We offer a conceptually straightforward and efficient way to formulate and solve problems on the electromagnetics of moving media based on a representation of Maxwell’s equations in terms of differential forms on spacetime together with junction conditions at moving interfaces. This framework is used to address several issues on the theoretical description underlying the interpretation of the Wilson–Wilson experiment.

1.
M.
Wilson
and
H. A.
Wilson
, “
On the electric effect of rotating a magnetic insulator in a magnetic field
,”
Proc. R. Soc. London, Ser. A
89
,
99
106
(
1913
).
2.
G. N.
Pellegrini
and
A. R.
Swift
, “
Maxwell’s equations in a rotating medium: Is there a problem?
Am. J. Phys.
63
,
694
705
(
1995
).
3.
W. C.
Röntgen
, “
Über die durch Bewegung eines im homogenen electrischen Felde befindlichen Dielectricums hervorgerufene electrodynamische Kraft
,”
Ann. Phys.
(Leipzig)
35
,
264
270
(
1888
);
W. C.
Röntgen
, “
Beschreibung des Apparates, mit welchem die Versuche über die electrodynamische Wirkung bewegter Dielectrica ausgeführt wurden
,”
Ann. Phys.
40
,
93
108
(
1890
);
A.
Eichenwald
, “
Über die magnetischen Wirkungen bewegter Körper im elektrostatischen Felde
,”
Ann. Phys.
11
,
1
30
(
1903
);
A.
Eichenwald
, “
Über die magnetischen Wirkungen bewegter Körper im elektrostatischen Felde
,”
Ann. Phys.
13
,
919
943
(
1904
).
4.
A.
Einstein
and
J.
Laub
, “
On the fundamental electromagnetic equations for moving bodies
,”
Ann. Phys.
(Leipzig)
26
,
532
540
(
1908
).
5.
J. B.
Hertzberg
,
S. R.
Bickman
,
M. T.
Hummon
,
D.
Krause
, Jr.
,
S. K.
Peck
, and
L. R.
Hunter
, “
Measurement of the relativistic potential difference across a rotating magnetic dielectric cylinder
,”
Am. J. Phys.
69
,
648
654
(
2001
).
6.
M. L.
Burrows
, “
Comment on ‘Maxwell’s equations in a rotating medium: Is there a problem?’ by G. N. Pellegrini and A. R. Swift
,”
Am. J. Phys.
65
,
929
931
(
1997
).
7.
T. A.
Weber
, “
Measurements on a rotating frame in relativity, and the Wilson and Wilson experiment
,”
Am. J. Phys.
65
,
946
953
(
1997
).
8.
C. T.
Ridgely
, “
Applying relativistic electrodynamics to a rotating material medium
,”
Am. J. Phys.
66
,
114
121
(
1998
).
9.
K. T.
McDonald
, “
The Wilson–Wilson experiment
,” ⟨www.physics.princeton.edu/mcdonald/examples/wilson.pdf⟩. We thank a referee for pointing out this article to us.
10.
F. W.
Hehl
and
Y. N.
Obukhov
,
Foundations of Classical Electrodynamics
(
Birkhäuser
,
Boston
,
2003
), p.
359
.
11.
H.
Amar
, “
Elementary application of differential forms to electromagnetism
,”
Am. J. Phys.
48
,
252
253
(
1980
).
12.
Y.
Hoshino
, “
An elementary application of exterior differential forms in quantum mechanics
,”
Am. J. Phys.
46
,
1148
1150
(
1978
).
13.
N.
Schleifer
, “
Differential forms as a basis for vector analysis–with applications to electrodynamics
,”
Am. J. Phys.
51
,
1139
1145
(
1983
).
14.
H.
Flanders
,
Differential Forms with Applications to the Physical Sciences
(
Dover
,
Mineola, NY
,
1989
).
15.
W. L.
Burke
,
Applied Differential Geometry
(
Cambridge U. P.
,
Cambridge
,
1985
).
16.
R. W. R.
Darling
,
Differential Forms and Connections
(
Cambridge U. P.
,
Cambridge
,
1994
).
17.
I. M.
Benn
and
R. W.
Tucker
,
An Introduction to Spinors and Geometry with Applications in Physics
(
Hilger
,
Bristol
,
1987
).
18.
All tensors in this article have dimensions constructed from the SI dimensions [M],[L],[T],[Q], where [Q] has the unit of coulombs. We adopt [g]=[L2],[G]=[j]=[Q],[F]=[Q]/[ϵ0], where the permittivity of free space ϵ0 has the dimensions [Q2T2M1L3] and c=1/ϵ0μ0 denotes the speed of light in vacuo. Note that with [g]=[L2], for p-forms α in n dimensions, we have [α]=[α][Ln2p].
19.
In regions where iVdṼ0, the medium has an acceleration.
20.
J.
Van Bladel
, “
Relativistic theory of rotating discs
,”
Proc. IEEE
61
,
260
268
(
1973
).
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