole}}+\mathbf {m} \times \left(\nabla \times \mathbf {B} \right)-\left(\nabla \cdot \mathbf {B} \right)\mathbf {m} .}
3093:
2890:
2442:
3319:
5687:
7992:
4201:
7887:
3528:
components, those will drop off with distance more rapidly, so that only the dipole component will dominate the magnetic field of the system at distances far away from it.
7075:
6321:
6102:
6029:
5818:
5632:
5271:
5191:
5169:
5147:
4160:{\displaystyle \mathbf {B} (\mathbf {r} )={\frac {\mu _{0}}{4\pi }}{\frac {3\mathbf {\hat {r}} (\mathbf {\hat {r}} \cdot \mathbf {m} )-\mathbf {m} }{|\mathbf {r} |^{3}}}.}
3989:
3780:
3758:
3732:
3551:
7399:
7016:
4664:
1866:
5656:
5017:
3960:{\displaystyle \mathbf {H} (\mathbf {r} )={\frac {1}{4\pi }}{\frac {3\mathbf {\hat {r}} (\mathbf {\hat {r}} \cdot \mathbf {m} )-\mathbf {m} }{|\mathbf {r} |^{3}}}.}
8013:
7496:
1772:
8338:
and many elementary particles also have intrinsic magnetic moments, an explanation of which requires a quantum mechanical treatment and relates to the intrinsic
3510:
Magnetic field lines around a "magnetostatic dipole". The magnetic dipole itself is located in the center of the figure, seen from the side, and pointing upward.
2065:
7476:
6705:
2292:
It points in the direction from South to North pole. The analogy with electric dipoles should not be taken too far because magnetic dipoles are associated with
604:
7578:-factor of atoms and molecules must account for the orbital and intrinsic moments of its electrons and possibly the intrinsic moment of its nuclei as well.
5280:
2768:
3396:
2573:
and the integral is a volume integral. When the current density in the integral is replaced by a loop of current I in a plane enclosing an area S then the
1453:
1056:
6702:
If a magnetic dipole is formed by making a current loop smaller and smaller, but keeping the product of current and area constant, the limiting field is
6523:
1445:
577:
1742:
instead. If the magnetic field surrounding an object is known well enough, though, then the magnetic moment can be calculated from that magnetic field.
7505:
3465:
In addition, an applied magnetic field can change the magnetic moment of the object itself; for example by magnetizing it. This phenomenon is known as
2255:
7411:
6038:
1944:
3524:
magnetic field (described below) in the space surrounding the system. While the net magnetic field produced by the system can also have higher-order
2717:
and the magnetic moment of a particle. While this relation is straightforward to develop for macroscopic currents using the amperian loop model (see
589:
2721:), neither the magnetic pole model nor the amperian loop model truly represents what is occurring at the atomic and molecular levels. At that level
5200:
1122:
calculations of the magnetic moment. In this definition, the magnetic dipole moment of a system is the negative gradient of its intrinsic energy,
9920:
8561:. Typically, the overall magnetic moment of a molecule is a combination of the following contributions, in the order of their typical strength:
9217:
Mohr, Peter J.; Newell, David B.; Taylor, Barry N. (21 Jul 2015). "CODATA Recommended Values of the
Fundamental Physical Constants: 2014".
7021:
9195:
8662:
Many transition metal complexes are magnetic. The spin-only formula is a good first approximation for high-spin complexes of first-row
2841:
840:
609:
2883:, acting on the magnetic moment itself. There are two expressions for the force acting on a magnetic dipole, depending on whether the
2373:
3304:
5117:
Traditionally, the equations for the magnetic dipole moment (and higher order terms) are derived from theoretical quantities called
3785:
3477:. Additionally, the magnetic field can affect the currents that create the magnetic fields (such as the atomic orbits) which causes
1546:{\displaystyle 1{\text{ statA}}{\cdot }{\text{cm}}^{2}=3.33564095\times 10^{-14}{\text{ A}}{\cdot }{\text{m}}^{2}~~{\text{ (ESU)}}}
8158:
619:
5791:{\displaystyle \mathbf {A} (\mathbf {r} )={\frac {\mu _{0}}{4\pi }}{\frac {\mathbf {m} \times \mathbf {r} }{|\mathbf {r} |^{3}}},}
2669:
973:
direction of the magnetic field. Its direction points from the south pole to north pole of the magnet (i.e., inside the magnet).
2887:
is a current loop or two monopoles (analogous to the electric dipole). The force obtained in the case of a current loop model is
2584:
1999:
3273:
is the magnetic field at its position. Note that if there are no currents or time-varying electrical fields or magnetic charge,
9094:
4642:{\displaystyle \mathbf {F} (\mathbf {r} ,\mathbf {m} _{1},\mathbf {m} _{2})={\frac {3\mu _{0}}{4\pi |\mathbf {r} |^{4}}}\left,}
4175:
1441:
444:
17:
9811:
9784:
9729:
9698:
9649:
9611:
9580:
9503:
9472:
9411:
9368:
9286:
9170:
9132:
9064:
7855:
459:
454:
81:
5662:
that leads to the electric potential, and the integrals are the volume (triple) integrals over the coordinates that make up
9721:
1669:
units; they may need to be changed for use in other unit systems. For example, in SI units, a loop of current with current
980:
Examples of objects or systems that produce magnetic moments include: permanent magnets; astronomical objects such as many
469:
7723:
is the sum of the contributing magnetic moments, which include the intrinsic and orbital magnetic moments of the unpaired
2212:
1625:{\displaystyle 1\;{\frac {\text{erg}}{\text{G}}}=10^{-3}{\text{ A}}{\cdot }{\text{m}}^{2}~~{\text{ (Gaussian and EMU),}}}
7739:
to get a total angular momentum. For an atom with no nuclear magnetic moment, the magnitude of the atomic dipole moment,
1412:{\displaystyle \mathrm {A\cdot m^{2}} ={\frac {\mathrm {N\cdot m} }{\mathrm {T} }}={\frac {\mathrm {J} }{\mathrm {T} }},}
8592:
7705:(the lightest hydrogen isotope, consisting of a proton and an electron) is a vector sum of the following contributions:
7337:
7245:
This is similar to the magnetic moment created by the very large number of charged particles that make up that current:
1437:). Although torque (N¡m) and energy (J) are dimensionally equivalent, torques are never expressed in units of energy.
2879:
In a case when the external magnetic field is non-uniform, there will be a force, proportional to the magnetic field
71:
2542:{\displaystyle \mathbf {m} ={\tfrac {1}{2}}\iiint _{V}\mathbf {r} \times \mathbf {j} (\mathbf {r} )\,\mathrm {d} V,}
2343:
The
Amperian loop model: A current loop (ring) that goes into the page at the x and comes out at the dot produces a
2227:
339:
9572:
9338:
8487:
8326:
7742:
7327:{\displaystyle \mathbf {m} ={\tfrac {1}{2}}\iiint _{V}\mathbf {r} \times (\rho _{Q}\mathbf {v} )\,\mathrm {d} V\,,}
3393:
is the temperature. Therefore, the magnetic moment can also be defined in terms of the free energy of a system as
9639:
8351:
6031:
may be represented in terms of the magnetic pole strength density but is more usefully expressed in terms of the
254:
9397:
833:
599:
76:
7640:
Fundamentally, contributions to any system's magnetic moment may come from sources of two kinds: 1) motion of
7080:
In the amperian loop model, which applies for macroscopic currents, the gyromagnetic ratio is one half of the
3297:
One can relate the magnetic moment of a system to the free energy of that system. In a uniform magnetic field
1324:
614:
319:
6889:
Unlike the expressions in the previous section, this limit is correct for the internal field of the dipole.
3531:
The magnetic field of a magnetic dipole depends on the strength and direction of a magnet's magnetic moment
2812:
An electron, nucleus, or atom placed in a uniform magnetic field will precess with a frequency known as the
9925:
479:
219:
86:
9846:
7159:. The angular momentum of the very large number of charged particles that make up a current therefore is:
2425:
209:
9429:
6967:
1009:
772:
647:
544:
519:
439:
9755:
9603:
6987:
929:
272:
6000:{\displaystyle \psi (\mathbf {r} )={\frac {\mathbf {m} \cdot \mathbf {r} }{4\pi |\mathbf {r} |^{3}}}.}
2203:. This is sometimes known as the Gilbert model. In this model, a small magnet is modeled by a pair of
9930:
9330:
9273:
7973:
7736:
5918:
5883:{\displaystyle \mathbf {m} ={\frac {1}{2}}\iiint _{V}\mathbf {r} \times \mathbf {j} \,\mathrm {d} V,}
5274:
5194:
5118:
2463:
985:
826:
787:
314:
304:
244:
239:
179:
2644:
9935:
9893:
9162:
8422:{\displaystyle \mathbf {m} _{\text{S}}=-{\frac {g_{\text{S}}\mu _{\text{B}}\mathbf {S} }{\hbar }},}
8343:
8330:
7701:
of contributions from one or both types of sources. For example, the magnetic moment of an atom of
7625:
7138:{\displaystyle \mathbf {L} =\mathbf {r} \times \mathbf {p} =\mu \,\mathbf {r} \times \mathbf {v} ,}
5911:
5665:
2570:
2195:
An electrostatic analog for a magnetic moment: two opposing charges separated by a finite distance.
1996:
is the same for the entire magnet (such as a straight bar magnet) the last equation simplifies to:
324:
7223:{\displaystyle \mathbf {L} =\iiint _{V}\,\mathbf {r} \times (\rho \mathbf {v} )\,\mathrm {d} V\,,}
7058:
6304:
6085:
6012:
5801:
5615:
5254:
5174:
5152:
5130:
3972:
3763:
3741:
3715:
3534:
2362:
2354:
757:
259:
9910:
9084:
8557:
Any molecule has a well-defined magnitude of magnetic moment, which may depend on the molecule's
8516:
8512:
8470:
7995:
7843:{\displaystyle {\mathfrak {m}}_{\text{atom}}=g_{\text{J}}\,\mu _{\text{B}}\,{\sqrt {j\,(j+1)\,}}}
7686:
of the magnetic moment of any elementary particle is entirely determined by the direction of its
7084:. This can be shown as follows. The angular momentum of a moving charged particle is defined as:
6299:
3469:. An applied magnetic field can flip the magnetic dipoles that make up the material causing both
2358:
637:
164:
154:
149:
8577:
7649:
3144:{\displaystyle \mathbf {F} _{\text{dipole}}=\left(\mathbf {m} \cdot \nabla \right)\mathbf {B} .}
762:
732:
9803:
Micromagnetism and
Electrical Resistance of Ferromagnetic Electrodes for Spin Injection Devices
9074:
7377:
1444:
system, there are several different sets of electromagnetism units, of which the main ones are
584:
354:
129:
9828:
9770:
9749:
9715:
9684:
9597:
9566:
9118:
5104:
For many magnets the first non-zero term is the magnetic dipole moment. (To date, no isolated
2941:{\displaystyle \mathbf {F} _{\text{loop}}=\nabla \left(\mathbf {m} \cdot \mathbf {B} \right).}
9745:
9489:
9089:
7001:
6113:
2829:
2044:
682:
369:
359:
309:
299:
9801:
9150:
7077:
is the angular momentum of the particle or particles that are creating the magnetic moment.
3374:{\displaystyle \mathrm {d} F=-S\,\mathrm {d} T-\mathbf {M} \,\cdot \mathrm {d} \mathbf {B} }
1115:
calculation of the expected magnetic moment for any known macroscopic current distribution.
9776:
9437:
9236:
9158:
7617:
7605:
7081:
5895:
5641:
5098:
2554:
1456:. Among these, there are two alternative (non-equivalent) units of magnetic dipole moment:
1339:(SI base unit of distance). This unit has equivalents in other SI derived units including:
807:
707:
672:
424:
289:
189:
174:
109:
7884:. The component of this magnetic moment along the direction of the magnetic field is then
7481:
7238:
of the moving particles. By convention the direction of the cross product is given by the
46:
8:
9690:
9151:
8636:
that is proportional to the external magnetic field. The nuclear magnetism of a magnetic
7653:
5690:
5125:
5090:
5077:
4024:
3090:
In the case of a pair of monopoles being used (i.e. electric dipole model), the force is
2620:
Practitioners using the current loop model generally represent the magnetic field by the
2459:
2183:, and varies depending on whether atoms in one region are aligned with atoms in another.
2039:
The magnetization is often not listed as a material parameter for commercially available
1001:
767:
747:
742:
549:
534:
419:
389:
284:
214:
9877:
9441:
9240:
6104:
is used for both equations since they produce equivalent results outside of the magnet.
4259:{\displaystyle \mathbf {F} =\nabla \left(\mathbf {m} _{2}\cdot \mathbf {B} _{1}\right),}
1853:
are the magnetic dipole moment and volume of a sufficiently small portion of the magnet
9915:
9631:
9523:
9401:
9252:
9226:
9004:
8453:
8294:
7566:-factor for the magnetic moment due to an electron orbiting a nucleus is one while the
7556:
7461:
6995:
6949:
2656:. Its moment is the vector sum of the moments of individual turns. If the solenoid has
2199:
The sources of magnetic moments in materials can be represented by poles in analogy to
1738:, though not all magnetometers measure magnetic moment: Some are configured to measure
642:
382:
184:
144:
8346:. It is these intrinsic magnetic moments that give rise to the macroscopic effects of
7951:{\displaystyle {\mathfrak {m}}_{{\text{atom}},z}=-m\,g_{\text{J}}\,\mu _{\text{B}}\,.}
464:
9807:
9780:
9725:
9694:
9645:
9607:
9576:
9499:
9491:
Permanent Magnet and
Electromechanical Devices: Materials, Analysis, and Applications
9468:
9407:
9374:
9364:
9282:
9166:
9128:
8633:
6963:
5105:
2722:
2208:
989:
702:
7866:
9538:
9445:
9256:
9244:
9124:
9069:
8755:
8751:
8663:
8339:
7698:
7683:
7668:
7645:
7613:
7570:-factor for the magnetic moment of electron due to its intrinsic angular momentum (
6955:
2813:
2714:
2293:
1717:
1021:
946:
802:
717:
677:
667:
554:
509:
492:
409:
344:
114:
38:
9665:
5251:
In the amperian loop model, the relevant magnetic field is the magnetic induction
2834:
A magnetic moment in an externally produced magnetic field has a potential energy
9627:
9248:
9079:
8651:, in a weak (or zero) magnetic field exhibits nuclear magnetism, and can be in a
7641:
7594:
7239:
5635:
5094:
5083:
3495:
2884:
2574:
737:
662:
657:
524:
399:
364:
124:
777:
9851:
CODATA internationally recommended values of the
Fundamental Physical Constants
9495:
9040:
8789:
8621:
8500:
8466:
8449:
7687:
7582:
7571:
7402:
6979:
6971:
6107:
5659:
4990:{\displaystyle \mathbf {F} ={\frac {3\mu _{0}}{4\pi |\mathbf {r} |^{4}}}\left.}
3735:
3474:
2727:
2323:
2309:
2301:
2211:. Each pole is the source of magnetic force which weakens with distance. Since
2200:
1987:
1932:
1910:{\displaystyle \mathbf {M} ={\frac {\mathrm {d} \mathbf {m} }{\mathrm {d} V}},}
1739:
1699:
1682:
1651:
1449:
1119:
1050:
965:
697:
692:
514:
404:
329:
279:
229:
202:
159:
134:
104:
97:
8521:
The nuclear system is a complex physical system consisting of nucleons, i.e.,
5062:{\displaystyle {\boldsymbol {\tau }}=\mathbf {m} _{2}\times \mathbf {B} _{1}.}
9904:
9635:
9465:
Electrodynamics of
Continuous Media: Volume 8 (Course of Theoretical Physics)
9360:
8796:
8686:
8656:
8614:
8566:
8541:
8439:
8430:
8143:{\displaystyle -j,\ -(j-1),\ \cdots ,\ -1,\ 0,\ +1,\ \cdots ,\ +(j-1),\ +j~.}
7881:
7702:
7629:
7601:
6937:
6032:
3470:
2578:
2040:
1822:{\displaystyle \mathbf {M} ={\frac {\mathbf {m} _{\Delta V}}{V_{\Delta V}}},}
1751:
1713:
1422:
1025:
812:
797:
782:
722:
434:
349:
334:
249:
234:
139:
27:
Magnetic strength and orientation of an object that produces a magnetic field
9378:
7694:
indicating that any electron's magnetic moment is antiparallel to its spin.
1650:. The ratio of these two non-equivalent CGS units (EMU/ESU) is equal to the
9301:
8783:
8779:
8652:
8629:
8588:
8570:
8558:
8545:
8533:
7590:
7235:
4008:
3478:
2950:
Assuming existence of magnetic monopole, the force is modified as follows:
2313:
2305:
2137:
2115:{\displaystyle \mathbf {m} ={\frac {1}{\mu _{0}}}\mathbf {B} _{\text{r}}V,}
1990:. For uniform magnetization (where both the magnitude and the direction of
1735:
1734:
The magnetic moments of objects are typically measured with devices called
1729:
1647:
1426:
1328:
1042:
911:
792:
687:
652:
594:
529:
449:
414:
294:
169:
6882:{\displaystyle \mathbf {B} (\mathbf {r} )={\frac {\mu _{0}}{4\pi }}\left.}
5109:
two models give different predictions for the internal field (see below).
9889:
9543:
8581:
8157:
occurs: the direction of spin changes. This behavior is described by the
6986:(rotate about the axis of the applied field). This phenomenon is used in
3506:
2617:
which is how the magnetic dipole moment for an
Amperian loop is derived.
2349:-field (lines). The north pole is to the right and the south to the left.
2308:. Practitioners using the magnetic pole approach generally represent the
712:
564:
394:
56:
9281:(9th ed.), International Bureau of Weights and Measures, Dec 2022,
6503:
5121:
which are simpler to deal with mathematically than the magnetic fields.
3782:
as the product of its magnitude times the unit vector in its direction (
2339:
8644:
8154:
7720:
7691:
6983:
2621:
2191:
1863:
This equation is often represented using derivative notation such that
1655:
1639:
1635:
429:
9463:
Landau, L. D.; Lifshitz, E. M.; Pitaevskii, L. P. (January 15, 1984).
5320:{\displaystyle \mathbf {B} (\mathbf {r} )=\nabla \times \mathbf {A} .}
2799:{\displaystyle {\boldsymbol {\tau }}=\mathbf {m} \times \mathbf {B} .}
968:. The magnetic dipole moment of an object determines the magnitude of
8347:
4180:
As discussed earlier, the force exerted by a dipole loop with moment
3525:
3466:
3451:{\displaystyle m=\left.-{\frac {\partial F}{\partial B}}\right|_{T}.}
2817:
1986:
where the triple integral denotes integration over the volume of the
1757:
1084:{\displaystyle {\boldsymbol {\tau }}=\mathbf {m} \times \mathbf {B} }
752:
727:
539:
61:
9449:
9231:
8946:
8804:
8335:
7724:
7657:
7609:
7156:
6693:{\displaystyle \mathbf {H} (\mathbf {r} )={\frac {1}{4\pi }}\left.}
2880:
2730:) of the particle and the particle's orbital angular momentum. See
2653:
2180:
1005:
997:
504:
499:
119:
2418:
857:
9524:"An Analytic Solution for the Force between Two Magnetic Dipoles"
8968:
8874:
8640:
such as C or O will contribute to the molecule's magnetic moment.
8637:
8537:
8526:
7964:
7960:
The negative sign occurs because electrons have negative charge.
7586:
7548:{\displaystyle \mathbf {m} =g\,{\frac {e}{2\mu }}\,\mathbf {L} ,}
5917:
In the magnetic pole perspective, the first non-zero term of the
5658:
is the magnetic pole strength density in analogy to the electric
3386:
2466:. This leads to the definition of the magnetic dipole moment as:
2283:{\displaystyle \mathbf {m} =p\,\mathrm {\boldsymbol {\ell }} \,.}
1712:
Other units for measuring the magnetic dipole moment include the
1017:
894:
474:
7451:{\displaystyle \mathbf {m} ={\frac {e}{2\mu }}\,\mathbf {L} \,,}
6116:
for a magnetic dipole in the amperian loop model, therefore, is
6073:{\displaystyle \mathbf {m} =\iiint \mathbf {M} \,\mathrm {d} V.}
5097:(represented by two equal and opposite magnetic poles), and the
1979:{\displaystyle \mathbf {m} =\iiint \mathbf {M} \,\mathrm {d} V,}
8838:
8606:
8522:
7621:
6975:
5689:. The denominators of these equation can be expanded using the
5124:
In the magnetic pole model, the relevant magnetic field is the
3521:
3501:
2357:
discovered that electric currents produce a magnetic field and
1659:
1434:
1332:
1046:
1013:
981:
969:
961:
922:
899:
559:
66:
7600:. This is the basis for defining the magnetic moment units of
5093:(represented by an isolated magnetic north or south pole) the
3827:{\displaystyle \mathbf {r} =|\mathbf {r} |\mathbf {\hat {r}} }
7635:
5242:{\displaystyle {\mathbf {H} }({\mathbf {r} })=-\nabla \psi .}
4012:
1430:
1336:
918:
903:
9427:
Boyer, Timothy H. (1988). "The Force on a
Magnetic Dipole".
8754:
of the magnetic moment, often measured in Bohr magnetons or
7562:
depends on the particle and configuration. For example, the
6978:
applied to a relatively isolated magnetic dipole such as an
6108:
External magnetic field produced by a magnetic dipole moment
8910:
7727:
of the magnet's material and the nuclear magnetic moments.
5009:
3408:
2043:
materials, though. Instead the parameter that is listed is
993:
4655:
is the unit vector pointing from magnet 1 to magnet 2 and
3991:-field are the same except for a multiplicative factor of
3151:
And one can be put in terms of the other via the relation
1053:
to the field vector itself. The relationship is given by:
2652:
A generalization of the above current loop is a coil, or
2176:
1643:
9462:
5273:. Since magnetic monopoles do not exist, there exists a
2737:
9644:. Vol. 2. Pearson/Addison-Wesley. pp. 13â12.
8617:, due to unpaired spins of its outermost two electrons.
6970:, or "rotation by magnetization", and its inverse, the
2660:
identical turns (single-layer winding) and vector area
1666:
1041:
The magnetic moment can be defined as a vector (really
9522:
Yung, K. W.; Landecker, P. B.; Villani, D. D. (1998).
9153:
8580:
is often proportional to the external magnetic field (
7261:
6498:
4169:
3489:
2482:
9833:
Modern Coordination Chemistry: Principles and methods
9599:
Introduction to functional magnetic resonance imaging
8363:
8167:
8016:
7976:
7890:
7776:
7745:
7712:
the orbital motion of the electron around the proton,
7508:
7484:
7464:
7414:
7380:
7340:
7251:
7165:
7090:
7061:
7024:
7004:
6708:
6526:
6329:
6307:
6122:
6088:
6041:
6015:
5927:
5826:
5804:
5700:
5668:
5644:
5618:
5336:
5283:
5257:
5203:
5177:
5155:
5133:
5071:
5020:
4667:
4290:
4204:
4033:
3975:
3840:
3788:
3766:
3744:
3718:
3559:
3553:
but drops off as the cube of the distance such that:
3537:
3399:
3322:
3157:
3096:
2956:
2893:
2844:
2771:
2672:
2587:
2472:
2428:
2376:
2258:
2230:
2068:
2002:
1947:
1869:
1775:
1558:
1462:
1429:(SI derived unit of magnetic flux density), and J is
1347:
1137:
1059:
1031:
9626:
9521:
2300:). Nevertheless, magnetic poles are very useful for
960:
is the combination of strength and orientation of a
7048:{\displaystyle \mathbf {m} =\gamma \,\mathbf {L} ,}
3514:Any system possessing a net magnetic dipole moment
2207:magnetic monopoles of equal magnitude but opposite
9467:(2 ed.). Butterworth-Heinemann. p. 130.
9350:
9348:
8599:
8421:
8281:
8142:
7986:
7950:
7842:
7762:
7547:
7490:
7470:
7450:
7393:
7367:{\displaystyle \mathbf {j} =\rho _{Q}\mathbf {v} }
7366:
7326:
7222:
7137:
7069:
7047:
7010:
6881:
6692:
6488:
6315:
6288:
6096:
6072:
6023:
5999:
5882:
5812:
5790:
5681:
5650:
5626:
5604:
5319:
5265:
5241:
5185:
5163:
5141:
5061:
4989:
4641:
4258:
4159:
3983:
3959:
3826:
3774:
3752:
3726:
3702:
3545:
3450:
3373:
3251:
3143:
3080:
2940:
2869:
2798:
2697:
2609:
2541:
2436:
2413:
2398:
2282:
2238:
2114:
2024:
1978:
1909:
1821:
1624:
1545:
1411:
1304:
1083:
8320:
7593:in the case of fermions) multiple of the reduced
6782:
6767:
6593:
6578:
4102:
4087:
3902:
3887:
3818:
2870:{\displaystyle U=-\mathbf {m} \cdot \mathbf {B} }
2718:
2297:
9902:
9853:. National Institute of Standards and Technology
9714:Tipler, Paul Allen; Llewellyn, Ralph A. (2002).
9216:
8746:In atomic and nuclear physics, the Greek symbol
8632:, a much weaker magnetic moment of the electron
8552:
6954:The magnetic moment has a close connection with
2639:
2399:{\displaystyle \mathbf {m} =I{\boldsymbol {S}},}
9754:(8th ed.). London: Edward Arnold. p.
9713:
9345:
8506:
6943:
2731:
2056:. The formula needed in this case to calculate
9392:
9390:
9388:
8576:orbital motion of its electrons, which in the
2304:calculations, particularly in applications to
2239:{\displaystyle \mathrm {\boldsymbol {\ell }} }
977:inverse cube of the distance from the object.
9116:
8342:of the particles as discussed in the article
7763:{\displaystyle {\mathfrak {m}}_{\text{atom}}}
7730:
6974:, or "magnetization by rotation". Further, a
5171:does not include, by definition, the part of
4661:is the distance. An equivalent expression is
2753:on an object having a magnetic dipole moment
1020:âas of the nucleus of an atom); and loops of
834:
4284:. The result of calculating the gradient is
2698:{\displaystyle \mathbf {m} =NI\mathbf {S} .}
2246:separating them. The magnetic dipole moment
1745:
1665:All formulae in this article are correct in
9847:"Search results matching 'magnetic moment'"
9835:. New York: Interscience. pp. 405â407.
9829:"The magnetochemistry of complex compounds"
9826:
9385:
7697:The net magnetic moment of any system is a
7667:Contributions due to particle spin sum the
2707:
2610:{\displaystyle \mathbf {m} =I\mathbf {S} ,}
2136:is the residual flux density, expressed in
2025:{\displaystyle \mathbf {m} =\mathbf {M} V,}
1131:, with respect to external magnetic field:
9335:Magnetostatic Principles in Ferromagnetism
8473:effects it is slightly larger in reality:
7636:Atoms, molecules, and elementary particles
7581:In the atomic world the angular momentum (
3969:The equivalent equations for the magnetic
3292:
1562:
856:
841:
827:
45:
9707:
9542:
9354:
9325:
9323:
9321:
9319:
9317:
9315:
9230:
8499:is a negative constant multiplied by the
8002:quantum number, which can take on any of
7944:
7933:
7922:
7837:
7821:
7815:
7804:
7536:
7520:
7444:
7438:
7320:
7311:
7216:
7207:
7184:
7118:
7036:
6058:
5868:
5581:
5456:
3484:
3357:
3340:
2527:
2276:
2270:
1964:
1049:on the object from an externally applied
9751:Ions, Electrons, and Ionizing Radiations
9744:
9738:
9666:"CODATA Value: electron magnetic moment"
9564:
9268:
9266:
9112:
9110:
7408:Comparing the two equations results in:
6513:
6502:
5010:Torque of one magnetic dipole on another
3505:
2643:
2581:and the resulting dipole moment becomes
2417:
2338:
2190:
2177:spin and orbital angular momentum states
1935:. The net magnetic moment of the magnet
1118:An alternative definition is useful for
964:or other object or system that exerts a
9875:
9799:
9793:
9676:
9620:
9517:
9515:
9487:
9396:
9100:
8741:
8486:. The deviation from 2 is known as the
8357:The magnetic moment of the electron is
5914:and the integral is a volume integral.
5022:
2773:
2630:, analogous to the electrostatic field
2430:
2389:
2272:
2232:
1061:
590:Electromagnetism and special relativity
14:
9921:Electric and magnetic fields in matter
9903:
9831:. In Lewis, J.; Wilkins, R.G. (eds.).
9682:
9595:
9589:
9312:
9148:
9117:Cullity, B. D.; Graham, C. D. (2008).
7648:; and 2) the intrinsic magnetism due
5112:
5014:The torque of magnet 1 on magnet 2 is
3310:can be related to the magnetic moment
2334:
2252:is related to the fictitious poles as
2186:
1924:is the elementary magnetic moment and
9426:
9329:
9263:
9107:
9065:Orders of magnitude (magnetic moment)
8565:magnetic moments due to its unpaired
8493:Again it is important to notice that
7970:(not to be confused with the moment,
7856:total angular momentum quantum number
7709:the intrinsic moment of the electron,
5193:due to free currents, there exists a
5149:. Since the demagnetizing portion of
2742:
2738:Effects of an external magnetic field
2444:of a planar current having magnitude
2216:depends on two factors: the strength
610:Maxwell equations in curved spacetime
9768:
9762:
9558:
9512:
9188:
8762:Intrinsic magnetic moments and spins
8587:the combined magnetic moment of its
7719:Similarly, the magnetic moment of a
6507:The magnetic field of a current loop
4275:is the magnetic field due to moment
2823:
2437:{\displaystyle {\boldsymbol {\mu }}}
2370:. The dipole moment of this loop is
1105:is the external magnetic field, and
1099:is the torque acting on the dipole,
7979:
7894:
7780:
7749:
7715:the intrinsic moment of the proton.
6994:The ratio of the two is called the
6499:Internal magnetic field of a dipole
4170:Forces between two magnetic dipoles
3490:Magnetic field of a magnetic moment
2146:is the volume of the magnet (in m).
1335:(SI base unit of current) and m is
24:
9531:Magnetic and Electrical Separation
9120:Introduction to Magnetic Materials
9095:Magnetic dipoleâdipole interaction
8532:Most common nuclei exist in their
8269:
8257:
8194:
8182:
7478:is the charge of the particle and
7313:
7209:
6356:
6142:
6060:
5870:
5583:
5458:
5303:
5230:
5072:Theory underlying magnetic dipoles
4213:
4176:Magnetic dipoleâdipole interaction
3425:
3417:
3362:
3342:
3324:
3225:
3201:
3125:
3053:
3019:
2993:
2909:
2529:
1966:
1894:
1882:
1806:
1793:
1400:
1395:
1383:
1378:
1372:
1356:
1349:
1283:
1268:
1232:
1217:
1181:
1166:
1032:Definition, units, and measurement
1010:composites of elementary particles
25:
9947:
9869:
9565:Krey, Uwe; Owen, Anthony (2007).
9275:The International System of Units
8411:
7574:) is a little larger than 2. The
7405:of the moving charged particles.
2036:is the volume of the bar magnet.
1425:(SI derived unit of force), T is
9827:Figgis, B.N.; Lewis, J. (1960).
8488:anomalous magnetic dipole moment
8406:
8366:
8327:Anomalous magnetic dipole moment
8262:
8246:
8217:
8208:
8187:
8159:LandauâLifshitzâGilbert equation
7538:
7510:
7440:
7416:
7360:
7342:
7304:
7283:
7253:
7200:
7186:
7167:
7149:is the mass of the particle and
7128:
7120:
7108:
7100:
7092:
7063:
7038:
7026:
6962:. This effect is expressed on a
6864:
6853:
6815:
6803:
6792:
6779:
6764:
6718:
6710:
6675:
6664:
6626:
6614:
6603:
6590:
6575:
6536:
6528:
6459:
6448:
6423:
6408:
6400:
6392:
6342:
6332:
6309:
6259:
6248:
6223:
6208:
6200:
6192:
6150:
6132:
6124:
6090:
6054:
6043:
6017:
5975:
5957:
5949:
5935:
5864:
5856:
5828:
5806:
5766:
5754:
5746:
5710:
5702:
5671:
5620:
5566:
5557:
5538:
5486:
5441:
5432:
5413:
5403:
5352:
5342:
5310:
5293:
5285:
5259:
5216:
5206:
5179:
5157:
5135:
5046:
5031:
4966:
4951:
4928:
4913:
4896:
4873:
4858:
4843:
4823:
4805:
4790:
4770:
4752:
4737:
4706:
4669:
4618:
4601:
4583:
4566:
4551:
4528:
4513:
4498:
4478:
4461:
4446:
4428:
4411:
4396:
4370:
4324:
4309:
4300:
4292:
4238:
4223:
4206:
4135:
4123:
4112:
4099:
4084:
4043:
4035:
3977:
3935:
3923:
3912:
3899:
3884:
3850:
3842:
3815:
3803:
3790:
3768:
3746:
3720:
3673:
3662:
3637:
3622:
3614:
3606:
3569:
3561:
3539:
3367:
3353:
3242:
3232:
3208:
3189:
3175:
3160:
3134:
3118:
3099:
3070:
3060:
3036:
3028:
3005:
2986:
2963:
2926:
2918:
2896:
2863:
2855:
2789:
2781:
2688:
2674:
2600:
2589:
2520:
2512:
2504:
2474:
2378:
2260:
2096:
2070:
2012:
2004:
1960:
1949:
1887:
1871:
1788:
1777:
1323:The unit for magnetic moment in
1255:
1204:
1153:
1139:
1077:
1069:
9839:
9820:
9806:. Cuvillier Verlag. p. 6.
9658:
9641:The Feynman Lectures on Physics
9481:
9456:
9420:
9357:Introduction to Electrodynamics
8600:Examples of molecular magnetism
8352:electron paramagnetic resonance
8350:, and other phenomena, such as
8307:is the damping coefficient and
7987:{\displaystyle {\mathfrak {m}}}
3289:and the two expressions agree.
2414:Localized current distributions
2157:is the permeability of vacuum (
9302:"K&J Magnetics â Glossary"
9294:
9210:
9141:
8321:Magnetic moment of an electron
8119:
8107:
8044:
8032:
7834:
7822:
7308:
7290:
7204:
7193:
6868:
6860:
6821:
6810:
6796:
6773:
6722:
6714:
6679:
6671:
6632:
6621:
6607:
6584:
6540:
6532:
6465:
6454:
6429:
6418:
6412:
6396:
6347:
6337:
6265:
6254:
6229:
6218:
6212:
6196:
6136:
6128:
5981:
5970:
5939:
5931:
5772:
5761:
5714:
5706:
5297:
5289:
5221:
5211:
5006:is in the opposite direction.
4976:
4955:
4944:
4938:
4917:
4906:
4900:
4883:
4853:
4847:
4815:
4794:
4783:
4762:
4741:
4730:
4712:
4701:
4628:
4622:
4596:
4593:
4587:
4561:
4555:
4538:
4508:
4502:
4488:
4482:
4456:
4438:
4432:
4406:
4376:
4365:
4334:
4296:
4141:
4130:
4116:
4093:
4047:
4039:
3941:
3930:
3916:
3893:
3854:
3846:
3808:
3798:
3679:
3668:
3643:
3632:
3626:
3610:
3573:
3565:
2524:
2516:
1723:
1259:
1208:
1157:
13:
1:
8764:of some elementary particles
8553:Magnetic moment of a molecule
7498:is the mass of the particle.
5682:{\displaystyle \mathbf {r} '}
2640:Magnetic moment of a solenoid
1325:International System of Units
1036:
615:Relativistic electromagnetism
9772:Advances in chemical physics
9355:Griffiths, David J. (1999).
9249:10.1103/RevModPhys.88.035009
9051:
9020:
8984:
8962:
8926:
8890:
8854:
8818:
8507:Magnetic moment of a nucleus
7070:{\displaystyle \mathbf {L} }
6944:Relation to angular momentum
6892:These fields are related by
6316:{\displaystyle \mathbf {H} }
6097:{\displaystyle \mathbf {m} }
6024:{\displaystyle \mathbf {m} }
5904:is the position vector, and
5813:{\displaystyle \mathbf {m} }
5638:in the amperian loop model,
5627:{\displaystyle \mathbf {j} }
5266:{\displaystyle \mathbf {B} }
5186:{\displaystyle \mathbf {H} }
5164:{\displaystyle \mathbf {H} }
5142:{\displaystyle \mathbf {H} }
3984:{\displaystyle \mathbf {B} }
3775:{\displaystyle \mathbf {r} }
3753:{\displaystyle \mathbf {r} }
3727:{\displaystyle \mathbf {H} }
3546:{\displaystyle \mathbf {m} }
3460:
2759:in a uniform magnetic field
2563:is the position vector, and
2298:Relation to angular momentum
1654:in free space, expressed in
7:
9596:Buxton, Richard B. (2002).
9488:Furlani, Edward P. (2001).
9149:Callen, Herbert B. (1985).
9058:
8659:nuclear spin configuration.
3738:produced by the magnet and
10:
9952:
9769:Rice, Stuart Alan (2004).
9604:Cambridge University Press
8593:nuclear spin configuration
8536:, although nuclei of some
8510:
8324:
7731:Magnetic moment of an atom
6988:nuclear magnetic resonance
6947:
5081:
5075:
4173:
3499:
3493:
2888:
2827:
1755:
1749:
1727:
340:LiĂŠnardâWiechert potential
9876:Bowtell, Richard (2009).
9683:Tilley, R. J. D. (2004).
9568:Basic Theoretical Physics
9403:Classical Electrodynamics
9331:Brown, William Fuller Jr.
9219:Reviews of Modern Physics
7737:angular momentum coupling
7394:{\displaystyle \rho _{Q}}
5275:magnetic vector potential
5195:magnetic scalar potential
3261:In all these expressions
2885:model used for the dipole
2363:electric currents attract
2169:
2047:(or remanence), denoted
1746:Relation to magnetization
1619: (Gaussian and EMU),
928:
909:
893:
879:
855:
605:Mathematical descriptions
315:Electromagnetic radiation
305:Electromagnetic induction
245:Magnetic vector potential
240:Magnetic scalar potential
9894:University of Nottingham
9800:Steiner, Marcus (2004).
8344:Electron magnetic moment
8331:Electron magnetic moment
8303:is the magnetic moment,
7626:electron magnetic moment
5912:electric current density
3152:
2708:Quantum mechanical model
2571:electric current density
1318:
1111:is the magnetic moment.
1045:) relating the aligning
9085:Magnetic susceptibility
8591:, which depends on the
8517:Nuclear magnetic moment
8513:Nucleon magnetic moment
7996:magnetic quantum number
7011:{\displaystyle \gamma }
6968:Einsteinâde Haas effect
6300:magnetic field strength
4189:on another with moment
3293:Relation to free energy
1685:the magnetic moment is
155:Electrostatic induction
150:Electrostatic discharge
9080:Toroidal dipole moment
9075:Electric dipole moment
8471:quantum electrodynamic
8423:
8283:
8144:
7988:
7952:
7844:
7764:
7585:) of a particle is an
7549:
7492:
7472:
7452:
7395:
7368:
7328:
7224:
7139:
7071:
7049:
7012:
6883:
6694:
6508:
6490:
6317:
6290:
6098:
6074:
6025:
6001:
5884:
5814:
5792:
5683:
5652:
5628:
5606:
5321:
5267:
5243:
5187:
5165:
5143:
5063:
4991:
4643:
4260:
4161:
3985:
3961:
3828:
3776:
3754:
3728:
3704:
3547:
3511:
3485:Effects on environment
3452:
3375:
3253:
3145:
3082:
2942:
2871:
2800:
2699:
2649:
2611:
2543:
2454:
2450:and enclosing an area
2438:
2400:
2350:
2284:
2240:
2222:magnetic pole strength
2196:
2116:
2062:in (units of Aâ
m) is:
2026:
1980:
1911:
1823:
1626:
1547:
1413:
1306:
1085:
585:Electromagnetic tensor
18:Magnetic dipole moment
9406:(2 ed.). Wiley.
9159:John Wiley & Sons
9090:Orbital magnetization
8573:contribution), if any
8424:
8284:
8145:
7989:
7953:
7845:
7765:
7550:
7493:
7473:
7453:
7396:
7369:
7329:
7225:
7140:
7072:
7050:
7013:
6884:
6695:
6506:
6491:
6318:
6291:
6114:magnetic flux density
6099:
6075:
6026:
6002:
5885:
5815:
5793:
5684:
5653:
5651:{\displaystyle \rho }
5629:
5607:
5322:
5268:
5244:
5188:
5166:
5144:
5064:
4992:
4644:
4261:
4162:
3986:
3962:
3829:
3777:
3755:
3729:
3705:
3548:
3509:
3453:
3376:
3254:
3146:
3083:
2943:
2872:
2830:Force between magnets
2801:
2700:
2647:
2612:
2544:
2439:
2421:
2401:
2355:Hans Christian Ărsted
2342:
2285:
2241:
2194:
2117:
2045:residual flux density
2027:
1981:
1912:
1824:
1627:
1548:
1414:
1307:
1086:
578:Covariant formulation
370:Synchrotron radiation
310:Electromagnetic pulse
300:Electromagnetic field
9686:Understanding Solids
9575:. pp. 151â152.
9101:References and notes
8742:Elementary particles
8361:
8165:
8014:
7974:
7888:
7774:
7743:
7654:elementary particles
7618:charge-to-mass ratio
7606:charge-to-mass ratio
7506:
7491:{\displaystyle \mu }
7482:
7462:
7412:
7378:
7338:
7249:
7163:
7088:
7082:charge-to-mass ratio
7059:
7022:
7002:
6706:
6524:
6327:
6305:
6120:
6086:
6039:
6013:
5925:
5896:vector cross product
5824:
5802:
5698:
5666:
5642:
5616:
5334:
5281:
5255:
5201:
5175:
5153:
5131:
5018:
4997:The force acting on
4665:
4288:
4202:
4031:
3973:
3838:
3786:
3764:
3742:
3716:
3557:
3535:
3397:
3320:
3155:
3094:
2954:
2891:
2842:
2769:
2670:
2585:
2555:vector cross product
2470:
2426:
2374:
2322:, in analogy to the
2256:
2228:
2066:
2000:
1945:
1867:
1773:
1681:(see below), but in
1677:has magnetic moment
1556:
1460:
1433:(SI derived unit of
1345:
1135:
1057:
1002:elementary particles
870:, enclosing an area
620:Stressâenergy tensor
545:Reluctance (complex)
290:Displacement current
9926:Physical quantities
9691:John Wiley and Sons
9632:Leighton, Robert B.
9628:Feynman, Richard P.
9442:1988AmJPh..56..688B
9398:Jackson, John David
9306:www.kjmagnetics.com
9241:2016RvMP...88c5009M
9177:where the relevant
8765:
6960:gyromagnetic effect
6514:Magnetic pole model
5691:multipole expansion
5126:demagnetizing field
5119:magnetic potentials
5113:Magnetic potentials
5078:Multipole expansion
4025:vacuum permeability
2648:Image of a solenoid
2460:multipole expansion
2335:Ampèrian loop model
2187:Magnetic pole model
1331:is Aâ
m, where A is
1024:such as exerted by
535:Magnetomotive force
420:Electromotive force
390:Alternating current
325:Jefimenko equations
285:Cyclotron radiation
9882:â Magnetic Moment"
9779:. pp. 208ff.
9544:10.1155/1998/79537
9147:See, for example,
8761:
8628:, mostly exhibits
8613:, exhibits strong
8465:is 2 according to
8419:
8295:gyromagnetic ratio
8279:
8140:
7984:
7948:
7840:
7760:
7632:for more details.
7545:
7488:
7468:
7448:
7391:
7364:
7324:
7270:
7220:
7155:is the particle's
7135:
7067:
7045:
7008:
6996:gyromagnetic ratio
6950:gyromagnetic ratio
6879:
6690:
6509:
6486:
6313:
6286:
6094:
6070:
6021:
5997:
5880:
5810:
5788:
5679:
5648:
5624:
5602:
5600:
5317:
5263:
5239:
5183:
5161:
5139:
5106:magnetic monopoles
5059:
4987:
4639:
4256:
4157:
3981:
3957:
3824:
3772:
3750:
3724:
3700:
3543:
3512:
3448:
3389:of the system and
3371:
3267:is the dipole and
3249:
3141:
3078:
3076:
2938:
2867:
2796:
2743:Torque on a moment
2734:for more details.
2695:
2650:
2607:
2539:
2491:
2455:
2434:
2396:
2359:AndrÊ-Marie Ampère
2351:
2280:
2236:
2224:), and the vector
2197:
2112:
2022:
1976:
1907:
1819:
1622:
1543:
1409:
1302:
1081:
913:SI base units
383:Electrical network
220:Gauss magnetic law
185:Static electricity
145:Electric potential
9813:978-3-86537-176-8
9786:978-0-471-44528-9
9731:978-0-7167-4345-3
9700:978-0-470-85275-0
9651:978-0-8053-9045-2
9613:978-0-521-58113-4
9582:978-3-540-36804-5
9505:978-0-12-269951-1
9474:978-0-7506-2634-7
9413:978-0-471-43132-9
9370:978-0-13-805326-0
9288:978-92-822-2272-0
9172:978-0-471-86256-7
9134:978-0-471-47741-9
9056:
9055:
8756:nuclear magnetons
8739:
8738:
8664:transition metals
8414:
8402:
8392:
8373:
8277:
8243:
8224:
8202:
8176:
8136:
8127:
8103:
8094:
8082:
8073:
8061:
8052:
8028:
7941:
7930:
7903:
7838:
7812:
7801:
7788:
7757:
7646:electric currents
7534:
7471:{\displaystyle e}
7436:
7269:
6964:macroscopic scale
6850:
6832:
6785:
6770:
6748:
6661:
6643:
6596:
6581:
6559:
6476:
6440:
6378:
6276:
6240:
6178:
5992:
5843:
5783:
5740:
5579:
5521:
5454:
5394:
4958:
4920:
4903:
4850:
4797:
4744:
4723:
4625:
4590:
4558:
4505:
4485:
4435:
4387:
4152:
4105:
4090:
4073:
3952:
3905:
3890:
3873:
3821:
3690:
3654:
3592:
3432:
3316:of the system as
3182:
3167:
3106:
2970:
2903:
2824:Force on a moment
2723:quantum mechanics
2490:
2103:
2092:
1902:
1814:
1620:
1616:
1613:
1603:
1592:
1571:
1570:
1567:
1541:
1537:
1534:
1524:
1513:
1480:
1469:
1404:
1387:
1297:
1278:
1262:
1246:
1227:
1211:
1195:
1176:
1160:
943:
942:
851:
850:
550:Reluctance (real)
520:Gyratorâcapacitor
465:Resonant cavities
355:Maxwell equations
16:(Redirected from
9943:
9931:Moment (physics)
9897:
9863:
9862:
9860:
9858:
9843:
9837:
9836:
9824:
9818:
9817:
9797:
9791:
9790:
9766:
9760:
9759:
9742:
9736:
9735:
9720:(4th ed.).
9711:
9705:
9704:
9680:
9674:
9673:
9670:physics.nist.gov
9662:
9656:
9655:
9624:
9618:
9617:
9593:
9587:
9586:
9562:
9556:
9555:
9553:
9551:
9546:
9528:
9519:
9510:
9509:
9485:
9479:
9478:
9460:
9454:
9453:
9424:
9418:
9417:
9394:
9383:
9382:
9359:(3rd ed.).
9352:
9343:
9342:
9327:
9310:
9309:
9298:
9292:
9291:
9280:
9270:
9261:
9260:
9234:
9214:
9208:
9207:
9205:
9203:
9198:. IEEE Magnetics
9196:"Magnetic units"
9192:
9186:
9184:
9180:
9176:
9157:(2nd ed.).
9156:
9145:
9139:
9138:
9125:Wiley-IEEE Press
9123:(2nd ed.).
9114:
9070:Moment (physics)
9048:
9035:
9033:
9032:
9029:
9026:
9018:
9017:
9012:
8999:
8997:
8996:
8993:
8990:
8982:
8981:
8976:
8960:
8959:
8954:
8941:
8939:
8938:
8935:
8932:
8924:
8923:
8918:
8905:
8903:
8902:
8899:
8896:
8888:
8887:
8882:
8869:
8867:
8866:
8863:
8860:
8852:
8851:
8846:
8833:
8831:
8830:
8827:
8824:
8816:
8814:
8766:
8760:
8749:
8694:
8670:
8669:
8540:have long-lived
8498:
8485:
8484:
8481:
8478:
8461:
8447:
8433:
8428:
8426:
8425:
8420:
8415:
8410:
8409:
8404:
8403:
8400:
8394:
8393:
8390:
8383:
8375:
8374:
8371:
8369:
8340:angular momentum
8312:
8306:
8302:
8292:
8288:
8286:
8285:
8280:
8278:
8276:
8272:
8266:
8265:
8260:
8254:
8249:
8244:
8242:
8231:
8226:
8225:
8222:
8220:
8211:
8203:
8201:
8197:
8191:
8190:
8185:
8179:
8177:
8169:
8149:
8147:
8146:
8141:
8134:
8125:
8101:
8092:
8080:
8071:
8059:
8050:
8026:
8009:
7994:) is called the
7993:
7991:
7990:
7985:
7983:
7982:
7969:
7957:
7955:
7954:
7949:
7943:
7942:
7939:
7932:
7931:
7928:
7912:
7911:
7904:
7901:
7898:
7897:
7876:
7870:
7861:
7853:
7849:
7847:
7846:
7841:
7839:
7817:
7814:
7813:
7810:
7803:
7802:
7799:
7790:
7789:
7786:
7784:
7783:
7769:
7767:
7766:
7761:
7759:
7758:
7755:
7753:
7752:
7681:
7679:
7676:
7642:electric charges
7614:nuclear magneton
7599:
7577:
7569:
7565:
7559:
7554:
7552:
7551:
7546:
7541:
7535:
7533:
7522:
7513:
7497:
7495:
7494:
7489:
7477:
7475:
7474:
7469:
7457:
7455:
7454:
7449:
7443:
7437:
7435:
7424:
7419:
7400:
7398:
7397:
7392:
7390:
7389:
7373:
7371:
7370:
7365:
7363:
7358:
7357:
7345:
7333:
7331:
7330:
7325:
7316:
7307:
7302:
7301:
7286:
7281:
7280:
7271:
7262:
7256:
7233:
7229:
7227:
7226:
7221:
7212:
7203:
7189:
7183:
7182:
7170:
7154:
7148:
7144:
7142:
7141:
7136:
7131:
7123:
7111:
7103:
7095:
7076:
7074:
7073:
7068:
7066:
7054:
7052:
7051:
7046:
7041:
7029:
7017:
7015:
7014:
7009:
6982:can cause it to
6956:angular momentum
6935:
6913:
6888:
6886:
6885:
6880:
6875:
6871:
6867:
6856:
6851:
6846:
6838:
6833:
6831:
6830:
6829:
6824:
6818:
6813:
6807:
6806:
6795:
6787:
6786:
6778:
6772:
6771:
6763:
6756:
6749:
6747:
6739:
6738:
6729:
6721:
6713:
6699:
6697:
6696:
6691:
6686:
6682:
6678:
6667:
6662:
6657:
6649:
6644:
6642:
6641:
6640:
6635:
6629:
6624:
6618:
6617:
6606:
6598:
6597:
6589:
6583:
6582:
6574:
6567:
6560:
6558:
6547:
6539:
6531:
6495:
6493:
6492:
6487:
6482:
6478:
6477:
6475:
6474:
6473:
6468:
6462:
6457:
6451:
6446:
6441:
6439:
6438:
6437:
6432:
6426:
6421:
6415:
6411:
6403:
6395:
6386:
6379:
6377:
6366:
6346:
6345:
6336:
6335:
6322:
6320:
6319:
6314:
6312:
6295:
6293:
6292:
6287:
6282:
6278:
6277:
6275:
6274:
6273:
6268:
6262:
6257:
6251:
6246:
6241:
6239:
6238:
6237:
6232:
6226:
6221:
6215:
6211:
6203:
6195:
6186:
6179:
6177:
6169:
6168:
6159:
6154:
6153:
6135:
6127:
6103:
6101:
6100:
6095:
6093:
6082:The same symbol
6079:
6077:
6076:
6071:
6063:
6057:
6046:
6030:
6028:
6027:
6022:
6020:
6006:
6004:
6003:
5998:
5993:
5991:
5990:
5989:
5984:
5978:
5973:
5961:
5960:
5952:
5946:
5938:
5919:scalar potential
5909:
5903:
5893:
5889:
5887:
5886:
5881:
5873:
5867:
5859:
5854:
5853:
5844:
5836:
5831:
5819:
5817:
5816:
5811:
5809:
5797:
5795:
5794:
5789:
5784:
5782:
5781:
5780:
5775:
5769:
5764:
5758:
5757:
5749:
5743:
5741:
5739:
5731:
5730:
5721:
5713:
5705:
5688:
5686:
5685:
5680:
5678:
5674:
5657:
5655:
5654:
5649:
5633:
5631:
5630:
5625:
5623:
5611:
5609:
5608:
5603:
5601:
5594:
5586:
5580:
5578:
5574:
5573:
5569:
5560:
5550:
5549:
5545:
5541:
5527:
5522:
5520:
5509:
5500:
5496:
5489:
5469:
5461:
5455:
5453:
5449:
5448:
5444:
5435:
5425:
5424:
5420:
5416:
5406:
5400:
5395:
5393:
5385:
5384:
5375:
5366:
5362:
5355:
5345:
5326:
5324:
5323:
5318:
5313:
5296:
5288:
5272:
5270:
5269:
5264:
5262:
5248:
5246:
5245:
5240:
5220:
5219:
5210:
5209:
5192:
5190:
5189:
5184:
5182:
5170:
5168:
5167:
5162:
5160:
5148:
5146:
5145:
5140:
5138:
5068:
5066:
5065:
5060:
5055:
5054:
5049:
5040:
5039:
5034:
5025:
5005:
4996:
4994:
4993:
4988:
4983:
4979:
4975:
4974:
4969:
4960:
4959:
4954:
4949:
4937:
4936:
4931:
4922:
4921:
4916:
4911:
4905:
4904:
4899:
4894:
4882:
4881:
4876:
4867:
4866:
4861:
4852:
4851:
4846:
4841:
4832:
4831:
4826:
4814:
4813:
4808:
4799:
4798:
4793:
4788:
4779:
4778:
4773:
4761:
4760:
4755:
4746:
4745:
4740:
4735:
4724:
4722:
4721:
4720:
4715:
4709:
4704:
4692:
4691:
4690:
4677:
4672:
4660:
4654:
4648:
4646:
4645:
4640:
4635:
4631:
4627:
4626:
4621:
4616:
4610:
4609:
4604:
4592:
4591:
4586:
4581:
4575:
4574:
4569:
4560:
4559:
4554:
4549:
4537:
4536:
4531:
4522:
4521:
4516:
4507:
4506:
4501:
4496:
4487:
4486:
4481:
4476:
4470:
4469:
4464:
4455:
4454:
4449:
4437:
4436:
4431:
4426:
4420:
4419:
4414:
4405:
4404:
4399:
4388:
4386:
4385:
4384:
4379:
4373:
4368:
4356:
4355:
4354:
4341:
4333:
4332:
4327:
4318:
4317:
4312:
4303:
4295:
4283:
4274:
4265:
4263:
4262:
4257:
4252:
4248:
4247:
4246:
4241:
4232:
4231:
4226:
4209:
4197:
4188:
4166:
4164:
4163:
4158:
4153:
4151:
4150:
4149:
4144:
4138:
4133:
4127:
4126:
4115:
4107:
4106:
4098:
4092:
4091:
4083:
4076:
4074:
4072:
4064:
4063:
4054:
4046:
4038:
4023:is known as the
4015:
4006:
3990:
3988:
3987:
3982:
3980:
3966:
3964:
3963:
3958:
3953:
3951:
3950:
3949:
3944:
3938:
3933:
3927:
3926:
3915:
3907:
3906:
3898:
3892:
3891:
3883:
3876:
3874:
3872:
3861:
3853:
3845:
3833:
3831:
3830:
3825:
3823:
3822:
3814:
3811:
3806:
3801:
3793:
3781:
3779:
3778:
3773:
3771:
3759:
3757:
3756:
3751:
3749:
3733:
3731:
3730:
3725:
3723:
3709:
3707:
3706:
3701:
3696:
3692:
3691:
3689:
3688:
3687:
3682:
3676:
3671:
3665:
3660:
3655:
3653:
3652:
3651:
3646:
3640:
3635:
3629:
3625:
3617:
3609:
3600:
3593:
3591:
3580:
3572:
3564:
3552:
3550:
3549:
3544:
3542:
3519:
3457:
3455:
3454:
3449:
3444:
3443:
3438:
3434:
3433:
3431:
3423:
3415:
3392:
3384:
3380:
3378:
3377:
3372:
3370:
3365:
3356:
3345:
3327:
3315:
3309:
3302:
3288:
3280:
3272:
3266:
3258:
3256:
3255:
3250:
3245:
3240:
3236:
3235:
3216:
3212:
3211:
3192:
3184:
3183:
3180:
3178:
3169:
3168:
3165:
3163:
3150:
3148:
3147:
3142:
3137:
3132:
3128:
3121:
3108:
3107:
3104:
3102:
3087:
3085:
3084:
3079:
3077:
3073:
3068:
3064:
3063:
3044:
3040:
3039:
3031:
3012:
3008:
3000:
2996:
2989:
2972:
2971:
2968:
2966:
2947:
2945:
2944:
2939:
2934:
2930:
2929:
2921:
2905:
2904:
2901:
2899:
2876:
2874:
2873:
2868:
2866:
2858:
2837:
2814:Larmor frequency
2805:
2803:
2802:
2797:
2792:
2784:
2776:
2764:
2758:
2752:
2715:angular momentum
2704:
2702:
2701:
2696:
2691:
2677:
2665:
2659:
2635:
2629:
2616:
2614:
2613:
2608:
2603:
2592:
2568:
2562:
2552:
2548:
2546:
2545:
2540:
2532:
2523:
2515:
2507:
2502:
2501:
2492:
2483:
2477:
2464:vector potential
2453:
2449:
2443:
2441:
2440:
2435:
2433:
2409:
2405:
2403:
2402:
2397:
2392:
2381:
2361:discovered that
2348:
2330:
2321:
2294:angular momentum
2289:
2287:
2286:
2281:
2275:
2263:
2251:
2245:
2243:
2242:
2237:
2235:
2219:
2164:
2162:
2156:
2145:
2135:
2121:
2119:
2118:
2113:
2105:
2104:
2101:
2099:
2093:
2091:
2090:
2078:
2073:
2061:
2055:
2035:
2031:
2029:
2028:
2023:
2015:
2007:
1995:
1985:
1983:
1982:
1977:
1969:
1963:
1952:
1940:
1930:
1923:
1916:
1914:
1913:
1908:
1903:
1901:
1897:
1891:
1890:
1885:
1879:
1874:
1862:
1860:
1852:
1840:
1828:
1826:
1825:
1820:
1815:
1813:
1812:
1800:
1799:
1791:
1785:
1780:
1768:
1718:nuclear magneton
1708:
1707:
1705:
1704:
1697:
1694:
1680:
1676:
1672:
1631:
1629:
1628:
1623:
1621:
1618:
1614:
1611:
1610:
1609:
1604:
1601:
1598:
1593:
1590:
1588:
1587:
1572:
1568:
1565:
1564:
1552:
1550:
1549:
1544:
1542:
1539:
1535:
1532:
1531:
1530:
1525:
1522:
1519:
1514:
1511:
1509:
1508:
1487:
1486:
1481:
1478:
1475:
1470:
1467:
1418:
1416:
1415:
1410:
1405:
1403:
1398:
1393:
1388:
1386:
1381:
1370:
1365:
1364:
1363:
1311:
1309:
1308:
1303:
1298:
1296:
1295:
1294:
1281:
1280:
1279:
1276:
1266:
1264:
1263:
1258:
1253:
1247:
1245:
1244:
1243:
1230:
1229:
1228:
1225:
1215:
1213:
1212:
1207:
1202:
1196:
1194:
1193:
1192:
1179:
1178:
1177:
1174:
1164:
1162:
1161:
1156:
1151:
1142:
1130:
1110:
1104:
1098:
1090:
1088:
1087:
1082:
1080:
1072:
1064:
1022:electric current
996:, etc.; various
947:electromagnetism
914:
889:
862:Magnetic moment
860:
853:
852:
843:
836:
829:
510:Electric machine
493:Magnetic circuit
455:Parallel circuit
445:Network analysis
410:Electric current
345:London equations
190:Triboelectricity
180:Potential energy
49:
39:Electromagnetism
30:
29:
21:
9951:
9950:
9946:
9945:
9944:
9942:
9941:
9940:
9936:Magnetic moment
9901:
9900:
9872:
9867:
9866:
9856:
9854:
9845:
9844:
9840:
9825:
9821:
9814:
9798:
9794:
9787:
9767:
9763:
9743:
9739:
9732:
9724:. p. 310.
9712:
9708:
9701:
9693:. p. 368.
9681:
9677:
9664:
9663:
9659:
9652:
9625:
9621:
9614:
9606:. p. 136.
9594:
9590:
9583:
9563:
9559:
9549:
9547:
9526:
9520:
9513:
9506:
9498:. p. 140.
9486:
9482:
9475:
9461:
9457:
9450:10.1119/1.15501
9425:
9421:
9414:
9395:
9386:
9371:
9363:. p. 258.
9353:
9346:
9328:
9313:
9300:
9299:
9295:
9289:
9278:
9272:
9271:
9264:
9215:
9211:
9201:
9199:
9194:
9193:
9189:
9182:
9178:
9173:
9146:
9142:
9135:
9127:. p. 103.
9115:
9108:
9103:
9061:
9046:
9030:
9027:
9024:
9023:
9021:
9015:
9013:
9010:
8994:
8991:
8988:
8987:
8985:
8979:
8977:
8974:
8957:
8955:
8952:
8936:
8933:
8930:
8929:
8927:
8921:
8919:
8916:
8900:
8897:
8894:
8893:
8891:
8885:
8883:
8880:
8864:
8861:
8858:
8857:
8855:
8849:
8847:
8844:
8828:
8825:
8822:
8821:
8819:
8812:
8810:
8794:
8792:
8777:
8775:
8770:
8763:
8750:represents the
8747:
8744:
8692:
8685:
8683:
8681:
8676:
8674:
8650:
8627:
8612:
8602:
8555:
8519:
8509:
8494:
8482:
8479:
8476:
8474:
8464:
8459:
8443:
8436:
8431:
8405:
8399:
8395:
8389:
8385:
8384:
8382:
8370:
8365:
8364:
8362:
8359:
8358:
8333:
8323:
8315:
8308:
8304:
8298:
8290:
8268:
8267:
8261:
8256:
8255:
8253:
8245:
8235:
8230:
8221:
8216:
8215:
8207:
8193:
8192:
8186:
8181:
8180:
8178:
8168:
8166:
8163:
8162:
8015:
8012:
8011:
8003:
7978:
7977:
7975:
7972:
7971:
7967:
7938:
7934:
7927:
7923:
7900:
7899:
7893:
7892:
7891:
7889:
7886:
7885:
7879:
7874:
7868:
7864:
7859:
7851:
7816:
7809:
7805:
7798:
7794:
7785:
7779:
7778:
7777:
7775:
7772:
7771:
7754:
7748:
7747:
7746:
7744:
7741:
7740:
7733:
7677:
7674:
7672:
7638:
7597:
7595:Planck constant
7575:
7567:
7563:
7557:
7537:
7526:
7521:
7509:
7507:
7504:
7503:
7483:
7480:
7479:
7463:
7460:
7459:
7439:
7428:
7423:
7415:
7413:
7410:
7409:
7385:
7381:
7379:
7376:
7375:
7359:
7353:
7349:
7341:
7339:
7336:
7335:
7312:
7303:
7297:
7293:
7282:
7276:
7272:
7260:
7252:
7250:
7247:
7246:
7240:right-hand rule
7231:
7208:
7199:
7185:
7178:
7174:
7166:
7164:
7161:
7160:
7150:
7146:
7127:
7119:
7107:
7099:
7091:
7089:
7086:
7085:
7062:
7060:
7057:
7056:
7037:
7025:
7023:
7020:
7019:
7003:
7000:
6999:
6952:
6946:
6915:
6903:
6893:
6863:
6852:
6839:
6837:
6825:
6820:
6819:
6814:
6809:
6808:
6802:
6791:
6777:
6776:
6762:
6761:
6757:
6755:
6754:
6750:
6740:
6734:
6730:
6728:
6717:
6709:
6707:
6704:
6703:
6674:
6663:
6650:
6648:
6636:
6631:
6630:
6625:
6620:
6619:
6613:
6602:
6588:
6587:
6573:
6572:
6568:
6566:
6565:
6561:
6551:
6546:
6535:
6527:
6525:
6522:
6521:
6501:
6469:
6464:
6463:
6458:
6453:
6452:
6447:
6445:
6433:
6428:
6427:
6422:
6417:
6416:
6407:
6399:
6391:
6387:
6385:
6384:
6380:
6370:
6365:
6341:
6340:
6331:
6330:
6328:
6325:
6324:
6308:
6306:
6303:
6302:
6269:
6264:
6263:
6258:
6253:
6252:
6247:
6245:
6233:
6228:
6227:
6222:
6217:
6216:
6207:
6199:
6191:
6187:
6185:
6184:
6180:
6170:
6164:
6160:
6158:
6149:
6148:
6131:
6123:
6121:
6118:
6117:
6110:
6089:
6087:
6084:
6083:
6059:
6053:
6042:
6040:
6037:
6036:
6016:
6014:
6011:
6010:
5985:
5980:
5979:
5974:
5969:
5962:
5956:
5948:
5947:
5945:
5934:
5926:
5923:
5922:
5905:
5899:
5891:
5869:
5863:
5855:
5849:
5845:
5835:
5827:
5825:
5822:
5821:
5805:
5803:
5800:
5799:
5776:
5771:
5770:
5765:
5760:
5759:
5753:
5745:
5744:
5742:
5732:
5726:
5722:
5720:
5709:
5701:
5699:
5696:
5695:
5670:
5669:
5667:
5664:
5663:
5643:
5640:
5639:
5636:current density
5619:
5617:
5614:
5613:
5599:
5598:
5587:
5582:
5565:
5564:
5556:
5555:
5551:
5537:
5536:
5532:
5528:
5526:
5513:
5508:
5501:
5485:
5484:
5480:
5474:
5473:
5462:
5457:
5440:
5439:
5431:
5430:
5426:
5412:
5411:
5407:
5402:
5401:
5399:
5386:
5380:
5376:
5374:
5367:
5351:
5350:
5346:
5341:
5337:
5335:
5332:
5331:
5309:
5292:
5284:
5282:
5279:
5278:
5258:
5256:
5253:
5252:
5215:
5214:
5205:
5204:
5202:
5199:
5198:
5178:
5176:
5173:
5172:
5156:
5154:
5151:
5150:
5134:
5132:
5129:
5128:
5115:
5086:
5084:Magnetic dipole
5080:
5074:
5050:
5045:
5044:
5035:
5030:
5029:
5021:
5019:
5016:
5015:
5012:
5004:
4998:
4970:
4965:
4964:
4950:
4948:
4947:
4932:
4927:
4926:
4912:
4910:
4909:
4895:
4893:
4892:
4877:
4872:
4871:
4862:
4857:
4856:
4842:
4840:
4839:
4827:
4822:
4821:
4809:
4804:
4803:
4789:
4787:
4786:
4774:
4769:
4768:
4756:
4751:
4750:
4736:
4734:
4733:
4729:
4725:
4716:
4711:
4710:
4705:
4700:
4693:
4686:
4682:
4678:
4676:
4668:
4666:
4663:
4662:
4656:
4650:
4617:
4615:
4614:
4605:
4600:
4599:
4582:
4580:
4579:
4570:
4565:
4564:
4550:
4548:
4547:
4532:
4527:
4526:
4517:
4512:
4511:
4497:
4495:
4494:
4477:
4475:
4474:
4465:
4460:
4459:
4450:
4445:
4444:
4427:
4425:
4424:
4415:
4410:
4409:
4400:
4395:
4394:
4393:
4389:
4380:
4375:
4374:
4369:
4364:
4357:
4350:
4346:
4342:
4340:
4328:
4323:
4322:
4313:
4308:
4307:
4299:
4291:
4289:
4286:
4285:
4282:
4276:
4273:
4267:
4242:
4237:
4236:
4227:
4222:
4221:
4220:
4216:
4205:
4203:
4200:
4199:
4196:
4190:
4187:
4181:
4178:
4172:
4145:
4140:
4139:
4134:
4129:
4128:
4122:
4111:
4097:
4096:
4082:
4081:
4077:
4075:
4065:
4059:
4055:
4053:
4042:
4034:
4032:
4029:
4028:
4027:. For example:
4022:
4004:
3999:
3997:
3976:
3974:
3971:
3970:
3945:
3940:
3939:
3934:
3929:
3928:
3922:
3911:
3897:
3896:
3882:
3881:
3877:
3875:
3865:
3860:
3849:
3841:
3839:
3836:
3835:
3813:
3812:
3807:
3802:
3797:
3789:
3787:
3784:
3783:
3767:
3765:
3762:
3761:
3745:
3743:
3740:
3739:
3719:
3717:
3714:
3713:
3683:
3678:
3677:
3672:
3667:
3666:
3661:
3659:
3647:
3642:
3641:
3636:
3631:
3630:
3621:
3613:
3605:
3601:
3599:
3598:
3594:
3584:
3579:
3568:
3560:
3558:
3555:
3554:
3538:
3536:
3533:
3532:
3520:will produce a
3515:
3504:
3498:
3496:Magnetic dipole
3492:
3487:
3463:
3439:
3424:
3416:
3414:
3410:
3407:
3406:
3398:
3395:
3394:
3390:
3382:
3366:
3361:
3352:
3341:
3323:
3321:
3318:
3317:
3311:
3307:
3298:
3295:
3282:
3274:
3268:
3262:
3241:
3231:
3224:
3220:
3207:
3200:
3196:
3188:
3179:
3174:
3173:
3164:
3159:
3158:
3156:
3153:
3133:
3117:
3116:
3112:
3103:
3098:
3097:
3095:
3092:
3091:
3075:
3074:
3069:
3059:
3052:
3048:
3035:
3027:
3026:
3022:
3010:
3009:
3004:
2985:
2984:
2980:
2973:
2967:
2962:
2961:
2957:
2955:
2952:
2951:
2925:
2917:
2916:
2912:
2900:
2895:
2894:
2892:
2889:
2862:
2854:
2843:
2840:
2839:
2835:
2832:
2826:
2788:
2780:
2772:
2770:
2767:
2766:
2760:
2754:
2748:
2745:
2740:
2710:
2687:
2673:
2671:
2668:
2667:
2661:
2657:
2642:
2631:
2625:
2599:
2588:
2586:
2583:
2582:
2575:volume integral
2564:
2558:
2550:
2528:
2519:
2511:
2503:
2497:
2493:
2481:
2473:
2471:
2468:
2467:
2451:
2445:
2429:
2427:
2424:
2423:
2416:
2407:
2388:
2377:
2375:
2372:
2371:
2344:
2337:
2326:
2317:
2271:
2259:
2257:
2254:
2253:
2247:
2231:
2229:
2226:
2225:
2217:
2189:
2172:
2160:
2158:
2155:
2149:
2143:
2134:
2128:
2100:
2095:
2094:
2086:
2082:
2077:
2069:
2067:
2064:
2063:
2057:
2054:
2048:
2033:
2011:
2003:
2001:
1998:
1997:
1991:
1965:
1959:
1948:
1946:
1943:
1942:
1936:
1925:
1918:
1893:
1892:
1886:
1881:
1880:
1878:
1870:
1868:
1865:
1864:
1855:
1854:
1851:
1842:
1839:
1830:
1805:
1801:
1792:
1787:
1786:
1784:
1776:
1774:
1771:
1770:
1764:
1760:
1754:
1748:
1732:
1726:
1698:
1695:
1690:
1689:
1687:
1686:
1678:
1674:
1670:
1634:where statA is
1617:
1605:
1600:
1599:
1594:
1589:
1580:
1576:
1563:
1557:
1554:
1553:
1538:
1526:
1521:
1520:
1515:
1510:
1501:
1497:
1482:
1477:
1476:
1471:
1466:
1461:
1458:
1457:
1399:
1394:
1392:
1382:
1371:
1369:
1359:
1355:
1348:
1346:
1343:
1342:
1321:
1290:
1286:
1282:
1275:
1271:
1267:
1265:
1254:
1252:
1251:
1239:
1235:
1231:
1224:
1220:
1216:
1214:
1203:
1201:
1200:
1188:
1184:
1180:
1173:
1169:
1165:
1163:
1152:
1150:
1149:
1138:
1136:
1133:
1132:
1129:
1123:
1106:
1100:
1092:
1076:
1068:
1060:
1058:
1055:
1054:
1039:
1034:
956:magnetic dipole
951:magnetic moment
912:
885:
882:
875:
847:
818:
817:
633:
625:
624:
580:
570:
569:
525:Induction motor
495:
485:
484:
400:Current density
385:
375:
374:
365:Poynting vector
275:
273:Electrodynamics
265:
264:
260:Right-hand rule
225:Magnetic dipole
215:BiotâSavart law
205:
195:
194:
130:Electric dipole
125:Electric charge
100:
28:
23:
22:
15:
12:
11:
5:
9949:
9939:
9938:
9933:
9928:
9923:
9918:
9913:
9911:Magnetostatics
9899:
9898:
9871:
9870:External links
9868:
9865:
9864:
9838:
9819:
9812:
9792:
9785:
9761:
9746:Crowther, J.A.
9737:
9730:
9717:Modern Physics
9706:
9699:
9675:
9657:
9650:
9636:Sands, Matthew
9619:
9612:
9588:
9581:
9557:
9511:
9504:
9496:Academic Press
9480:
9473:
9455:
9436:(8): 688â692.
9419:
9412:
9384:
9369:
9344:
9311:
9293:
9287:
9262:
9209:
9187:
9171:
9140:
9133:
9105:
9104:
9102:
9099:
9098:
9097:
9092:
9087:
9082:
9077:
9072:
9067:
9060:
9057:
9054:
9053:
9050:
9044:
9041:alpha particle
9037:
9036:
9019:
9008:
9001:
9000:
8983:
8972:
8965:
8964:
8961:
8950:
8943:
8942:
8925:
8914:
8907:
8906:
8889:
8878:
8871:
8870:
8853:
8842:
8835:
8834:
8817:
8808:
8801:
8800:
8793:quantum number
8787:
8772:
8771:name (symbol)
8743:
8740:
8737:
8736:
8733:
8729:
8728:
8725:
8721:
8720:
8717:
8713:
8712:
8709:
8705:
8704:
8701:
8697:
8696:
8690:
8678:
8668:
8667:
8660:
8648:
8641:
8625:
8622:carbon dioxide
8618:
8610:
8601:
8598:
8597:
8596:
8585:
8574:
8567:electron spins
8554:
8551:
8542:excited states
8508:
8505:
8467:Dirac's theory
8462:
8434:
8418:
8413:
8408:
8398:
8388:
8381:
8378:
8368:
8322:
8319:
8313:
8275:
8271:
8264:
8259:
8252:
8248:
8241:
8238:
8234:
8229:
8219:
8214:
8210:
8206:
8200:
8196:
8189:
8184:
8175:
8172:
8139:
8133:
8130:
8124:
8121:
8118:
8115:
8112:
8109:
8106:
8100:
8097:
8091:
8088:
8085:
8079:
8076:
8070:
8067:
8064:
8058:
8055:
8049:
8046:
8043:
8040:
8037:
8034:
8031:
8025:
8022:
8019:
7981:
7947:
7937:
7926:
7921:
7918:
7915:
7910:
7907:
7896:
7877:
7862:
7836:
7833:
7830:
7827:
7824:
7820:
7808:
7797:
7793:
7782:
7751:
7732:
7729:
7717:
7716:
7713:
7710:
7692:negative value
7656:, such as the
7637:
7634:
7544:
7540:
7532:
7529:
7525:
7519:
7516:
7512:
7487:
7467:
7447:
7442:
7434:
7431:
7427:
7422:
7418:
7403:charge density
7388:
7384:
7362:
7356:
7352:
7348:
7344:
7323:
7319:
7315:
7310:
7306:
7300:
7296:
7292:
7289:
7285:
7279:
7275:
7268:
7265:
7259:
7255:
7219:
7215:
7211:
7206:
7202:
7198:
7195:
7192:
7188:
7181:
7177:
7173:
7169:
7134:
7130:
7126:
7122:
7117:
7114:
7110:
7106:
7102:
7098:
7094:
7065:
7044:
7040:
7035:
7032:
7028:
7007:
6980:atomic nucleus
6972:Barnett effect
6945:
6942:
6901:
6878:
6874:
6870:
6866:
6862:
6859:
6855:
6849:
6845:
6842:
6836:
6828:
6823:
6817:
6812:
6805:
6801:
6798:
6794:
6790:
6784:
6781:
6775:
6769:
6766:
6760:
6753:
6746:
6743:
6737:
6733:
6727:
6724:
6720:
6716:
6712:
6689:
6685:
6681:
6677:
6673:
6670:
6666:
6660:
6656:
6653:
6647:
6639:
6634:
6628:
6623:
6616:
6612:
6609:
6605:
6601:
6595:
6592:
6586:
6580:
6577:
6571:
6564:
6557:
6554:
6550:
6545:
6542:
6538:
6534:
6530:
6500:
6497:
6485:
6481:
6472:
6467:
6461:
6456:
6450:
6444:
6436:
6431:
6425:
6420:
6414:
6410:
6406:
6402:
6398:
6394:
6390:
6383:
6376:
6373:
6369:
6364:
6361:
6358:
6355:
6352:
6349:
6344:
6339:
6334:
6311:
6285:
6281:
6272:
6267:
6261:
6256:
6250:
6244:
6236:
6231:
6225:
6220:
6214:
6210:
6206:
6202:
6198:
6194:
6190:
6183:
6176:
6173:
6167:
6163:
6157:
6152:
6147:
6144:
6141:
6138:
6134:
6130:
6126:
6109:
6106:
6092:
6069:
6066:
6062:
6056:
6052:
6049:
6045:
6019:
5996:
5988:
5983:
5977:
5972:
5968:
5965:
5959:
5955:
5951:
5944:
5941:
5937:
5933:
5930:
5879:
5876:
5872:
5866:
5862:
5858:
5852:
5848:
5842:
5839:
5834:
5830:
5808:
5787:
5779:
5774:
5768:
5763:
5756:
5752:
5748:
5738:
5735:
5729:
5725:
5719:
5716:
5712:
5708:
5704:
5677:
5673:
5660:charge density
5647:
5622:
5597:
5593:
5590:
5585:
5577:
5572:
5568:
5563:
5559:
5554:
5548:
5544:
5540:
5535:
5531:
5525:
5519:
5516:
5512:
5507:
5504:
5502:
5499:
5495:
5492:
5488:
5483:
5479:
5476:
5475:
5472:
5468:
5465:
5460:
5452:
5447:
5443:
5438:
5434:
5429:
5423:
5419:
5415:
5410:
5405:
5398:
5392:
5389:
5383:
5379:
5373:
5370:
5368:
5365:
5361:
5358:
5354:
5349:
5344:
5340:
5339:
5316:
5312:
5308:
5305:
5302:
5299:
5295:
5291:
5287:
5261:
5238:
5235:
5232:
5229:
5226:
5223:
5218:
5213:
5208:
5181:
5159:
5137:
5114:
5111:
5076:Main article:
5073:
5070:
5058:
5053:
5048:
5043:
5038:
5033:
5028:
5024:
5011:
5008:
5002:
4986:
4982:
4978:
4973:
4968:
4963:
4957:
4953:
4946:
4943:
4940:
4935:
4930:
4925:
4919:
4915:
4908:
4902:
4898:
4891:
4888:
4885:
4880:
4875:
4870:
4865:
4860:
4855:
4849:
4845:
4838:
4835:
4830:
4825:
4820:
4817:
4812:
4807:
4802:
4796:
4792:
4785:
4782:
4777:
4772:
4767:
4764:
4759:
4754:
4749:
4743:
4739:
4732:
4728:
4719:
4714:
4708:
4703:
4699:
4696:
4689:
4685:
4681:
4675:
4671:
4638:
4634:
4630:
4624:
4620:
4613:
4608:
4603:
4598:
4595:
4589:
4585:
4578:
4573:
4568:
4563:
4557:
4553:
4546:
4543:
4540:
4535:
4530:
4525:
4520:
4515:
4510:
4504:
4500:
4493:
4490:
4484:
4480:
4473:
4468:
4463:
4458:
4453:
4448:
4443:
4440:
4434:
4430:
4423:
4418:
4413:
4408:
4403:
4398:
4392:
4383:
4378:
4372:
4367:
4363:
4360:
4353:
4349:
4345:
4339:
4336:
4331:
4326:
4321:
4316:
4311:
4306:
4302:
4298:
4294:
4280:
4271:
4255:
4251:
4245:
4240:
4235:
4230:
4225:
4219:
4215:
4212:
4208:
4194:
4185:
4171:
4168:
4156:
4148:
4143:
4137:
4132:
4125:
4121:
4118:
4114:
4110:
4104:
4101:
4095:
4089:
4086:
4080:
4071:
4068:
4062:
4058:
4052:
4049:
4045:
4041:
4037:
4020:
3995:
3979:
3956:
3948:
3943:
3937:
3932:
3925:
3921:
3918:
3914:
3910:
3904:
3901:
3895:
3889:
3886:
3880:
3871:
3868:
3864:
3859:
3856:
3852:
3848:
3844:
3820:
3817:
3810:
3805:
3800:
3796:
3792:
3770:
3748:
3736:magnetic field
3722:
3699:
3695:
3686:
3681:
3675:
3670:
3664:
3658:
3650:
3645:
3639:
3634:
3628:
3624:
3620:
3616:
3612:
3608:
3604:
3597:
3590:
3587:
3583:
3578:
3575:
3571:
3567:
3563:
3541:
3494:Main article:
3491:
3488:
3486:
3483:
3475:ferromagnetism
3462:
3459:
3447:
3442:
3437:
3430:
3427:
3422:
3419:
3413:
3409:
3405:
3402:
3369:
3364:
3360:
3355:
3351:
3348:
3344:
3339:
3336:
3333:
3330:
3326:
3294:
3291:
3248:
3244:
3239:
3234:
3230:
3227:
3223:
3219:
3215:
3210:
3206:
3203:
3199:
3195:
3191:
3187:
3177:
3172:
3162:
3140:
3136:
3131:
3127:
3124:
3120:
3115:
3111:
3101:
3072:
3067:
3062:
3058:
3055:
3051:
3047:
3043:
3038:
3034:
3030:
3025:
3021:
3018:
3015:
3013:
3011:
3007:
3003:
2999:
2995:
2992:
2988:
2983:
2979:
2976:
2974:
2965:
2960:
2959:
2937:
2933:
2928:
2924:
2920:
2915:
2911:
2908:
2898:
2865:
2861:
2857:
2853:
2850:
2847:
2825:
2822:
2795:
2791:
2787:
2783:
2779:
2775:
2744:
2741:
2739:
2736:
2709:
2706:
2694:
2690:
2686:
2683:
2680:
2676:
2641:
2638:
2606:
2602:
2598:
2595:
2591:
2538:
2535:
2531:
2526:
2522:
2518:
2514:
2510:
2506:
2500:
2496:
2489:
2486:
2480:
2476:
2432:
2415:
2412:
2395:
2391:
2387:
2384:
2380:
2336:
2333:
2324:electric field
2310:magnetic field
2279:
2274:
2269:
2266:
2262:
2234:
2220:of its poles (
2213:magnetic poles
2201:electrostatics
2188:
2185:
2171:
2168:
2167:
2166:
2153:
2147:
2141:
2132:
2111:
2108:
2098:
2089:
2085:
2081:
2076:
2072:
2052:
2021:
2018:
2014:
2010:
2006:
1975:
1972:
1968:
1962:
1958:
1955:
1951:
1933:volume element
1906:
1900:
1896:
1889:
1884:
1877:
1873:
1846:
1834:
1818:
1811:
1808:
1804:
1798:
1795:
1790:
1783:
1779:
1750:Main article:
1747:
1744:
1740:magnetic field
1728:Main article:
1725:
1722:
1683:Gaussian units
1652:speed of light
1608:
1597:
1586:
1583:
1579:
1575:
1561:
1529:
1518:
1507:
1504:
1500:
1496:
1493:
1490:
1485:
1474:
1465:
1408:
1402:
1397:
1391:
1385:
1380:
1377:
1374:
1368:
1362:
1358:
1354:
1351:
1320:
1317:
1301:
1293:
1289:
1285:
1274:
1270:
1261:
1257:
1250:
1242:
1238:
1234:
1223:
1219:
1210:
1206:
1199:
1191:
1187:
1183:
1172:
1168:
1159:
1155:
1148:
1145:
1141:
1127:
1120:thermodynamics
1079:
1075:
1071:
1067:
1063:
1051:magnetic field
1038:
1035:
1033:
1030:
1026:electromagnets
966:magnetic field
941:
940:
932:
926:
925:
916:
907:
906:
897:
891:
890:
883:
881:Common symbols
880:
877:
876:
861:
849:
848:
846:
845:
838:
831:
823:
820:
819:
816:
815:
810:
805:
800:
795:
790:
785:
780:
775:
770:
765:
760:
755:
750:
745:
740:
735:
730:
725:
720:
715:
710:
705:
700:
695:
690:
685:
680:
675:
670:
665:
660:
655:
650:
645:
640:
634:
631:
630:
627:
626:
623:
622:
617:
612:
607:
602:
600:Four-potential
597:
592:
587:
581:
576:
575:
572:
571:
568:
567:
562:
557:
552:
547:
542:
537:
532:
527:
522:
517:
515:Electric motor
512:
507:
502:
496:
491:
490:
487:
486:
483:
482:
477:
472:
470:Series circuit
467:
462:
457:
452:
447:
442:
440:Kirchhoff laws
437:
432:
427:
422:
417:
412:
407:
405:Direct current
402:
397:
392:
386:
381:
380:
377:
376:
373:
372:
367:
362:
360:Maxwell tensor
357:
352:
347:
342:
337:
332:
330:Larmor formula
327:
322:
317:
312:
307:
302:
297:
292:
287:
282:
280:Bremsstrahlung
276:
271:
270:
267:
266:
263:
262:
257:
252:
247:
242:
237:
232:
230:Magnetic field
227:
222:
217:
212:
206:
203:Magnetostatics
201:
200:
197:
196:
193:
192:
187:
182:
177:
172:
167:
162:
157:
152:
147:
142:
137:
135:Electric field
132:
127:
122:
117:
112:
107:
105:Charge density
101:
98:Electrostatics
96:
95:
92:
91:
90:
89:
84:
79:
74:
69:
64:
59:
51:
50:
42:
41:
35:
34:
33:Articles about
26:
9:
6:
4:
3:
2:
9948:
9937:
9934:
9932:
9929:
9927:
9924:
9922:
9919:
9917:
9914:
9912:
9909:
9908:
9906:
9895:
9891:
9887:
9886:Sixty Symbols
9883:
9881:
9874:
9873:
9852:
9848:
9842:
9834:
9830:
9823:
9815:
9809:
9805:
9804:
9796:
9788:
9782:
9778:
9774:
9773:
9765:
9757:
9753:
9752:
9747:
9741:
9733:
9727:
9723:
9719:
9718:
9710:
9702:
9696:
9692:
9688:
9687:
9679:
9671:
9667:
9661:
9653:
9647:
9643:
9642:
9637:
9633:
9629:
9623:
9615:
9609:
9605:
9601:
9600:
9592:
9584:
9578:
9574:
9570:
9569:
9561:
9545:
9540:
9536:
9532:
9525:
9518:
9516:
9507:
9501:
9497:
9493:
9492:
9484:
9476:
9470:
9466:
9459:
9451:
9447:
9443:
9439:
9435:
9432:
9431:
9423:
9415:
9409:
9405:
9404:
9399:
9393:
9391:
9389:
9380:
9376:
9372:
9366:
9362:
9361:Prentice Hall
9358:
9351:
9349:
9340:
9339:North-Holland
9336:
9332:
9326:
9324:
9322:
9320:
9318:
9316:
9307:
9303:
9297:
9290:
9284:
9277:
9276:
9269:
9267:
9258:
9254:
9250:
9246:
9242:
9238:
9233:
9228:
9225:(3): 035009.
9224:
9220:
9213:
9197:
9191:
9174:
9168:
9164:
9160:
9155:
9154:
9144:
9136:
9130:
9126:
9122:
9121:
9113:
9111:
9106:
9096:
9093:
9091:
9088:
9086:
9083:
9081:
9078:
9076:
9073:
9071:
9068:
9066:
9063:
9062:
9045:
9042:
9039:
9038:
9009:
9006:
9003:
9002:
8973:
8970:
8967:
8966:
8951:
8948:
8945:
8944:
8915:
8912:
8909:
8908:
8879:
8876:
8873:
8872:
8843:
8840:
8837:
8836:
8809:
8806:
8803:
8802:
8798:
8797:dimensionless
8791:
8788:
8785:
8781:
8776:dipole moment
8773:
8768:
8767:
8759:
8757:
8753:
8734:
8731:
8730:
8726:
8723:
8722:
8718:
8715:
8714:
8710:
8707:
8706:
8702:
8699:
8698:
8693:
8689:
8679:
8672:
8671:
8665:
8661:
8658:
8654:
8646:
8642:
8639:
8635:
8631:
8623:
8619:
8616:
8615:paramagnetism
8608:
8604:
8603:
8594:
8590:
8589:nuclear spins
8586:
8584:contribution)
8583:
8579:
8575:
8572:
8568:
8564:
8563:
8562:
8560:
8550:
8547:
8543:
8539:
8535:
8530:
8528:
8524:
8518:
8514:
8504:
8502:
8497:
8491:
8489:
8472:
8469:, but due to
8468:
8458:
8456:
8451:
8446:
8441:
8440:Bohr magneton
8437:
8416:
8396:
8386:
8379:
8376:
8355:
8353:
8349:
8345:
8341:
8337:
8332:
8328:
8318:
8311:
8301:
8296:
8273:
8250:
8239:
8236:
8232:
8227:
8212:
8204:
8198:
8173:
8170:
8160:
8156:
8153:momentum, so
8150:
8137:
8131:
8128:
8122:
8116:
8113:
8110:
8104:
8098:
8095:
8089:
8086:
8083:
8077:
8074:
8068:
8065:
8062:
8056:
8053:
8047:
8041:
8038:
8035:
8029:
8023:
8020:
8017:
8007:
8001:
7997:
7966:
7961:
7958:
7945:
7935:
7924:
7919:
7916:
7913:
7908:
7905:
7883:
7882:Bohr magneton
7872:
7857:
7831:
7828:
7825:
7818:
7806:
7795:
7791:
7738:
7728:
7726:
7722:
7714:
7711:
7708:
7707:
7706:
7704:
7700:
7695:
7693:
7689:
7685:
7670:
7665:
7661:
7659:
7655:
7651:
7647:
7643:
7633:
7631:
7630:Bohr magneton
7627:
7623:
7619:
7615:
7611:
7607:
7603:
7602:Bohr magneton
7596:
7592:
7588:
7584:
7579:
7573:
7561:
7542:
7530:
7527:
7523:
7517:
7514:
7499:
7485:
7465:
7445:
7432:
7429:
7425:
7420:
7406:
7404:
7386:
7382:
7354:
7350:
7346:
7321:
7317:
7298:
7294:
7287:
7277:
7273:
7266:
7263:
7257:
7243:
7241:
7237:
7217:
7213:
7196:
7190:
7179:
7175:
7171:
7158:
7153:
7132:
7124:
7115:
7112:
7104:
7096:
7083:
7078:
7042:
7033:
7030:
7005:
6997:
6991:
6989:
6985:
6981:
6977:
6973:
6969:
6965:
6961:
6957:
6951:
6941:
6939:
6938:magnetization
6933:
6929:
6926:
6922:
6918:
6911:
6907:
6900:
6896:
6890:
6876:
6872:
6857:
6847:
6843:
6840:
6834:
6826:
6799:
6788:
6758:
6751:
6744:
6741:
6735:
6731:
6725:
6700:
6687:
6683:
6668:
6658:
6654:
6651:
6645:
6637:
6610:
6599:
6569:
6562:
6555:
6552:
6548:
6543:
6517:
6515:
6505:
6496:
6483:
6479:
6470:
6442:
6434:
6404:
6388:
6381:
6374:
6371:
6367:
6362:
6359:
6353:
6350:
6301:
6298:Further, the
6296:
6283:
6279:
6270:
6242:
6234:
6204:
6188:
6181:
6174:
6171:
6165:
6161:
6155:
6145:
6139:
6115:
6105:
6080:
6067:
6064:
6050:
6047:
6034:
6033:magnetization
6007:
5994:
5986:
5966:
5963:
5953:
5942:
5928:
5920:
5915:
5913:
5908:
5902:
5897:
5877:
5874:
5860:
5850:
5846:
5840:
5837:
5832:
5785:
5777:
5750:
5736:
5733:
5727:
5723:
5717:
5692:
5675:
5661:
5645:
5637:
5595:
5591:
5588:
5575:
5570:
5561:
5552:
5546:
5542:
5533:
5529:
5523:
5517:
5514:
5510:
5505:
5503:
5497:
5493:
5490:
5481:
5477:
5470:
5466:
5463:
5450:
5445:
5436:
5427:
5421:
5417:
5408:
5396:
5390:
5387:
5381:
5377:
5371:
5369:
5363:
5359:
5356:
5347:
5327:
5314:
5306:
5300:
5276:
5249:
5236:
5233:
5227:
5224:
5196:
5127:
5122:
5120:
5110:
5107:
5102:
5100:
5096:
5092:
5085:
5079:
5069:
5056:
5051:
5041:
5036:
5026:
5007:
5001:
4984:
4980:
4971:
4961:
4941:
4933:
4923:
4889:
4886:
4878:
4868:
4863:
4836:
4833:
4828:
4818:
4810:
4800:
4780:
4775:
4765:
4757:
4747:
4726:
4717:
4697:
4694:
4687:
4683:
4679:
4673:
4659:
4653:
4636:
4632:
4611:
4606:
4576:
4571:
4544:
4541:
4533:
4523:
4518:
4491:
4471:
4466:
4451:
4441:
4421:
4416:
4401:
4390:
4381:
4361:
4358:
4351:
4347:
4343:
4337:
4329:
4319:
4314:
4304:
4279:
4270:
4253:
4249:
4243:
4233:
4228:
4217:
4210:
4193:
4184:
4177:
4167:
4154:
4146:
4119:
4108:
4078:
4069:
4066:
4060:
4056:
4050:
4026:
4019:
4014:
4010:
4003:
3994:
3967:
3954:
3946:
3919:
3908:
3878:
3869:
3866:
3862:
3857:
3794:
3737:
3710:
3697:
3693:
3684:
3656:
3648:
3618:
3602:
3595:
3588:
3585:
3581:
3576:
3529:
3527:
3523:
3518:
3508:
3503:
3497:
3482:
3480:
3476:
3472:
3471:paramagnetism
3468:
3458:
3445:
3440:
3435:
3428:
3420:
3411:
3403:
3400:
3388:
3358:
3349:
3346:
3337:
3334:
3331:
3328:
3314:
3306:
3301:
3290:
3286:
3278:
3271:
3265:
3259:
3246:
3237:
3228:
3221:
3217:
3213:
3204:
3197:
3193:
3185:
3170:
3138:
3129:
3122:
3113:
3109:
3088:
3065:
3056:
3049:
3045:
3041:
3032:
3023:
3016:
3014:
3001:
2997:
2990:
2981:
2977:
2975:
2948:
2935:
2931:
2922:
2913:
2906:
2886:
2882:
2877:
2859:
2851:
2848:
2845:
2831:
2821:
2819:
2815:
2810:
2806:
2793:
2785:
2777:
2763:
2757:
2751:
2735:
2733:
2729:
2724:
2720:
2716:
2705:
2692:
2684:
2681:
2678:
2664:
2655:
2646:
2637:
2634:
2628:
2623:
2618:
2604:
2596:
2593:
2580:
2579:line integral
2576:
2572:
2567:
2561:
2556:
2536:
2533:
2508:
2498:
2494:
2487:
2484:
2478:
2465:
2461:
2448:
2420:
2411:
2393:
2385:
2382:
2369:
2364:
2360:
2356:
2347:
2341:
2332:
2329:
2325:
2320:
2315:
2311:
2307:
2303:
2302:magnetostatic
2299:
2295:
2290:
2277:
2267:
2264:
2250:
2223:
2214:
2210:
2206:
2202:
2193:
2184:
2182:
2178:
2152:
2148:
2142:
2139:
2131:
2127:
2126:
2125:
2122:
2109:
2106:
2087:
2083:
2079:
2074:
2060:
2051:
2046:
2042:
2041:ferromagnetic
2037:
2019:
2016:
2008:
1994:
1989:
1973:
1970:
1956:
1953:
1941:therefore is
1939:
1934:
1929:
1922:
1904:
1898:
1875:
1859:
1850:
1845:
1838:
1833:
1816:
1809:
1802:
1796:
1781:
1767:
1759:
1753:
1752:Magnetization
1743:
1741:
1737:
1736:magnetometers
1731:
1721:
1719:
1715:
1714:Bohr magneton
1710:
1703:
1702:
1693:
1684:
1668:
1663:
1661:
1657:
1653:
1649:
1645:
1641:
1637:
1632:
1606:
1595:
1584:
1581:
1577:
1573:
1559:
1527:
1516:
1505:
1502:
1498:
1494:
1491:
1488:
1483:
1472:
1463:
1455:
1451:
1447:
1443:
1438:
1436:
1432:
1428:
1424:
1419:
1406:
1389:
1375:
1366:
1360:
1352:
1340:
1338:
1334:
1330:
1326:
1316:
1312:
1299:
1291:
1287:
1272:
1248:
1240:
1236:
1221:
1197:
1189:
1185:
1170:
1146:
1143:
1126:
1121:
1116:
1112:
1109:
1103:
1097:
1096:
1073:
1065:
1052:
1048:
1044:
1029:
1027:
1023:
1019:
1015:
1011:
1007:
1003:
999:
995:
991:
987:
983:
978:
974:
971:
967:
963:
959:
957:
952:
948:
939:
936:
933:
931:
927:
924:
920:
917:
915:
908:
905:
901:
898:
896:
892:
888:
884:
878:
873:
869:
866:of a current
865:
859:
854:
844:
839:
837:
832:
830:
825:
824:
822:
821:
814:
811:
809:
806:
804:
801:
799:
796:
794:
791:
789:
786:
784:
781:
779:
776:
774:
771:
769:
766:
764:
761:
759:
756:
754:
751:
749:
746:
744:
741:
739:
736:
734:
731:
729:
726:
724:
721:
719:
716:
714:
711:
709:
706:
704:
701:
699:
696:
694:
691:
689:
686:
684:
681:
679:
676:
674:
671:
669:
666:
664:
661:
659:
656:
654:
651:
649:
646:
644:
641:
639:
636:
635:
629:
628:
621:
618:
616:
613:
611:
608:
606:
603:
601:
598:
596:
593:
591:
588:
586:
583:
582:
579:
574:
573:
566:
563:
561:
558:
556:
553:
551:
548:
546:
543:
541:
538:
536:
533:
531:
528:
526:
523:
521:
518:
516:
513:
511:
508:
506:
503:
501:
498:
497:
494:
489:
488:
481:
478:
476:
473:
471:
468:
466:
463:
461:
458:
456:
453:
451:
448:
446:
443:
441:
438:
436:
435:Joule heating
433:
431:
428:
426:
423:
421:
418:
416:
413:
411:
408:
406:
403:
401:
398:
396:
393:
391:
388:
387:
384:
379:
378:
371:
368:
366:
363:
361:
358:
356:
353:
351:
350:Lorentz force
348:
346:
343:
341:
338:
336:
333:
331:
328:
326:
323:
321:
318:
316:
313:
311:
308:
306:
303:
301:
298:
296:
293:
291:
288:
286:
283:
281:
278:
277:
274:
269:
268:
261:
258:
256:
253:
251:
250:Magnetization
248:
246:
243:
241:
238:
236:
235:Magnetic flux
233:
231:
228:
226:
223:
221:
218:
216:
213:
211:
208:
207:
204:
199:
198:
191:
188:
186:
183:
181:
178:
176:
173:
171:
168:
166:
163:
161:
158:
156:
153:
151:
148:
146:
143:
141:
140:Electric flux
138:
136:
133:
131:
128:
126:
123:
121:
118:
116:
113:
111:
108:
106:
103:
102:
99:
94:
93:
88:
85:
83:
80:
78:
77:Computational
75:
73:
70:
68:
65:
63:
60:
58:
55:
54:
53:
52:
48:
44:
43:
40:
37:
36:
32:
31:
19:
9885:
9879:
9855:. Retrieved
9850:
9841:
9832:
9822:
9802:
9795:
9771:
9764:
9750:
9740:
9716:
9709:
9685:
9678:
9669:
9660:
9640:
9622:
9598:
9591:
9567:
9560:
9550:November 24,
9548:. Retrieved
9534:
9530:
9490:
9483:
9464:
9458:
9433:
9430:Am. J. Phys.
9428:
9422:
9402:
9356:
9334:
9305:
9296:
9274:
9222:
9218:
9212:
9200:. Retrieved
9190:
9152:
9143:
9119:
8745:
8687:
8630:diamagnetism
8624:molecule, CO
8578:ground state
8571:paramagnetic
8559:energy state
8556:
8546:energy state
8534:ground state
8531:
8520:
8495:
8492:
8454:
8448:is electron
8444:
8356:
8334:
8309:
8299:
8151:
8005:
7999:
7962:
7959:
7734:
7718:
7696:
7666:
7662:
7639:
7591:half-integer
7580:
7500:
7407:
7244:
7236:mass density
7151:
7079:
6992:
6959:
6953:
6931:
6927:
6924:
6920:
6916:
6909:
6905:
6898:
6894:
6891:
6701:
6518:
6510:
6297:
6111:
6081:
6008:
5916:
5906:
5900:
5328:
5250:
5123:
5116:
5103:
5087:
5013:
4999:
4657:
4651:
4277:
4268:
4191:
4182:
4179:
4017:
4001:
3992:
3968:
3711:
3530:
3516:
3513:
3479:diamagnetism
3464:
3312:
3299:
3296:
3284:
3276:
3269:
3263:
3260:
3089:
2949:
2878:
2833:
2811:
2807:
2761:
2755:
2749:
2746:
2711:
2662:
2651:
2632:
2626:
2619:
2565:
2559:
2456:
2446:
2367:
2352:
2345:
2327:
2318:
2314:irrotational
2306:ferromagnets
2291:
2248:
2221:
2204:
2198:
2173:
2150:
2129:
2123:
2058:
2049:
2038:
1992:
1937:
1927:
1920:
1857:
1848:
1843:
1836:
1831:
1765:
1761:
1733:
1730:magnetometer
1711:
1700:
1691:
1664:
1633:
1439:
1420:
1341:
1322:
1313:
1124:
1117:
1113:
1107:
1101:
1094:
1093:
1043:pseudovector
1040:
984:, including
979:
975:
955:
954:
950:
944:
937:
934:
895:SI unit
886:
871:
867:
863:
595:Four-current
530:Linear motor
415:Electrolysis
295:Eddy current
255:Permeability
224:
175:Polarization
170:Permittivity
9890:Brady Haran
9202:19 February
8647:molecule, H
8609:molecule, O
8582:diamagnetic
7690:, with the
7680:10 J/T
6958:called the
3834:) so that:
3305:free energy
2747:The torque
2163:10 H/m
1724:Measurement
1646:, and G is
1640:centimeters
1636:statamperes
1540: (ESU)
1468: statA
1421:where N is
988:, and some
565:Transformer
395:Capacitance
320:Faraday law
115:Coulomb law
57:Electricity
9905:Categories
9232:1507.07956
9161:. p.
8677:electrons
8645:dihydrogen
8511:See also:
8452:, and the
8325:See also:
8155:precession
8000:equatorial
7770:, is then
7721:bar magnet
7703:hydrogen-1
7699:vector sum
7644:, such as
7616:(assuming
7604:(assuming
7555:where the
6948:See also:
6035:field as:
5277:such that
5197:such that
5099:quadrupole
5082:See also:
4174:See also:
3500:See also:
2828:See also:
2622:solenoidal
2577:becomes a
2205:fictitious
1756:See also:
1492:3.33564095
1329:base units
1037:Definition
632:Scientists
480:Waveguides
460:Resistance
430:Inductance
210:Ampère law
9916:Magnetism
9722:Macmillan
9537:: 39â52.
8778:(10
8752:magnitude
8680:Spin-only
8673:Number of
8412:ℏ
8397:μ
8380:−
8348:magnetism
8336:Electrons
8251:×
8237:γ
8233:λ
8228:−
8213:×
8174:γ
8114:−
8096:⋯
8063:−
8054:⋯
8039:−
8030:−
8018:−
7936:μ
7917:−
7807:μ
7725:electrons
7684:direction
7669:magnitude
7531:μ
7486:μ
7433:μ
7383:ρ
7351:ρ
7295:ρ
7288:×
7274:∭
7197:ρ
7191:×
7176:∭
7125:×
7116:μ
7105:×
7034:γ
7018:so that:
7006:γ
6858:δ
6844:π
6800:−
6789:⋅
6783:^
6768:^
6745:π
6732:μ
6669:δ
6655:π
6646:−
6611:−
6600:⋅
6594:^
6579:^
6556:π
6443:−
6405:⋅
6375:π
6360:ψ
6357:∇
6354:−
6243:−
6205:⋅
6175:π
6162:μ
6146:×
6143:∇
6051:∭
5967:π
5954:⋅
5929:ψ
5861:×
5847:∭
5751:×
5737:π
5724:μ
5646:ρ
5562:−
5530:ρ
5524:∫
5518:π
5478:ψ
5437:−
5397:∫
5391:π
5378:μ
5307:×
5304:∇
5234:ψ
5231:∇
5228:−
5042:×
5023:τ
4962:×
4956:^
4942:⋅
4924:×
4918:^
4901:^
4869:⋅
4848:^
4834:−
4819:×
4801:×
4795:^
4766:×
4748:×
4742:^
4698:π
4684:μ
4623:^
4612:⋅
4588:^
4577:⋅
4556:^
4542:−
4524:⋅
4503:^
4483:^
4472:⋅
4433:^
4422:⋅
4362:π
4348:μ
4234:⋅
4214:∇
4120:−
4109:⋅
4103:^
4088:^
4070:π
4057:μ
3920:−
3909:⋅
3903:^
3888:^
3870:π
3819:^
3657:−
3619:⋅
3589:π
3526:multipole
3467:magnetism
3461:Magnetism
3426:∂
3418:∂
3412:−
3359:⋅
3350:−
3335:−
3229:⋅
3226:∇
3218:−
3205:×
3202:∇
3194:×
3126:∇
3123:⋅
3057:⋅
3054:∇
3046:−
3033:⋅
3020:∇
3002:×
2994:∇
2991:×
2923:⋅
2910:∇
2860:⋅
2852:−
2818:Resonance
2786:×
2774:τ
2509:×
2495:∭
2431:μ
2273:ℓ
2233:ℓ
2181:electrons
2084:μ
1957:∭
1807:Δ
1794:Δ
1758:Remanence
1673:and area
1642:, erg is
1596:⋅
1582:−
1517:⋅
1503:−
1495:×
1473:⋅
1376:⋅
1353:⋅
1284:∂
1269:∂
1260:^
1249:−
1233:∂
1218:∂
1209:^
1198:−
1182:∂
1167:∂
1158:^
1147:−
1074:×
1062:τ
1006:electrons
998:molecules
986:the Earth
930:Dimension
788:Steinmetz
718:Kirchhoff
703:Jefimenko
698:Hopkinson
683:Helmholtz
678:Heaviside
540:Permeance
425:Impedance
165:Insulator
160:Gauss law
110:Conductor
87:Phenomena
82:Textbooks
62:Magnetism
9892:for the
9748:(1949).
9638:(2006).
9573:Springer
9400:(1975).
9379:40251748
9333:(1962).
9059:See also
8947:deuteron
8805:electron
8774:Magnetic
8769:Particle
8675:unpaired
8634:orbitals
8607:dioxygen
8538:isotopes
8527:neutrons
8010:values:
7658:electron
7610:electron
7157:velocity
6914:, where
5676:′
5592:′
5571:′
5543:′
5467:′
5446:′
5418:′
5091:monopole
4016:, where
4007:10
2881:gradient
2654:solenoid
2209:polarity
1716:and the
1638:, cm is
1450:Gaussian
1018:neutrons
813:Wiechert
768:Poynting
658:Einstein
505:DC motor
500:AC motor
335:Lenz law
120:Electret
9438:Bibcode
9257:1115862
9237:Bibcode
9034:
9022:
9014:â10.746
8998:
8986:
8940:
8928:
8920:â44.904
8904:
8892:
8875:neutron
8868:
8856:
8832:
8820:
8638:isotope
8544:. Each
8523:protons
8457:-factor
8438:is the
8293:is the
7998:or the
7965:integer
7880:is the
7871:-factor
7865:is the
7854:is the
7624:). See
7620:of the
7608:of the
7587:integer
7560:-factor
7401:is the
7234:is the
6984:precess
6966:in the
6936:is the
5910:is the
5894:is the
5634:is the
3734:is the
3522:dipolar
3387:entropy
3385:is the
2569:is the
2553:is the
2462:of the
2422:Moment
2312:by the
2179:of the
2124:where:
1931:is the
1706:
1688:
1591: A
1512: A
1440:In the
1014:protons
982:planets
798:Thomson
773:Ritchie
763:Poisson
748:Neumann
743:Maxwell
738:Lorentz
733:LiĂŠnard
663:Faraday
648:Coulomb
475:Voltage
450:Ohm law
72:History
9857:11 May
9810:
9783:
9728:
9697:
9648:
9610:
9579:
9502:
9471:
9410:
9377:
9367:
9285:
9255:
9169:
9131:
9005:helion
8978:15.046
8969:triton
8884:â9.662
8848:14.106
8839:proton
8682:moment
8657:ortho-
8655:or an
8429:where
8289:where
8135:
8126:
8102:
8093:
8081:
8072:
8060:
8051:
8027:
7873:, and
7867:LandĂŠ
7850:where
7682:. The
7673:â9.284
7622:proton
7612:) and
7458:where
7334:where
7230:where
7145:where
7055:where
6976:torque
5890:where
5798:where
5612:where
5095:dipole
4649:where
4266:where
3712:where
3502:Dipole
3381:where
3303:, the
3181:dipole
3105:dipole
2816:. See
2624:field
2549:where
2406:where
2353:After
2316:field
2170:Models
2138:teslas
2032:where
1988:magnet
1917:where
1829:where
1763:field
1615:
1612:
1536:
1533:
1452:, and
1435:energy
1423:newton
1333:ampere
1091:where
1047:torque
1004:(e.g.
970:torque
962:magnet
958:moment
949:, the
900:Ampere
783:Singer
778:Savart
758:Ărsted
723:Larmor
713:Kelvin
668:Fizeau
638:Ampère
560:Stator
67:Optics
9777:Wiley
9527:(PDF)
9279:(PDF)
9253:S2CID
9227:arXiv
9047:â0 00
9043:(He)
9007:(He)
8956:4.330
8953:â0 00
8735:5.92
8727:4.90
8719:3.87
8711:2.83
8703:1.73
8653:para-
8475:2.002
6009:Here
2732:below
2719:below
2296:(see
1648:gauss
1431:joule
1427:tesla
1337:meter
1327:(SI)
1319:Units
994:stars
990:moons
904:meter
808:Weber
803:Volta
793:Tesla
708:Joule
693:Hertz
688:Henry
673:Gauss
555:Rotor
9859:2012
9808:ISBN
9781:ISBN
9726:ISBN
9695:ISBN
9646:ISBN
9608:ISBN
9577:ISBN
9552:2012
9500:ISBN
9469:ISBN
9408:ISBN
9375:OCLC
9365:ISBN
9283:ISBN
9204:2016
9167:ISBN
9129:ISBN
8975:â0 0
8971:(H)
8958:7346
8949:(H)
8913:(Îź)
8911:muon
8881:0 00
8877:(n)
8845:â0 0
8841:(H)
8815:.764
8807:(e)
8790:Spin
8643:The
8620:The
8605:The
8525:and
8515:and
8501:spin
8450:spin
8329:and
7963:The
7902:atom
7787:atom
7756:atom
7688:spin
7650:spin
7628:and
7589:(or
7583:spin
7572:spin
7374:and
6923:) =
6112:The
5820:is:
3473:and
3166:loop
2969:loop
2902:loop
2765:is:
2728:spin
1841:and
1769:as:
1644:ergs
1016:and
728:Lenz
653:Davy
643:Biot
9756:270
9539:doi
9446:doi
9245:doi
9181:is
9163:200
9016:174
9011:0 0
8980:094
8922:478
8917:0 0
8850:067
8813:284
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8477:319
8314:eff
8223:eff
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7675:764
7652:of
6998:or
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5921:is
4198:is
3287:= 0
3279:= 0
1566:erg
1454:EMU
1446:ESU
1442:CGS
1277:int
1226:int
1175:int
1128:int
1008:);
953:or
945:In
910:In
753:Ohm
9907::
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9775:.
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7660:.
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6990:.
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6897:=
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2636:.
2557:,
2331:.
2165:).
2159:4Ď
1720:.
1709:.
1692:IA
1679:IA
1667:SI
1662:.
1656:cm
1578:10
1506:14
1499:10
1479:cm
1448:,
1028:.
1000:;
992:,
9896:.
9880:Îź
9878:"
9861:.
9816:.
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8300:m
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7895:m
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7875:Îź
7869:g
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7860:g
7852:j
7835:)
7832:1
7829:+
7826:j
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7819:j
7811:B
7800:J
7796:g
7792:=
7781:m
7750:m
7678:Ă
7598:ħ
7576:g
7568:g
7564:g
7558:g
7543:,
7539:L
7528:2
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7518:g
7515:=
7511:m
7466:e
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7430:2
7426:e
7421:=
7417:m
7387:Q
7361:v
7355:Q
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7318:V
7314:d
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7299:Q
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7232:Ď
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7101:r
7097:=
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7043:,
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7027:m
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6932:r
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6688:.
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6665:m
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6133:r
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6068:.
6065:V
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6055:M
6048:=
6044:m
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5936:r
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5311:A
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4837:2
4829:1
4824:m
4816:)
4811:2
4806:m
4791:r
4784:(
4781:+
4776:2
4771:m
4763:)
4758:1
4753:m
4738:r
4731:(
4727:[
4718:4
4713:|
4707:r
4702:|
4695:4
4688:0
4680:3
4674:=
4670:F
4658:r
4637:,
4633:]
4629:)
4619:r
4607:2
4602:m
4597:(
4594:)
4584:r
4572:1
4567:m
4562:(
4552:r
4545:5
4539:)
4534:2
4529:m
4519:1
4514:m
4509:(
4499:r
4492:+
4489:)
4479:r
4467:2
4462:m
4457:(
4452:1
4447:m
4442:+
4439:)
4429:r
4417:1
4412:m
4407:(
4402:2
4397:m
4391:[
4382:4
4377:|
4371:r
4366:|
4359:4
4352:0
4344:3
4338:=
4335:)
4330:2
4325:m
4320:,
4315:1
4310:m
4305:,
4301:r
4297:(
4293:F
4281:1
4278:m
4272:1
4269:B
4254:,
4250:)
4244:1
4239:B
4229:2
4224:m
4218:(
4211:=
4207:F
4195:2
4192:m
4186:1
4183:m
4155:.
4147:3
4142:|
4136:r
4131:|
4124:m
4117:)
4113:m
4100:r
4094:(
4085:r
4079:3
4067:4
4061:0
4051:=
4048:)
4044:r
4040:(
4036:B
4021:0
4018:Îź
4013:m
4011:/
4009:H
4005:Ă
4002:Ď
4000:4
3996:0
3993:Îź
3978:B
3955:.
3947:3
3942:|
3936:r
3931:|
3924:m
3917:)
3913:m
3900:r
3894:(
3885:r
3879:3
3867:4
3863:1
3858:=
3855:)
3851:r
3847:(
3843:H
3816:r
3809:|
3804:r
3799:|
3795:=
3791:r
3769:r
3747:r
3721:H
3698:,
3694:)
3685:3
3680:|
3674:r
3669:|
3663:m
3649:5
3644:|
3638:r
3633:|
3627:)
3623:r
3615:m
3611:(
3607:r
3603:3
3596:(
3586:4
3582:1
3577:=
3574:)
3570:r
3566:(
3562:H
3540:m
3517:m
3446:.
3441:T
3436:|
3429:B
3421:F
3404:=
3401:m
3391:T
3383:S
3368:B
3363:d
3354:M
3347:T
3343:d
3338:S
3332:=
3329:F
3325:d
3313:M
3308:F
3300:B
3285:B
3277:B
3270:B
3264:m
3247:.
3243:m
3238:)
3233:B
3222:(
3214:)
3209:B
3198:(
3190:m
3186:+
3176:F
3171:=
3161:F
3139:.
3135:B
3130:)
3119:m
3114:(
3110:=
3100:F
3071:m
3066:)
3061:B
3050:(
3042:)
3037:B
3029:m
3024:(
3017:=
3006:B
2998:)
2987:m
2982:(
2978:=
2964:F
2936:.
2932:)
2927:B
2919:m
2914:(
2907:=
2897:F
2864:B
2856:m
2849:=
2846:U
2836:U
2794:.
2790:B
2782:m
2778:=
2762:B
2756:m
2750:Ď
2693:.
2689:S
2685:I
2682:N
2679:=
2675:m
2663:S
2658:N
2633:D
2627:B
2605:,
2601:S
2597:I
2594:=
2590:m
2566:j
2560:r
2551:Ă
2537:,
2534:V
2530:d
2525:)
2521:r
2517:(
2513:j
2505:r
2499:V
2488:2
2485:1
2479:=
2475:m
2452:S
2447:I
2408:S
2394:,
2390:S
2386:I
2383:=
2379:m
2368:I
2346:B
2328:E
2319:H
2278:.
2268:p
2265:=
2261:m
2249:m
2218:p
2161:Ă
2154:0
2151:Îź
2144:V
2140:.
2133:r
2130:B
2110:,
2107:V
2102:r
2097:B
2088:0
2080:1
2075:=
2071:m
2059:m
2053:r
2050:B
2034:V
2020:,
2017:V
2013:M
2009:=
2005:m
1993:M
1974:,
1971:V
1967:d
1961:M
1954:=
1950:m
1938:m
1928:V
1926:d
1921:m
1919:d
1905:,
1899:V
1895:d
1888:m
1883:d
1876:=
1872:M
1861:.
1858:V
1856:Î
1849:V
1847:Î
1844:V
1837:V
1835:Î
1832:m
1817:,
1810:V
1803:V
1797:V
1789:m
1782:=
1778:M
1766:M
1701:c
1696:/
1675:A
1671:I
1660:s
1658:â
1607:2
1602:m
1585:3
1574:=
1569:G
1560:1
1528:2
1523:m
1489:=
1484:2
1464:1
1407:,
1401:T
1396:J
1390:=
1384:T
1379:m
1373:N
1367:=
1361:2
1357:m
1350:A
1300:.
1292:z
1288:B
1273:U
1256:z
1241:y
1237:B
1222:U
1205:y
1190:x
1186:B
1171:U
1154:x
1144:=
1140:m
1125:U
1108:m
1102:B
1095:Ď
1078:B
1070:m
1066:=
1012:(
938:I
935:L
923:A
921:â
919:m
902:-
887:m
874:.
872:a
868:I
864:m
842:e
835:t
828:v
20:)
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