We show that the concept of electric current was elaborated only after the discovery by Oersted in 1820 of a connection between electricity and magnetism, and thanks to the subsequent work of Ampère. In his study of the interaction between a compass and an electric circuit, Ampère set up a crucial experiment when he put a compass above his Voltaic pile, and another one above the connecting wire. Indeed, this experiment supported his creation of a new physical quantity, independent of the nature of physical phenomena, identical in the pile and in the wire, and only characterized by its direction and its intensity. To the experimental definition of this physical quantity—the electric current—by the oriented deviation of a magnetic needle, Ampère added in his manuscripts the substance of the two present theoretical definitions of the intensity of the current, namely, the ratio of charge to time q/t, and the ratio of electromotive force to the conducting wire's resistance E/R.

1.
On the history of electricity in 18th century see
J. L.
Heilbron
,
Electricity in the 17th and 18th Centuries: A Study of Early Modern Physics
, 2nd ed. (
Dover Publications
,
New York
,
1999
).
On the history of electromagnetism, see
O.
Darrigol
,
Electrodynamics from Ampère to Einstein
(
Oxford U.P.
,
Oxford
,
2003
). A large part of the documents referred to in this paper are available on the website Ampère and the history of electricity (www.ampere.cnrs.fr) which gives access to Ampère publications, correspondence and archives, and presents a series of multimedia files on the history of electricity.
2.
W. N.
Cottingham
and
D. A.
Greenwood
,
Electricity and Magnetism
(
Cambridge U.P.
,
Cambridge
,
1991
), p.
31
.
3.
A.-M.
Ampère
, “
Expériences relatives à de nouveaux phénomènes électro-dynamiques
,”
Ann. Chim. Phys.
20
,
60
74
(
1822
).
4.

A Leyden jar is a glass jar with conducting metallic foils coating its inner and outer surfaces.

5.
A.
Volta
, “
On the electricity excited by the mere contact of conducting substances of different kinds
,”
Philos. Trans. R. Soc.
90
,
403
430
(
1800
) (original text in French); translated to English in Philos. Mag. 7, 289–311 (1800).
6.
On the reception of Volta battery, see
G.
Pancaldi
,
Volta: Science and Culture in the Age of Enlightenment
(
Princeton U.P.
,
Princeton, N.J.
,
2003
), chap. “Appropriating invention. The reception of the Voltaic battery in Europe.”
In France, C. J. Lehot was one of the few to take on Volta's thesis:
C. J.
Lehot
, “
Mémoire sur le galvanisme
,”
J. Phys. Chim. Hist. Nat.
52
,
135
149
(
1801
); a large extract of Lehot memoir is available in C. H. Wilkinson, Elements of Galvanism, in Theory and Practice, Vol. 1 (London, 1804), pp. 340–362.
7.
R. J.
Haüy
,
Elementary Treatise on Natural Philosophy
, Vol. 2 (
George Kearsley
,
London
,
1807
) [Traite elementaire de physique, Vol. 2 (Delance et Lesueur, Paris, 1803)].
8.
The word “battery” meant a battery of Leyden jars that could be discharged on one moment as a battery of cannons. For an early use of the denomination “pile” see:
W.
Nicholson
, “
Account of the new electrical or galvanic apparatus of sig. volta, and experiments performed with the same
,”
J. Nat. Philos. Chem. Arts.
4
,
179
187
(
1800
).
9.
W.
Nicholson
, Ibid.;
C. H.
Pfaff
, “
Notice des phénomènes d'attraction et de répulsion dépendant de la pile galvanique, observés par M. Ritter
,”
J. Phys. Chim. Hist. Nat.
53
,
152
155
(
1801
);
P.
Erman
, “
Sur les phénomènes électrométriques de la colonne de Volta
,”
J. Phys. Chim. Hist. Nat.
53
,
121
134
(
Barrau et Dumotiez, 1801
); other researches are described in J. Izarn, Manuel du Galvanisme (Longman, Hurst, Rees, Orme, and Brown, and R. Triphook, Paris, 1804) or G. J. Singer, Elements of Electricity and Electro-chemistry (London, 1814).
10.
E. G.
Robertson
, “
Nouvelles expériences sur le fluide galvanique
,”
Ann. Chim. (Paris)
37
,
132
150
(
1800
), p. 138. The potential difference between the ends of a closed-circuit battery was too weak to be detected by an electroscope, because the internal resistance of a Voltaic battery was much higher than the resistance of an external metallic conductor.
On what is measured by an electroscope, see
J. L.
Heilbron
,
Electricity in the 17th and 18th Centuries: A Study of Early Modern Physics
(
Dover Publications
,
Mineola, N.Y.
,
1999
), pp.
451
453
.
11.
R. J.
Haüy
, Ref. 7, p.
28
.
12.
Dictionnaire des sciences naturelles, Vol. 3 (
1816
), p.
115
.
13.
A.
Volta
, “
De l'électricité dite galvanique
,”
Ann. Chim. (Paris)
40
,
225
256
(
1801
), p. 227.
14.
On the history of the electrolysis of water, see
H.
Chang
,
Is Water H2O? Evidence, Realism and Pluralism
(
Springer
,
Dordrecht
,
2012
), chap. 2;
G.
Cuvier
, “
Rapport sur le galvanisme
,”
J. Phys. Chim. Hist. Nat.
52
,
318
321
(
1801
), p. 320;
P.
Erman
, Ref. 9, p. 129.
15.
Still in 1828 see the negative assessment of
Claude-Servais
Pouillet
,
Elémens de physique exp érimentale et de météorologie
, Vol. 1 (
Béchet jeune
,
Paris
,
1828
), p.
651
.
16.
H.
Davy
, “
An account of some Experiments made with the Galvanic apparatus of signor volta
,”
J. Nat. Philos. Chem. Arts.
4
,
275
281
(
1800
), p. 276.
17.
T.
von Grotthuss
, “
Memoir upon the decomposition of water, and of the Bodies which it holds in solution, by means of galvanic electricity
,”
Philos. Mag.
25
,
330
339
(
1806
).
18.
H.
Davy
, “
The Bakerian lecture, on some chemical agencies of electricity
,”
Philos. Mag.
28
,
3
18
, 104–119, 220–233 (
1807
);
H.
Davy
,
“Mémoire sur quelques effets chimiques de l'électricité,”
J. Phys. Chim. Hist. Nat.
64
,
422
461
(
1807
);
W. H.
Wollaston
, “
Experiments on the chemical production and agency of electricity
,”
Philos. Trans. R. Soc.
91
,
427
434
(
1801
);
W.
Henry
, “
Theory of excitement of Galvanic Electricity
,”
J. Nat. Philos. Chem. Arts.
35
,
259
271
(
1813
);
A.
Anderson
, “
On the decomposition of water in two or more separate vessels
,”
J. Nat. Philos. Chem. Arts.
30
,
183
189
(
1811
).
19.
G.
Cuvier
, Ref. 14.
20.
J. A.
Deluc
, “
Analysis of Galvanic pile. Part I
,”
J. Nat. Philos. Chem. Arts.
26
,
113
136
(
1810
);
on Deluc see
G.
Pancaldi
, “
Deluc, Davy, and the impact of the battery on natural philosophy
,” in
Jean-André Deluc Historian of Earth and Man
, edited by
J. L.
Heilbron
and
R.
Sigrist
(
Slatkine
,
Geneva
,
2011
), pp.
277
298
.
21.
G. J.
Singer
, “
Observations on some phenomena of electro-chemical decomposition
,”
J. Nat. Philos. Chem. Arts.
31
,
90
95
(
1812
);
Elements…, Ref. 9, pp. 204–206;
M.
Donovan
,
Essay on the Origin, Progress, and Present State of Galvanism
(
Hodges and McArthur
,
Dublin
,
1816
), p.
188
.
22.
L. J.
Gay-Lussac
and
L. J.
Thénard
,
Recherches Physico-Chimiques Faites Sur la Pile
, Vol. 1 (
Deterville
,
Paris
,
1811
), pp.
1
52
.
23.
G. J.
Singer
, Ref. 9, p.
430
.
24.
See
M.
von Marum
,
Description d'une Très-Grande Machine Électrique
(
Jean Enschedé et fils, et Jean van Walré
,
Haarlem
,
1785
); G. J. Singer, Ref. 9, pp. 204–206.
25.
T.
von Grotthuss
, Ref. 17, p.
335
.
26.
J. W.
Ritter
, “
Experiments on magnetism
,”
J. Nat. Philos. Chem. Arts.
8
,
184
186
(
1804
);
R.
Martins
, “
Oersted, Ritter and magnetochemistry
,” in
Hans Christian Ørsted and the Romantic Legacy in Science: Ideas, Disciplines, Practices
, edited by
R. M.
Brain
,
R. S.
Cohen
, and
O.
Knudsen
(
Springer
,
New York
,
2007
), pp.
339
385
;
R.
Martins
,
H.C. Ørsted's Theory of Force: An Unpublished Textbook in Dynamical Chemistry
, edited by
A. S.
Jacobsen
,
A. D.
Jackson
,
K.
Jelved
, and
H.
Kragh
(
Det Kongelige Danske Videnskabernes Selskab
,
Reitzel
,
2003
);
J. N.
Hachette
, “
Expérience sur le magnétisme de la pile électrique
,”
Correspond. l'École Polytech.
5
,
151
153
(
1805
).
27.
This Romagnosi experiment has been improperly considered at several occasions since 19th century as a prefiguration of Oersted's one, see
R.
Martins
, “
Romagnosi and Volta's Pile: Early difficulties in the interpretation of voltaic electricity
,” in
Nuova Voltiana: Studies on Volta and his Times
, edited by
F.
Bevilacqua
and
L.
Fregonese
, vol. 3 (
Hoepli
,
Milano
,
2001
), pp.
81
102
.
28.
A.
Boisgiraud
, “
On the action of the voltaic pile upon the magnetic needle
,”
Philos. Mag.
57
,
203
206
(
1821
).
29.
H. C.
Oersted
,
Experimenta Circa Effectum Conflictus Electrici in Acum Magneticam
(
Hafniae
,
Schultz
,
1820
);
fac-simile in
B.
Dibner
,
Oersted and the Discovery of Electromagnetism
(
Burndy Library
,
Norwalk, Connecticut
,
1961
), p. 23;
B.
Dibner
,
“Expériences sur l'effet du conflict électrique sur l'aiguille aimantée,”
Ann. Chim. Phys.
14
,
417
425
(
1820
);
B.
Dibner
,
“Expériences sur un effet que le courant de la Pile excite dans l'Aiguille aimantée,”
J. Phys. Chim. Hist. Nat.
91
,
72
78
(
1820
);
B.
Dibner
,
“Experiments on the effects of a current of electricity on the magnetic needle,”
Ann. Philos. (London)
16
,
273
276
(
1820
);
B.
Dibner
,
“Versuche über die wirkung des elektrischen conflicts auf die magnetnadel,”
Ann. Phys. (Leipzig)
66
,
295
304
(
1820
).
30.
The controversy began shortly after the announcement of the discovery:
H. C.
Oersted
, “
On electro-magnetism
,”
Ann. Philos.
2
,
321
337
(
1821
).
See
N.
Kipnis
, “
Chance in science: The discovery of electromagnetism by H.C. Oersted
,”
Sci. Educ.
14
,
1
28
(
2005
);
O. I.
Franken
,
H. C. Ørsted a Man of the Two Cultures
(
Bang & Olufsen
,
Birkerod
,
1981
);
K. L.
Caneva
, “
Colding, Oersted and the meaning of force
,”
Hist. Stud. Phys. Biol. Sci.
28
,
1
138
(
1977
);
R.
Martins
, “
Resistance to the discovery of electromagnetism: Oersted and the symmetry of the magnetic field
,” in
Volta and the History of Electricity
, edited by
F.
Bevilacqua
and
E.
Giannetto
(
Hoepli
,
Pavia, Milano
,
2003
), pp.
245
265
.
31.
H. C.
Oersted
, “
Experiments on the effects…
,” Ref. 29, p.
276
.
32.
H. C.
Oersted
, “
Expériences sur l'effet du conflit…
,” Ref. 29, p.
419
. Other examples of inaccurate translations: the ambiguous latin expression effectibus unius vel alterius vis electricae, rather accurately translated in English “effects of either of the electricities” (ordinary electricity or galvanism), became in French “action de l'un ou de l'autre pôle, considérés séparément” in Ann. Chim. Phys. or “forces d'attraction et de répulsion électrique” in J. Phys. Chim. Hist. Nat. These French mistranslations emphasized the weight of the electrostatic understanding of the Voltaic battery.
33.
Ibid., pp.
274
275
.
34.
Ibid., p.
273
. Johann Wilhelm Ritter was probably the main physicist alluded to by Oersted.
35.
H. C.
Oersted
, “
Sur la propagation de l'électricité
,”
J. Phys. Chim. Hist. Nat.
62
,
369
375
(
1806
).
36.
H. C.
Oersted
,
Ansicht der Chemischen Naturgesetze, Durch die Neueren Entdeckungen Gewonnen
(
Realschulbuchhandlung
,
Berlin
,
1812
);
H. C.
Oersted
,
Recherches sur l'identité des Forces Électriques et Chimiques
(
Paris
,
1813
); see an analysis of this account in Ann. Philos. (London) 13, 368–377; 456–463; 14, 47–50 (1819).
37.
H. C.
Oersted
, Recherches…, Ref. 36, pp.
236
238
.
38.
H. C.
Oersted
, Ref. 35, p.
372
.
39.
P.
Erman
, “
Extract of a memoir upon two new classes of galvanic conductors
,”
Philos. Mag.
28
,
297
304
(
1807
), p. 303.
40.
H. C.
Oersted
, Ref. 30, p.
321
.
41.
H. C.
Oersted
, “
Experiments…
,” Ref. 29, p.
274
.
42.
Ibid., p.
276
.
43.
See also Ref. 30, p.
323
.
44.
Ibid., p.
321
;
see also
M.
Faraday
, “
Historical Sketch of Electro-magnetism
,”
Ann. Philos. (London)
3
,
107
108
(
1822
).
45.
F.
Steinle
, “
Experiment, instrument und begriffsbildung: Ampère, das galvanometer und der stromkreis
,” in
Christoph Meinel, Instrument-Experiment. HistorischeStudien
(
GNT-Verlag
,
Berlin
,
2010
), pp.
98
108
.
46.

In the English translation, the title uses “current of electricity” while the body of the text uses “electric conflict.”

47.
Note of the editor
Jules
Joubert
,
Collection de Mémoires relatifs à la Physique
, Vol. 2, Mémoires sur l'électrodynamique, 1ère partie (
Paris
,
1885
), p.
2
.
48.
Oersted experiment was repeated on 19th August 1820 in Geneva by Gaspard de la Rive in the presence of François Arago (
A.
Pictet
, “
Bibliothèque universelle
,”
Sci. Arts
14
,
281
284
(
1820
)). The announcement was made by Arago at the Academy of sciences on September 4 (“Extraits des séances de l'académie royale des sciences,” Ann. Chim. Phys. 15, 78–82 (1820), p. 80); Ampère began to read his memoirs at the Academy of sciences on September 18 and 25. During the following weeks, Davy in England, Van Beck in Netherlands, Berzelius in Sweden, Erman in Germany, Gazzieri in Italy, etc. published memoirs in the wake of Oersted experiment.
49.
M.
Faraday
, “
Historical sketch of electro-magnetism
,”
Ann. Philos. (new series)
2
,
274
290
(
1821
).
50.
On Ampère first researches see
K.
Caneva
, “
Ampère, the etherians and the Oersted connexion
,”
Br. J. Hist. Sci.
13
,
121
138
(
1980
);
C.
Blondel
,
Ampère et la Création de l'électrodynamique
(
Bibliothèque nationale
,
Paris
,
1982
);
L. P.
Williams
, “
What were Ampère's earliest discoveries in electrodynamics?
,”
ISIS
74
,
492
508
(
1983
);
F.
Steinle
,
Exploratory Experiments. Ampère, Faraday and the Origins of Electrodynamics
(
University of Pittsburgh Press
,
Pittsburgh
,
2016
);
A.
Assis
and
J. P.
Chaib
,
Ampère's Electrodynamics
(
Apeiron
,
Montreal
,
2015
) https://amzn.com/1987980034 (with a translation of Ampère first memoir on electrodynamics and of his book Theory of Electrodynamic Phenomena, uniquely deduced from Experience, 1826).
51.
A.-M.
Ampère
, “
Mémoire […] sur les effets des courants électriques
,”
Ann. Chim. Phys.
15
,
59
76
, 170–218 (
1820
);
translation in A. Assis and J. P. Chaib, Ampère's Electrodynamics […], Ref. 50, pp.
289
320
.
52.
Archives Ampère, chemise 208bis, p. 89; “Mémoire […]” Ref. 51, p.
203
.
53.
Archives Ampère, chemise 205, pp.
2
, 8.
54.
J.-B.
Biot
,
Précis Élémentaire de Physique expérimentale
, Vol. 2, 3rd ed. (
Deterville
,
Paris
,
1824
), p.
773
.
55.
Letter from Ampère to Auguste de La Rive, 11th October 1822, in
Louis de
Launay
,
Correspondance du Grand Ampère
, Vol. 2 (
Paris
,
1936
), p.
610
. (http://www.ampere.cnrs.fr/correspondance/L1822-10-11-a.html).
56.
A.-M.
Ampère
, “Mémoire […]” Ref. 51, p.
65
.
This argument was supported in particular by G. J. Singer, Ref. 9, p.
430
.
It was taken on later on by
Auguste
de la Rive
, “
Mémoire sur quelques-uns des phénomènes que représente l'électricité voltaïque dans son passage à travers les conducteurs liquides
,”
Ann. Chim. Phys.
28
,
190
221
(
1825
), p. 193.
57.
A.-M.
Ampère
, “
Analyse des mémoires lus par M. Ampère à l'Académie des sciences, dans les séances des 18 et 25 septembre, des 9 et 30 octobre 1820
,”
Ann. Gen. Sci. Phys.
6
,
238
257
(
1820
), p. 247;
“Mémoire […]” Ref. 51, p. 72.
58.
A.-M.
Ampère
, “Mémoire […]” Ref. 51, p.
72
(highlighted by ourselves).
59.
A. M.
Ampère
, Ref. 3, p.
60
.
60.
It means around 12 couples, 30 cm × 30 cm, see
A.-M.
Ampère
, “
Réponse de M. Ampère à la lettre de M. Van Beck sur une nouvelle exp érience électro-magnétique
,”
J. Phys. Chim. Hist. Nat.
93
,
447
467
(
1821
), p. 448.
61.
Archives Ampère, chemise 208bis, p. 128; Letter from Ampère to X, 7 septembre 1821 (http://www.ampere.cnrs.fr/correspondance/L1821-09-07-a.html).
62.
A.-M.
Ampère
, Ref. 57, p.
240
.
63.
The experiment was described by Ampère in his “Mémoire […]” Ref. 51, pp.
66
-
68
, and in his later publications.
64.
F.
Steinle
, Ref. 50, pp.
110
112
.
65.

Archives Ampère, chemise 208bis, p. 101 (crossed off passage in the manuscript).

66.
Archives Ampère, chemise 205, p.
8
.
67.
Archives Ampère, chemise 208bis, p.
129
.
68.
A.-M.
Ampère
, “Mémoire […]” Ref. 51, pp.
197
198
(highlighted by ourselves).
69.
Ibid., p.
67
.
70.
Archives Ampère, chemise 205, p.
7
(“Potasse dissoute entre cuivre et zinc. Le contraire”) and p. 239.
71.
F.
Steinle
, Ref. 50, p.
98
(Archives Ampère, chemise 205, p. 239).
72.
G.
Cuvier
, Ref. 14, p.
321
;
C. J.
Lehot
, Ref. 6;
G. J.
Singer
, Ref. 9, p.
430
.
73.
Archives Ampère, chemise 208bis, p.
75
.
74.
F.
Arago
, “
Expériences relatives à l'aimantation du fer et de l'acier par l'action du courant voltaïque
,”
Ann. Chim. Phys.
15
,
93
103
(
1820
);
A.-M.
Ampère
, “Mémoire […]” Ref. 51, p.
197
.
75.

The electrolysis of water by electric discharges had been carried out by Martinus van Marum in 1802, Extrait d'une lettre […] sur la décomposition de l'eau à l'aide d'un nouvel appareil électrique, Ann. Chim. (Paris) 41, 77–78 (1802). Ampère planned to study the action on a magnetized needle of electrical discharges through a conducting wire but he does not seem to have obtained concluding results (Archives Ampère, chemise 205, 7–8).

76.

For an earlier use of the expressions courant électrique and circuit électrique, see, for example, P. Erman, Ref. 9, p. 181. The expression “galvanic current” was the most common together with “current of galvanic electricity,” “current of electricity,” “current of electrical fluid,” etc.

77.
Archives Ampère, chemise 162, p.
50
(Autumn
1820
).
78.
Archives Ampère, chemise 173, p.
125
(probably
1823
). The word conductibility characterised both the nature of the metal and the (supposed constant) diameter of the wire.
79.
A.-M.
Ampère
,
Théorie [mathématique] des Phénomènes Électrodynamiques
(
Méquignon-Marvis
,
Paris
,
1826
), p.
199
.
80.
M. R.
Stetzer
 et al, “
New insights into student understanding of complete circuits and the conservation of current
,”
Am. J. Phys.
81
,
134
143
(
2013
);
M.
Leone
, “
History of physics as a tool to detect the conceptual difficulties experienced by students: The case of simple electric circuits in primary education
,”
Sci. Educ.
23
,
923
953
(
2014
).
81.
A sequence of teaching based on this historical research has been led since several years by A. Benseghir at the Ferhat Abbas University of Setif (Algeria). For a pedagogical use of the controversy between Ampère and Biot, see
M.
Braga
,
A.
Guerra
, and
J. C.
Reis
, “
The role of historical-philosophical controversies in teaching sciences: The debate between Biot and Ampère
,”
Sci. Educ.
21
,
921
934
(
2012
).
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