We calculate the magnetic fields of cylindrical coils due to a surface current and a volume current and compare our theoretical results to measured magnetic fields of two coil types: single-layer solenoid and cylindrical thick coil by a simple experimental apparatus. Good agreement is found with the theoretical results.
REFERENCES
1.
David J.
Griffiths
, Introduction to Electrodynamics
(Prentice Hall
, Upper Saddle River, NJ
, 1999
), 3rd ed., pp. 227
–228
.2.
B. B.
Dasgupta
, “Magnetic field due to a solenoid
,” Am. J. Phys.
52
, 258
(1984
).3.
V.
Namias
, “On the magnetic field due to a solenoid of arbitrary cross section
,” Am. J. Phys.
53
, 588
(1985
).4.
K.
Fillmore
, “Magnetic field of a noncircular solenoid
,” Am. J. Phys.
53
, 782
–783
(1985
).5.
O.
Espinosa
and V.
Slusarenko
, “The magnetic field of an infinite solenoid
,” Am. J. Phys.
71
(9
), 953
–954
(2003
).6.
Edward M.
Purcell
, Electricity and Magnetism
(McGraw-Hill
, New York
, 1985
), 2nd ed., pp. 226
–231
.7.
John D.
Jackson
, Classical Electrodynamics
(Wiley
, New York
, 1999
), 3rd ed., pp. 225
–227
.8.
C.
Chia
and Y.
Wang
, “The magnetic field along the axis of a long finite solenoid
,” Phys. Teach.
40
, 288
–289
(2002
).9.
J.
Farley
and R. H.
Price
, “Field just outside a long solenoid
,” Am. J. Phys.
69
, 751
–754
(2001
).10.
G. V.
Brown
and L.
Flax
, “Superposition of semi-infinite solenoids for calculating magnetic fields of thick solenoids
,” J. Appl. Phys.
35
, 1764
–1767
(1964
).11.
R. H.
Jackson
, “Off-axis expansion solution of Laplace’s equation. Application to accurate and rapid calculation of coil magnetic fields
,” IEEE Trans. Electron Devices
46
, 1050
–1062
(1999
).12.
J. T.
Conway
, “Exact solutions for the magnetic fields of axisymmetric solenoids and current distributions
,” IEEE Trans. Magn.
37
, 2977
–2988
(2001
).13.
Daryl W.
Preston
and Eric R.
Deitz
, The Art of Experimental Physics
(Wiley
, New York
, 1991
), pp. 121
–125
, 303
–315
.14.
C. G.
Deacon
and H. C.
Clarke
, “Use of a linear offset Hall effect transducer in student laboratory experiments to measure magnetic fields
,” Am. J. Phys.
61
, 947
–948
(1993
).15.
D.
Bishir
, “A simple demonstration of the magnetic field of a solenoid
,” Am. J. Phys.
64
, 1525
(1996
).16.
H. B.
Dwight
, “The magnetic field of a circular cylindrical coil
,” Philos. Mag.
11
, 948
–957
(1931
).17.
M. W.
Garrett
, “Axially symmetric systems for generating and measuring magnetic fields. Part I
,” J. Appl. Phys.
22
, 1091
–1107
(1951
).18.
A. I.
Rusinov
, “High precision computation of a solenoid magnetic fields by Garett’s methods
,” IEEE Trans. Magn.
30
, 2685
–2688
(1994
).19.
Philip M.
Morse
and Herman
Feshbach
, Methods of Theoretical Physics, Part II
(McGraw-Hill
, New York
, 1953
), p. 1263
.20.
The common notation for the Gauss hypergeometric function has the form where , , and are parameters.
21.
MATHEMATICA, ⟨http://www.wolfram.com⟩.
22.
The common notation for Struve functions is .
23.
See EPAPS Document No. E-AJPIAS-74-021606 for the plots and tables for all measurements. This document can be reached via a direct link in the online article’s HTML reference section or via the EPAPS homepage (http://www.aip.org/pubservs/epaps.html).
24.
The Earth’s magnetic field for different locations can be determined at ⟨http://www.ngdc.noaa.gov/seg/geomag/magfield.shtml⟩.
25.
I. S.
Gradshteyn
and I. M.
Ryzhik
, Table of Integrals, Series, and Products
(Academic
, New York
, 2000
), 6th ed..© 2006 American Association of Physics Teachers.
2006
American Association of Physics Teachers
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