389:
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1435:
inside the solenoid produces an electric field both inside and outside the solenoid, in the same way in which a charge distribution produces an electric field both inside and outside the distribution. In this sense the information from inside and outside is mediated by the electric field which must
1808:
What? Do you mean to tell me that I can tell you how much magnetic field there is inside of here by measuring currents through here and here – through wires which are entirely outside – through wires in which there is no magnetic field... In quantum mechanical interference experiments there can be
1315:
526:
251:
1154:
1366:, the result of the Maxwell-Lodge effect, like the Aharonov-Bohm effect, seems contradictory. In fact, even though the magnetic field is zero outside the solenoid and the electromagnetic radiation is negligible, a test charge experiences the presence of an electric field.
326:
1188:
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158:
1014:
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situations in which classically there would be no expected influence whatever. But nevertheless there is an influence. Is it action at distance? No, A is as real as B-realer, whatever that means
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Resuming the original definition of
Maxwell on the potential vector, according to which is a vector that its circuitation along a closed curve is equal to the flow of
1867:
1712:
1558:
270:
636:
891:
But if the current changes very slowly, one finds oneself in an almost stationary situation in which the radiative effects are negligible and therefore, excluding
93:
1483:, if you do not want to use the potential vector, which in the classical context has always been considered a mathematical aid, unlike the quantum case, in which
1369:
The question arises as to how the information on the presence of the magnetic field from inside the solenoid reaches the electric charge. In terms of the fields
711:
656:
610:
590:
570:
550:
1310:{\displaystyle \mathbf {E} 2\pi r=-\pi a^{2}{\frac {d\mathbf {B} }{dt}}\quad \Rightarrow \quad \mathbf {E} =-{\frac {a^{2}}{2r}}{\frac {d\mathbf {B} }{dt}}}
521:{\displaystyle \int _{S}\mathbf {B} \cdot d\mathbf {S} =\int _{S}\nabla \times \mathbf {A} \cdot d\mathbf {S} =\oint _{l}\mathbf {A} \cdot d\mathbf {l} }
246:{\displaystyle {\begin{cases}\nabla \times \mathbf {E} &=-{\dfrac {\partial \mathbf {B} }{\partial t}}\\\nabla \cdot \mathbf {B} &=0\end{cases}}}
1149:{\displaystyle \int _{l}\mathbf {E} \cdot dl=-{\frac {d}{dt}}\int _{S}{\mathbf {B} \cdot dS}=-{\frac {d}{dt}}\int _{\pi a^{2}}{\mathbf {B} \cdot dS}}
774:
337:
1824:
G. Rousseaux, R. Kofman, O. Minazzoli (2008). "The
Maxwell-Lodge effect: significance of electromagnetic potentials in the classical theory".
1669:
G. Rousseaux, R. Kofman, O. Minazzoli (2008). "The
Maxwell-Lodge effect: significance of electromagnetic potentials in the classical theory".
1515:
G. Rousseaux, R. Kofman, O. Minazzoli (2008). "The
Maxwell-Lodge effect: significance of electromagnetic potentials in the classical theory".
1909:
1731:
1647:
888:
must also change, producing electromagnetic waves in the surrounding space that can induce an e.m.f. outside the solenoid.
21:
1960:
1439:
From the calculations it seems evident that the source can be considered either the variation of the potential vector
1354:
Bearing in mind that the concept of field was introduced into physics to ensure that actions on objects are always
1955:
257:
716:
44:
50:
The term appeared in the scientific literature in a 2008 article, referring to an article of 1889 by physicist
101:
661:
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321:{\displaystyle \mathbf {E} =-\mathbf {\nabla } \phi -{\frac {\partial \mathbf {A} }{\partial t}}}
261:
40:
is practically static inside and null outside. It can be considered a classical analogue of the
1876:
1573:
41:
1934:
1896:
1841:
1791:
1756:
1686:
1593:
1532:
615:
1774:
D. Goodstein, J. Goodstein (2000). "Richard
Feynman and the History of Superconductivity".
1633:
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1359:
69:
25:
1436:
be continuous over all space due to the
Maxwell equations and their boundary condition.
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we can calculate the induced e.m.f., as Lodge did in his 1889 article, considering
51:
388:
1845:
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1536:
1363:
1358:, i.e. by contact (direct and mediated by a field) and not by remote action, as
830:{\displaystyle \mathbf {A} (r)={\frac {1}{2}}a^{2}{\frac {\mathbf {B} }{r}}}
1795:
964:
952:
1910:"Riscoprire il potenziale vettore per ambientarlo nella scuola superiore"
1732:"Riscoprire il potenziale vettore per ambientarlo nella scuola superiore"
552:
the closed line around the solenoid, or convenience a circumference, and
377:{\displaystyle \mathbf {E} =-{\frac {\partial \mathbf {A} }{\partial t}}}
29:
47:, where instead the field is exactly static inside and null outside.
977:
It is possible to make calculations without referring to the field
1929:
1877:"On an Electrostatic Field produced by varying Magnetic Induction"
1751:
1574:"On an Electrostatic Field produced by varying Magnetic Induction"
1008:. Indeed, in the framework of Maxwell equations as written above:
387:
1611:
J. C. Maxwell (1873). "A treatise on electricity and magnetism".
1343:
is practically null in places where the e.m.f. manifests itself.
970:
A module as a function of the distance from the solenoid's center
958:
B module as a function of the distance from the solenoid's center
392:
Solenoid and B field with the flow through a surface S of base l
1461:, if you choose to introduce it, or that of the magnetic field
418:
through the surface having the above curve as its edge, i.e.
239:
1908:
Sara
Barbieri, Michela Cavinato e Marco Giliberti (2013).
1730:
Sara
Barbieri, Michela Cavinato e Marco Giliberti (2013).
658:, the surface crossing it is subjected to a magnetic flux
863:
constant, which means, due to (1), at constant current.
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Consider an infinite solenoid (ideal solenoid) with
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95:flows. The magnetic field inside the solenoid is,
87:
1413:the explanation is very simple: the variation of
1648:"The external magnetic field of a long solenoid"
1487:proclaimed its existence as a physical reality.
66:turns per length unit, through which a current
145:while the field outside the solenoid is null.
841:From (2) we have that the e.m.f. is null for
8:
1866:: CS1 maint: multiple names: authors list (
1711:: CS1 maint: multiple names: authors list (
1557:: CS1 maint: multiple names: authors list (
913:, the only possible cause of the e.m.f. is
866:On the other hand, if the current changes,
761:{\displaystyle C(l)=2\pi r\mathbf {A} (r)}
32:in which current changes slowly, feels an
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331:that without electric charges reduces to
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1182:negligible outside the solenoid. Thus
134:{\displaystyle \mathbf {B} =\mu nI(t)}
686:{\displaystyle \pi a^{2}\mathbf {B} }
7:
1321:This doesn't avoid the problem that
467:
384: (2)
365:
355:
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14:
1615:. Oxford: Clarendon press: 27–28.
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1826:The European Physical Journal D
1671:The European Physical Journal D
1517:The European Physical Journal D
1251:
1247:
1001:{\displaystyle \mathbf {A} (r)}
937:{\displaystyle \mathbf {A} (r)}
693:which is equal to circuitation
612:the radius of the solenoid and
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995:
989:
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755:
749:
729:
723:
128:
122:
82:
76:
1:
1476:{\displaystyle \mathbf {B} }
1454:{\displaystyle \mathbf {A} }
1428:{\displaystyle \mathbf {B} }
1406:{\displaystyle \mathbf {E} }
1384:{\displaystyle \mathbf {B} }
1336:{\displaystyle \mathbf {B} }
1175:{\displaystyle \mathbf {B} }
906:{\displaystyle \mathbf {B} }
881:{\displaystyle \mathbf {B} }
856:{\displaystyle \mathbf {B} }
411:{\displaystyle \mathbf {B} }
141: (1)
1939:10.1088/0143-0807/34/5/1209
1917:European Journal of Physics
1761:10.1088/0143-0807/34/5/1209
1739:European Journal of Physics
1719:Particularly at fig. 6 p. 6
1977:
1901:10.1088/1478-7814/10/1/320
1881:The Philosophical Magazine
1846:10.1140/epjd/e2008-00142-y
1691:10.1140/epjd/e2008-00142-y
1598:10.1088/1478-7814/10/1/320
1578:The Philosophical Magazine
1537:10.1140/epjd/e2008-00142-y
148:From the second and third
22:electromagnetic induction
256:and from definitions of
1628:Cite journal requires
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1385:
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1002:
938:
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707:
687:
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632:
631:{\displaystyle r>a}
606:
586:
566:
546:
522:
412:
393:
378:
322:
247:
135:
89:
1875:Oliver Lodge (1889).
1796:10.1007/s000160050035
1572:Oliver Lodge (1889).
1497:Principle of locality
1478:
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36:(e.m.f.) even if the
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592:as border. Assuming
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425:
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338:
271:
159:
102:
88:{\displaystyle I(t)}
70:
45:Aharonov–Bohm effect
18:Maxwell-Lodge effect
1893:1888PPSL...10..116L
1838:2008EPJD...49..249R
1788:2000PhP.....2...30G
1683:2008EPJD...49..249R
1658:on 4 February 2021.
1590:1888PPSL...10..116L
1529:2008EPJD...49..249R
572:the surface having
150:Maxwell's equations
34:electromotive force
20:is a phenomenon of
1961:1889 introductions
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1451:
1425:
1403:
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1333:
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998:
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768:. From that stems
758:
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262:electric potential
258:magnetic potential
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42:quantum mechanical
1305:
1283:
1245:
1108:
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803:
706:{\displaystyle l}
651:{\displaystyle l}
605:{\displaystyle a}
585:{\displaystyle l}
565:{\displaystyle S}
545:{\displaystyle l}
372:
316:
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1968:
1956:Electromagnetism
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1654:. Archived from
1652:fermi.la.asu.edu
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1818:Further reading
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1493:
1485:Richard Feynman
1463:
1462:
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1415:
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1393:
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1371:
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1360:Albert Einstein
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26:electric charge
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1905:
1887:(1): 469–479.
1872:
1832:(2): 249–256.
1819:
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1813:
1776:Phys. Perspect
1766:
1722:
1677:(2): 249–256.
1661:
1639:
1630:|journal=
1603:
1584:(1): 469–479.
1564:
1523:(2): 249–256.
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1362:feared in the
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1350:Interpretation
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38:magnetic field
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1200:
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800:
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312:
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24:in which an
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1364:EPR paradox
58:Description
1950:Categories
1782:(30): 45.
1503:References
1930:1303.5619
1804:118288008
1752:1303.5619
1261:−
1249:⇒
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