A solenoid is a coil wound many times on a cylinder of length greater than its diameter. Solenoids are mainly used as electromagnets, because a magnetic field is formed when current flows through a solenoid. The solenoid described in secondary school and university textbooks is a single-layered solenoid. Further, textbooks and papers focusing on education primarily describe the magnetic fields caused by infinite solenoids. However, most solenoids used in laboratory or daily life are finite solenoids with multiple layers to achieve a strong magnetic field. Examples include solenoid valves, Faraday rotators, and modulators.

1.
G. L.
Pollack
and
D. R.
Stump
,
Electromagnetism
(
Addison-Wesley
,
Boston
,
2001
).
2.
R. A.
Serway
and
J. W.
Jewett
,
Principles of Physics a Calculus-Based Text
(
Brooks Cole Pub. Co
.,
Boston
,
2014
).
3.
R.
Reitz
,
F. J.
Milford
, and
R. W.
Christy
,
Foundations of Electromagnetic Theory
(
Addison-Wesley
,
Boston
,
2008
).
4.
J. D.
Jackson
,
Classical Electrodynamics
(
John Wiley & Sons, Inc
.,
Hoboken
,
1998
).
5.
D. J.
Griffiths
,
Introduction to Electrodynamics
(
Prentice Hall
,
Upper Saddle River
,
1999
).
6.
B. B.
Dasgupta
, “
Magnetic field due to a solenoid
,”
Am. J. Phys.
52
,
258
(
1984
).
7.
V.
Namias
, “
On the magnetic field due to a solenoid of arbitrary cross section
,”
Am. J. Phys.
53
,
588
(
1985
).
8.
K.
Fillmore
, “
Magnetic field of a noncircular solenoid
,”
Am. J. Phys.
53
,
782
783
(
1985
).
9.
O.
Espinosa
and
V.
Slusarenko
, “
The magnetic field of an infinite solenoid
,”
Am. J. Phys.
71
,
953
954
(
2003
).
10.
R. M.
Duffy
and
R. P.
Netterfield
, “
Design of Faraday rotators and modulators
,”
Rev. Sci. Instrum.
55
,
743
746
(
1984
).
11.
R.
Ravaud
,
G.
Lemarquand
,
S.
Babic
,
V.
Lemarquand
, and
C.
Akyel
, “
Cylindrical magnets and coils: Fields, forces, and inductances
,”
IEEE Trans. Magn.
46
,
3585
3590
(
2010
).
12.
W.
Robertson
,
B.
Cazzolato
, and
A.
Zander
, “
A simplified force equation for coaxial cylindrical magnets and thin coils
,”
IEEE Trans. Magn.
47
,
2045
2049
(
2011
).
13.
J. J.
Perez-Loya
and
U.
Lundin
, “
Simple method to calculate the force between thin walled solenoids
,”
Progr. Electromagn. Res.
51
,
93
100
(
2016
).
14.
N.
Derby
and
S.
Olbert
, “
Cylindrical magnets and ideal solenoids
,”
Am. J. Phys.
78
,
229
235
(
2010
).
15.
F.
Behroozi
, “
Weighing a magnet as it falls with terminal velocity through an aluminum pipe
,”
Phys. Teach.
56
,
474
477
(
2018
).
16.
M.
Kwon
,
J.
Jung
,
T.
Jang
, and
S.
Sohn
, “
Magnetic forces between a magnet and a solenoid
,”
Phys. Teach.
58
,
330
334
(
2020
).
17.
F. X.
Hart
, “
The magnetic field along the axis of a short, thick solenoid
,”
Phys. Teach.
56
,
104
106
(
2018
).
18.
J. M.
Camacho
and
V.
Sosa
, “
Alternative method to calculate the magnetic field of permanent magnets with azimuthal symmetry
,”
Rev. Mex. Fis. E.
59
,
8
17
(
2013
).
AAPT members receive access to The Physics Teacher and the American Journal of Physics as a member benefit. To learn more about this member benefit and becoming an AAPT member, visit the Joining AAPT page.