URS
IN
LECTRICAL
NGIN ERING
RECT
URRENTS
Vol. 1
by
Chester
Dawes
Published by Forgotten Books 2013
Originally published 1920
PIBN 1000030103
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Alchemy
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G L E G T R I GA L E N G I N E E R I N G
T E X TS
A COURSE IN
ELEfJTBIIJIL ENGINEEBING
VOLUME I
D IRE CT C U R R E NTS
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PRIRCIPLBS OP ALTBRRATIRG-CBRRSRT %ACBIRBRY
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PVDCIPLBS OP DIRNCT-CDRRERT
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Vol. II.—Al%mating Currentg
E L E CT B I C AL E N G I N E E B I N G TE X T 8
A CO UBSE IN
VOLUME I
D I B F CT CU B B E N T S
CHESTEB L. DAWES, S. B.
nxersznx8, ETC.
Fiaaw EDITION
McGRAW-H ILL BOOK COMPANY , Inc.
NEW YORK: 370 SEVENTH AVEN UE
LONDON:e
OUYERIE8T„E.C.4
1 920
! ’*
@
n •x va R o u x i v‹esiTY
€hullsE£RinQ 6urtOOL
asev4aa c«cc ec ‹isam
Coz•saiaa'z, 1620, air sea
M c G e w - H z a z B o o z Coueaxz, I x c .
PDEFAGE
Por noœe time paat the editoro of the McGraw-Hill Electrical
Engineering Texts have experie nœ d a demand for a comprehensix•e text covering in a émplo manner the general field of Electrical
Engineering Accordingly, theæ two volumes were written at their
requegt, after the scope and general character of the two volumes
had been carefully considered.
Ao the title impûeg, the books begin with the most elementary
conceptions of magoetism and current-flow and gradually advance to a more or less thorough discussion of the many typea of
direct and alternating current macÙnery, transmission devieeo,
etc., which are met in practiœ. Theæ two books are intended for
Electrical Engineering studentn ao a stepping stone to the moro
advanced Electrical Engineering Texts which are already a part of
the ærien.
Theæ two volumes ghould be useful also to otudents not planning to specialize in the electrical engineering field, who are taking courtes in Electrical Engineering as a part of their general
traiaing. Such men often find dioculty in obtaiaing detailed and
otraightforward diocussiono of the subject in any one text and the
brevity of their course dœn not give them time to assimi- late
fragmentary information obtainable only by consulting a number
of referenœs. Men taking foremen’o and industrial couræg in
Electrical Engineering, which aa a rule are carried on only in the
evening, require text booko su0iciently comprehen- sive, but at
the same time not involving much mathematical analyais.
Ordinarily, this type of gtudent dœo not have ready access to
reference libraries and is usually out of contact with hio
instructors except during the short time available for class-room
æork. In proparing this work the needo of the foregoing typeo of
otudents have been carefully kept in mind and as a result, a
liberal use of figures and illustrative problems has been made.
«
rnneacr
Alao frequent discuaaions of the methods of makingmeasuremento
and laboratory tests are included.
In any couæe in Hectôcal Engineeông, even though it be
intended for non-olectôcal engineeæ, the author fæls that the
student gains ûttle from a hwfied and oupeAcial treatment of the
aubject, aa such treatment tends only to develop the memoriz- ing
of certain formulæ which are soon forgotten. Accordingly the
attempt haa been made in this text to develop and explain each
phenomonon from a few fundamental and well-understood laws
rather than to give mere gtatements of facto. Such treat- ment will
develop the student’s reaooning powers and give him training that
æill be uæful in the solution of the more involved engineering
problems that may ariæ later in his career.
Throughout the text, egpecially in the treatment of the more
abstract portions, attempt haa been made to show the ultimate
heaüng upon general engineeÙng practiee. The student takea moro
interest in the theory when he aæs that it can be appûed to the
aolving of practical problems. & c a u æ this work il not intended for
advanœd otudents in ElectHc& Engineeông, little or no calculus il
uæd and the mathematicg il ûmited to ömple equationg.
The author is indebted to æver& of the manufactuông
companies who have cæjœrated in the matter of gupplying phœ
tographo, cuts and material for the text; and particularly to Prœ
feasor H. E. Cli8ord of The Harvard Engineeông School, for his
many suggestions and for the care and pains wöich he han taken in
the matter of editing the manuscHpts.
HARVARD
NIYER8ITT,
AABRIDO , M
/onuorp, 1920.
CIIAPTERI
MaONsma& AND M a O N B ' £ B . . . . . . . . . . .
.
1
1
1
1
1
1. Magnets and Magnet&m . .
3. Magnetic Materials.
3.
Magnets. . . . . . . .
4. Artiacial Magnets ...
Magnetic E e l d . . . . . . . . . .
ESecb of Breaking a Bar Magnet.
Webefs Theory . . . . . .
& Coeaequent Polea
9. Magnetic Force ...
10. Pole gt »gh . .
11. Unes of Force.
12. Eield Intenaity, Electromagnetic.
13. Eux Denaity . . . . . . . . . . . .
14. Gompaas Needle.
.. . .
15. Magnetic Egurea . . . . . . .
16. Magnetic Induction . . . .
17. I•aw of the Magnetic Eeld .
18. Other F o m s of Magnets .
19. Tztmine.ted Magneta .
Oe Magnet Screens .
21. Magnetizing. . .
32. Eaoh’8 Magnet&m. .
2
3
5
6
7
7
8
10
11
12
13
14
14
15
15
CHAPTER II
Ei«czeoaao u e i a a . . . . . . . . . . . .
?3
24.
25.
26.
27.
28.
29.
17
M.agnetic EeId Burrounding a Gonductor
Relation of Magnetic Eeld to Gunent . .
Magnetic Eeld of T'»o Parallel Gonductora
Magnetic Neld of a Single Turn . . . . . .
The Oolenoid . . . . . . . . . . .
The Gommercial Solenoid . . . . .
The Uoraeshoe Olenoid.
.
"
17
18
19
20
21
22
24
30. The Lifting Magnet .
31. Magnetic Separator.
32. The Magnetic Circuits of Dynamos. .
26
27
27
CHAPTER III
R sIBTANCE . . . . . . . .
31
31
33. Hectrical Resistance
3é, Vaib of Res&tance . . . . . . . . .
3ñ. Resistance and Direction of Current
36. Specific Reaistance or Resistivity.
. .
32
32
34
25
37. Volume Reaistivity.
38. Conductance. .
3S. Per Cent. Conductivity. .
40. Resistances in Series and in Parallel .
41. The G rcular M8. .
26
36
42. The C i r c u l a r - m i l - f o o t . . . . . .
43. Table of Resistivities. .
44.
Temperature Coefficient of Ræistance . .
29
40
46. Alloys . . . . . . . . .
47. Temperature Coemcients of Resistance
48. Temperature Goe&cients of Copper at Diflerent Initial Temperatures . . . . . . . . . . . . . .
49. The American Wire Gage (A. W. G . ) . . . . . . . . . . . .
ñ0. Working Table, Standard Annealed Copper Wire, SoUd; Ameri- can
Wire Gage (B. & S.).
English Units . . . . . . . . .
51. Bare Goncentric Lay Cables of Standard Annealed Copper.
42
E
h
H
R
•
m
w
RG
D
27
38
•
•
41
H
•
•G
R
9
D
R
9
52. Conductors . .
R
43
43
44
4û
46
46
CH*'EPTER IV
O i œ ’ s L a w AND T£tE ELECTRIC CIRCUIT . . . . . . . . . . . . .
53.
54.
55.
56.
mh
58.
59.
00.
61.
62.
63.
64.
65.
Electromagnetic Units . . . . . . . . . . . .
Nature of the Row of Electricity.
Diflerence of Potential.
Measurement of Voltage and Current.
’
L
D
D
G
o
•
o
•
R
•
D
oG
•
o
The Series Circuit .
The Parallel Circuit . . . . . . . . . . . .
Diviaion of Current in a Parallel C i r c u i t . . .
The Serie8-parallel C i r c u i t . . . . . . .
Electrical Power.
Electrical Energy.
Heat and Energy.
Thermal Units. .
o G
•
•
•
•
48
48
49
51
52
52
54
55
56
58
60
61
62
' jx
CON T E N T S
66. Potential Orop in Feeder Supplying One Concentrated Load
67. Potential Drop in Feeder Supplying Two Concentrated Loads at
Diflerent P o i n t s . . . . . . . . .
63
g . zâtimation of F e e d e r a . . . . . . . . . . .
6J
67
68. Power Loaa in a F e e d e r . . . . .
CHAPTER V
68
70.
71.
72.
73.
74.
75.
76.
77.
78.
79.
Battery Electromotive Force and Resistance.
Battery Resistance and Cwrent . . . . . . . . .
Batteries Receiving Energy .
Battery Cells in Seriea . .
Equal Batteriea in Parallel . .
Seriea-paraHel Grouping of Gells . . . . . . .
Grouping of Celb ...
Kirchhofl’s Laws . . . . . . . . . . . . . . . . . . . . .
AppUcations of Xirchhod’s Lawa. .
Assumed Direction of G u r r e n t . . . . . . . . . . . .
80.Further Application of K irehhod’a
68
70
71
73
73
75
76
77
79
81
82
GHAPTER VI
PRI
Rv
ND SECONDARY B TTRR1E8 . . . . . . . . . . . . . . .
81. Principle of Electric Batteries .
82. Definitions ...
...
. . . . . . .
. . . . . . .
8S. mmar y Cells . . . . . . .
..
.
84. InternalReaistance.
85. P ol ari z at i on..
.
. . . .
8fiA. Daniell Cell .
. . . . .
86B. Gravity C e l l . . . . . . . . .
87. Edison-Lalande Cell . . . . . . .
88. I›eClanché CeH ...
..
89. Weston Standard Cell.
. . . .
90. Dry C e l l s . . . . . .
. . .
91. Btorage B a t t e r i e s . . .
92. The I›ead Cell.
. . . . . . .
93. Faure or Pasted P l a t e . . . . . .
94. Stationary Batteries . . . . . . .
•
96.
•
£i}3aPatOT8......
G
G
•
G
•
86
..
. . . .
. . . . . . .
. . . . . .
. . .
. . .
. . .
.
.
.
. . .
. . .
. . .
. . . .
. . .
•
G
•
. . .
. . . .
. . . .
. .
. . . .
•
•
A
. . . . . . . .
97. Electrolyo ..
98. Speci6c Gravity ...
84
85
•
•
•
•
•
. . . . .
. ...
..
•
3
104
. .
105
. . . . . . . .
106
99. Inatalling and Removing from Service
. . . . .
107
100. Vehicle B a t t e r i e s . . . . . . . . . .
. . . . . . . .
101. Rating of Batteries.
.
G
.
.
.
.
87
88
89
9o
. 91
. 91
. . . . . 92
94
96
97
. .
. . . ..101
. . . . 103
...
.
.
108
. . . . . . . . 110
CON YEN YS
10s. Charging . . . . . .
.
102. Battery Iætallatioœ .
. . . . . . . . . .
..111
. . . . . . . . . . . . .
104. T e m p e r a t u r e . . . . . . . . . . . . . . . . .
...
. 114
. . 114
105. Capacities and Weights of Lead C e l l a . . . . .
.
. . .
114
100. The Nickel-iron-alkaline B a t A r y . . .
.
.
...
115
107. Charging and Discharging.
.
.
. . . . . .
...117
108. A p p l l c a t l o n s . . . . . . . . . . . . . . . . .
. . .. . 118
109. E&ciency of Storage B a t t e r i e s . . . . . . . . . . . . . . . ‘ 118
110. E l e c t r o p l a t i n g . . . . . . . . . . . . . . . . . . . . . . 120
CHAPTER VII
ÜLEC'£RICz.n InszROuENva ann EnPsCTRFCAi. M E A S t f R E M E N T 8 . . . .
ÏJÇ
111. Principle of Direct<urrent I n s t r u m e n t s . . . . . . . .
112. The D’Araonçal G a l v a n o m e t e r . . . . . . . . . . .
. . . 122
. . . . 123
... . . . . . . . . .
113. Galvanometer S h u n t s . . . . .
126
114. A m m e t e r s . . . .
.
.. . . . .
. . . . . . . . .
128
115. Voltmeters . . . . . . . . . . . . . . . . . . . .
134
116. Multipliera or Extension C o i l s . . . . . . . . . . . . . . . 135
117. HoYwire Instruments . . . . . . . . . . . . . . . . . . 136
118. Voltmeter-ammeter Method.
. . . . . . . .
. .
137
119. The Voltmeter M e t h o d . .
. . . . . . . . . . . . .
.139
120. The Wheatstone B r i d g e . . . . . . . . . . . . . . . . . . 141
121. The Slide Wire Bridge . . . . . . .
. . . . . . . . .
144 122.
The Murray Loop . . . . . . . . . . . . . . . . . . . . 147 123.
The Varley L o o p . . . . . . . . . . .
. . . . . . .
148
124. Insulation Teating ...
. . . . . .
. . . . . . . . . . 150 125.
The P o t e n t i o m e t e r . . . . . . . . . . . . . . . . . . . . 152
126. The I*eeds & Northrup Low Resistance Potentiometer . . 155
127. Voltage Measurements with the Potentiometer..
..
.. 15?
128.The Measurement of Current with Potentiometer . . . . .
158 129.
Measurement of Power . . . . . . . . . . . .
. . . . . . 160 130.
The Wattmeter ... . . . . . . . . . . . . . . . . . .
161 131. ’The
Watthour M e t e r . . . . . . . . . . . . . . . . . . . 162
132. Adjustæent of the Watthouz Meter . . . . . . . . . . . . 165
CHAPTER VIII
TRI M a o n u r i c C 1 R C £ f I T . . . . . . . . .
133.
134.
125.
136.
137.
138.
139.
140.
. . . . . . . . . . .
169
. . . . . . .
The Magnetic C i r c u i t . .
. . . . .
. 189
Ampere-turns . . . . . . . . . . . . . . . . . . . . . . 170
Reluctance of the Magnetic C i r c u i t . . . . . . . . . . . . . 171
Permeability of Iron and S t e e l . . . . . . . . . . . . . .
173
Law of the Magnetic C i r c u i t . . . . . . . . . . .
...
174
Method of Trial and Error ..
. . . . . . . . . . . . . 175
Determination of Ampere-turna . . . . . . . . . . . . . . 176
Use of the Magnetization Curvea . . . . . . . . . . . . . 178
m‘
CONYEN Yñ
141. Magœtie Calculatioæ in D y n a m æ . . . . . . .
242. X ys t e r e a î a . . .
243. Eystereaîa I«oss .
145.
ldfi.
147.
14ö.
149.
184
Induced Heotromotive Force . . . . . . . . . . .
Hœtromotive Force of Belf-induction . . . . . . . .
Energy of the Magnetic Field . . . . . . . . . .
Mutual Inductance.
.
Magnetic P u l l . . . . .
191
193
197
.
..
CRAPTER IX
E
CTR
T*
:#APA TANCE. . . . .
.
. 198
. . . . . .
198
150. Hectroatatie Ghargea..
..
. . . . . . . . .
151. Hectrostatic Induction .
. . . . . . . . . .. . .
199
1fi2. Heutrostatic Iânea ..
. . . .
. . . ...
. . . . . . 2
&
U J a . p a c i t a n c e . . . . . . . . . . . . . . . . . . . . ..
. 20a
inn. gpe«ific Inductive Capanity or Dielectric C o n s t a n t . . . ...
204
155. Equivalent Capacitance of Condensera in Parallel . . . . . . 205
156. Equivalent Capgcitance of Condensera in Seriea .
..
208
157. Energy Stored in Condenaeva .
..
. . . . . . . . . . 208
158.Calculation of Capacitance . . . . . . . . . . . . . . . . 209
1fi8. Measurement of Oapacitance . . . . . . . . . . . . . .
211
160. Cable Teating—l•ocation of a Total Disconnection ..
.. 213
C&APTER X
7as GanEztxeoæ . . . . . . . . .
. . . . . .
161. D e f î o i t i o n . . . . . . . . . . . . . . . .
162. Geœrated Electromotive Force . . . . .
163. Direction of Induced Hectromotive Force.
nd
q
D
H
R
*
D
G
*
R
R
P
Dp
g
. . . . . .
. 315
. . . . . . . . 2 1 5
. . . . . . . . 215
F1eming’a Right
G
w
m
p
q
o
o
o
164. Voltage Generated by the Revolution of a Coil.
.. 219
165. Gramme-rin g W i n d i n g . . . . . . . . . . . . . . . . . . 222
188. Drum W i n d i n g . . . . . . . . . . . . . . . . . .
. . . . 222
D
G
G
G
9
•
G
•
q•
G
G
D
•
o
1
9
•
o
o
•
•
•
o 224
188. Lap Windi
Several Go? Sidea per S l o t . . . . . . . . . . 229
169. Pat& Through an A r m a t u r e . . . . . . . . . .
. . . .. . 220
170. Multiplex Windings . . . . . . . . . . . . . . . . . . . 233
171. Equalising Connections in Lap Windings . . . . . . . . . . 236
172. Wave Winding. ..
. .. . . . . . . . . . . . . . . . . 23P
173. Number of B r l i a h e a . . . . . . . . . . . ...
...
. .. 243
174. Pat& Through a Wave W i n d i n g . . . . . . . ...
. . . . 244
175. Uam of the T«o Types of Windings . . . . . . . . . . . . 240 176.
Frame and G o r e s . . . . . . . . . . . . . . . . . . . . . 249 177. Gdd Gores
and Shoes . . . . . . . . . . . . . . . . . . 2ñ0
m”i
CONY,ENYE
CHAPTER XI
GnnERaTon CeaztzerxRisxIc8 . . . . .
. . . . . . . . . . . . . 257
182. Glectromotive Force in nn Armature . . . . . . . . . . .
.257
182. The Saturation C u r v e . . . . . . . . . . . . . . . . . . . 258
184. H y s t e r e a i a . . . . . .
..
. . . . . . . . . ...
. . . . 260
185. &termination of the Snturation Curve . . . . . . . . . . . 261
186. Field Resistance L i n e . . . . . . . . . . . . . . . . . .
. 262
187. Types of Generators . . . . . . . . . . . . . . . . . . . 263
188. The Shunt G e n e r a t o r . . . . . . . . . . . . . . . . . . . 264
189. Critical Field Resistance . . . . . . . . . . . . . . . . . 265
190.Generator Fails to Build U p . . . . . . . . . . . . . . .
.266
191. Armature R e a c t i o n . . . . . . . . . . . . .
. . . . . . . 267
192. Armature Reaction in Multi-polar M a c h i n e a . . . . . . . . . 272
193.Compensating Armature Reaction . . . . . . . . . . . . . 274
194. Commutation . . . . . . . . . . . . . ! . . . . . . .
. 276
195. The Hectromotive Force of Self-induction . . . . . . . . . 280
196. flparking at the Commutator . . . . . . . . . . . . . . . 281
197. Commutating Poles (or I n t e r p o l e a ) . . . . . . . . . . . . . 285
198.The Shunt Generator—Characteri&ics . . . . . . . . . . . 288
199. Generator R e g u l a t i o n . . . . . . . . . . . . . . . . - . . . 292
200. Total Characteristic ... . .. . . . . . . .
. . . . . . 293
201.The Compound Generator . . . . . . .
. . . ’ . . . . .
295
202. E8ect of S p e e d . . . . . . . . . . . . . . . . . . . . . . 299
202. Determination of Series Turns; Armature Characteristic ... 300
204. The Berie8G e n e r a t o r . . . . . . . . . . . . . . . . . . . 301
205. E8ect of Variable Speed Upon Characteristics..
. . . . . 305
206. The Unipolar or Homopolar Generator . . . .
. . . . .
305
207. The T i r r i l l R e g u l a t o r . . . . . . . .
. . . . . . 306
CHAPTER XII
.
..
. H9
TeE MoxoR . . . . . . . .
.. . . . . .
. ..
20d. Definition.
..
. . . .
. . . . 309
209. Principle . . . . . . . . . . . . . . . . . . . . . . . . 3 0 9
210. Force Developed with Conductor Carrying Current . . . . .
310
211. Heming’s LefYhand Rule . . . . . . . . . . . . . . . . . 311
212. Torque . . . . . . . .
. . . . . . . . . . . . . . . . . 212
213. Torque Developed by a M o t o r . . . . . . . . . . . . . . . 312
214. Counter Electromotive Force . . . . . . . . . . .
...316
215.Armature Reaction and Brush Position in a M o t o r . . . . .
319
216. The Shunt Motor . . . . . . . . . . . . . . . . . . . . 321
21Y. Tbe Seziw M o t o r . . . . . . . . . . . . . . . . . . . . . 324
218. 3Åe Coæpound Motor . . . . . . . . . . . . . . . . . . 328
319. Motor O t a r t e æ . . . . . . . . . . . . . . . . . . . . . . 329
221. Reaétance U n i t a . . . . . . . .
222. Speed C o n t r o l . . . . . . . .
223. Railway Motor C o n t r o l . . .
.
224. Dynamic Braking . . . . . . . .
225. Motor Teating—Prony Brake . . .
226. Meaaurementof Speed ..
.
.
.
.
.
.
.
.
.
.
.
.
. . . . . . . . . .
. . . . . . . . . .
. . . . . . . .
. . . .
. . .
. . . . .
.
.
. % 8
. . 238
. . 345
. . 347
..348
.. 353
CHAPTER XIII
Lonass; EPPIcIuncu; OPERATION . . . . . . . . . . . . . . . . .
355
229. E f f i c i e n c y . . . . . . . . . . . . . . .
. . . . .
.358
?20. E&cienciea of Motors and G e n e r a t o r s . . . . . . . . . . . . 380
231. Meaaurement of Stray Power . . . . . . . . . . . . . . . 361
232. Stray-power Curvea . . . . . . . . ..
. . . . . . ...
363
233. Oppoaition Teat—Xapp’s Method . . . . . . . . . . . . . 3 6 f i
234. Ratings and Heating . . . . . . . . .
. . . . . . . . .. 368
235. Parallel Running of Shunt G e n e r a t o r s . . . . . . . . . . . . 372
236.Parallel Running of Compound Generators . . . . . . . . ’ .274
237. Circuit Breakers.
. . . . . . . . . . . . . . . . . . . 377
CHAPTER XIV
PRansaIaaIon ann Di8TRIBovion or P o w s R . . . . . . . . . . . . 380
238. Power DiatHbution S y 8 t e m 8 . . . . . . . . . . . . . . . . 380
239. Voltage and W&ght of Conductor . . . . . . . . . . . . . 381
240. Size of C o n d u c t o æ . . . . . . . . . . . . . . . . . . . . 382
241. Distôbution Voltage .
...
. . . . . . . . . . . .
383
242. DätHbuted Loads .
.
. . . . . . . . . . . . . . . . 383
243. Sy8tems of F e e d i n g. .
. . . . . . . . . - . . . . . ..384
244. 0enea-Parallel System.. . . . . . . . . . . . . . . . . . 285
245. Ediæn ¥wire Syatem—Advantages . . . . . . . . . . . .
285
248. Voltage Unbalancing . . . . . . . . .
. . . . . . . . ..288
247. Tæœgenerator Method . . . . . . . . . . . . . . . . . . 290
248. fltorage Battery . . . . . . . . . .
. . . . . . . . . . . 390
249. Balancer S e t . . . . . . . . . . . . . . . . . . . . . . . 391
250. Three-æire G e n e r a t o r . . . . . . . . . . . . . . . . . . . 394
251. Feeders and M a i æ . . . . . . . . . . . . . . . . . . . . 395
252. ElectHc Railway Distributi‹›n . . . . . . . . . . . . . . . 396
253. Electrolysis . . . . . .
..
. .. .
. . . . . .
397
254. Central Station Batteries . . . . . . . . . . . . . . . . . 299
255. Resistance C o n t r o l . .
.
. . . . . . . . . . . .
.401
AOE
. . . . . . .
256. Counter Gectromotive Force C e l l s . . . . .
257. End CeC C o n t r o l . . . . . . . . . . . . . . . . . . . . .
258. Floating B a t % r y . . . . . . . . . . . . . . . . . . . . .
259. Seriea @ s t r i b u t i o n . . . .
. . . . . . . . . . . . . . .
401
402
403
405
APPENDIX A
Ruiamoxs or Uxlva . . . . . . . . . .
. . . . . . . . . . . . 407
APPENDIX B
APPENDIX C
Tanz« or Tzana rus @ . In.; Soi.in LAYERWlxDIno . . . . . . .
. 408
APPENDIX D
I .. .
............
Psoannaa on Cen›«ss I . . . . . . . . . . . . . . . . . . . .
Qenamoxa on CeamesR I I . . . . . . . . . . . . . . . . . . . .
Pgoaxx»:s on Cez:meis I I . . . . . . . . . . . . . . . . . . . .
Q « » $ « 0 r a O r Gu>»«»R III
PROB£x«a on Cxn
oxsmowsow Ca*
. . 416
. . . . . . . . . . . . . . . .
R III. . . .
xI . .
411
412
413
414
. . . . . . . . . . .. . . . 417
. . . . . . . . . . . . . 420
PBOBLEM8ON C *PTEBIL. . . . . . . . . . . . . . . . . . . . 421
smows ow Ca*
PROB<E BON
V. . . . . . . . . . . . . . . . . . . . 425
*
R
. . . . . . . . . . . . . . . . . . . . 427
Qwnsnoxa or Cea›msR VI . . . . . . . . . . . . . . . . . . . 420
PR«›«ua on C « r e s s V I . . . . . . . . . .
. . . . . . . . 434
Qguamona or Cxarrxs V I I . . . . ’ . . . . . . . . . . . . . . . 436
PROBLsaa on CeaPTER VII . . . . . . . . . . . . . . . . . . . 442
Qgusmona or Cxnersu VIII . . . . . . .
Psoai.Ens on CenP'£ER V I I I . . . . . . .
Qusamlons on CeaP'PEiR IX . . . . . . . .
Pnoaiasus or CaaïmsR I X . . . . . . . .
.
.
.
.
.
.
.
.
.
.
.
.
. . . . .
..447
. . . . . . . . . 449
. . . . . . . . 455
. . . . . . . . . 456
Qnnf$zIons or GaAP'Z'ER . . . . . . .
. . . . . . . .
Pgoai.sea op G g a m s s X . . . . . . . . . . . . . . . . .
Qgnsmona ox CanmsR XI . . . . . . . . . . . . . . . .
Psoanuaa on Cea
RX I . . . . . . . . . . . . . . . . .
Qwusxlona on Caamess X I I . . . . . . . . . . . . . . . .
Pgoai;nga op Cenmxu XII . . . . . .
. . . . . . . . .
Qggamona on CeawsR X I I I . . . . . . . . . . . . . . .
OBLEM8 ON ÜHAZ'«s X I I I . . . . . . . . . . . . . . . .
Qgnamona ox CeawrEs X I V . . . . . . . . . . . .
. . . .
Psogzsgs ox CeagrsR X I V . . . . . . . . . . . . . . . .
I
@@
q
q
t.
ut
u
et
y
u
t
p
u
+
«
•
•
t
u
t
u
u
e
e
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
. . .
458
460
461
485
467
470
474
476
. . . 477
. . . 480
e
u
ou
A C O U R S E IN
FLFCTRICAL FHGIFFFRING
DIDEGT GUD AENTS
GDAPTER I
1. Magoets and magnetism are involved in the operation of
practica3y a3 electrical apparatus. Therefore an understand- ing
of theñ underlying principles é essential to a clear conception of
the operation of a2 such apparatus.
2. Magneéc Materials.—Iron (or steel) is far superior to a3 other
metals and substances ao a magnetic material, and é practically
the only metal used for magnetic pwposeo. Cobalt and eickel (and
oome of theñ aPoyg) poaoeog magnetic properties, which are far
inferior to those of ñon. Liquid oxygen is aloo attracted to the
polea of magnets.
3. Natural Magoets.—Magnetic phenomena were firat noted by
the ancienta. Certain gtoneo, notably at Magnegia, Asia Mioor,
were found to have the propeNy of attracting bits of iron, hence
the name »iopnets was given to theae magic otonea.
The fact that such stones had the property of pointing north and
south, if augpended freely, was not discovered until the tenth or
twehth century. The practical use of such a stone in navigation
gave it the name of Lodeatone or leading stone. Natwal magnets
are compoaed of an ñon ore known in metaPwgy as magnetite,
having the chemical compoaition FeiOi.
4. Magnets.—If a piece of hardened steel be rubbed
with lodeotone, it w?l be found to have acquired a very appreciable amount of magnetism, which it w?l retaia indefinitely. i
Z
D2RSCf CURRHN1’5
Such a ateel magnet ia caPed an aNijfeioJ »ingoef. Artifieial
magnets commoaly derive theñ initial excitation from an electric
cwrent aa wG be shown later. If a piece of aoft steel or soft
iron be Similarly treated, it retaiaa but a very ama¥ portion of the
magnetism iaitia¥y imparted to it.
Theoe properties make it desirable to use hardened ateel when a
permanent magnet is desired and to uae soft iron or steel when it
is eooential that the magnetism reapond closely to changes of
magnetizing force. It is found that even hardened steel ageo or
losea aome of its magnetism with time. Where a high degree of
permanency is deoñed, ae in electrical instruments, or even in
magnetos, the magnets are aged artificially.
Fio. 1.—Magnetic field about a bar magnet.
fi. Magneéc Pie1d.—It is found that magnetism manifesta itseh
as if it existed in lines, called Ii»ea of mogaefiani or linee of
iodwtim. The region in opace through which theoe lines pass is
called the mognelic fietd. Further, E the lines of iztduction of ouch a
field be determined experimentally, it is found that they seem to
emanate from one region of the magnet and enter some other
region as shown ia Fig. 1. Theoe regions are c&led the pofei of the
magnet. The two poles are dintinguinhed by 4he position which they
oeek if suspended freely. The one which points north ia called the
north-aeeHng polh or north pole for short, and the other the soHhseeking pole, or zovth pole. In practice it is asaumed that the lines of
induction leave the magnet at the north pole and re-enter it at the
oouth pole. Within the
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DIRECT CURREN TE
occurring in the magnetization of ûon, is oØered by Weber’ø
Theory wäich haø been expanded by Ewing. The moleculeø of a
magnet are assumed to be an indefinitely great number of very
ømaß magnets aa shown in Pig. 3 (o). Under ordinary condition
these ømøll magnets are arranged in a haphazard way, æ shown at
(o), so that the variouø north and æuth polea aß neutralize one
another, and no external eØect ä produced. Upon the appûcation
of a magnetizing force, however, the small magneta tend to so
arrange themselves that their axes are paraßel
N
Fïo. 3.-Mebæ’smolecWsæfbeoryofmagneís
and their north poles are aß pointing in the aame general düection æ the magnetizing force. This & shown in Fig. 3 (b). It is
evident that ü the magnet be cut along the line XX, Pig. 3 (o), a
new north and a new øouth pole will result, which, before the
fractwe took place, neutr&ized each other.
Thia‘ theory & fwther substantiated by grinding a permanent
magnet into very ømall particles. Each of the small paÙicleø
poaoeøøes the properties of the bar magnet, each having its own
north and its own south pole. Further, the thæry oØeæ a
rational explanation of saturation, hygtereg&, etc., occurring
in ûon subjected to a magnetizing force. Thiø will be coæidered
8. Ooaanquont Polвs.—Conaequent polæ arø œcaaioaally
found in bar magnetø where di8erent poHioæ have been rubbød
by a north pole, or a south pole, or when exciting coila, actiaø in
opposition, have been placed upon the bar. Conøequent poles are
in reality due to the fact that the bar consätø of two
Fio. d.—Consequent polea.
or more magnets arranged øo that two north or two south polea
exiøt in the same portion of the magnet. Thiø & üluøtrated in Fig.
4. The magnetic field shown in Pig. 11, page 11, & in a way
Gugtrative of the field resulting from conæquent poles. In thiø
caøe, however, two bar magneta are uøed and a ømaß air-gap
exists between the adjacent north poleu.
9. %agneöc Force.—When a freely suspended north pole ä
brought in the vicinity of another
”
north pole, it ă repulsed, whereaø, ü a
south pole ä brought in the pre- ænce
of a noYh pole, it & immediately
(a) Repulslon
attracted toward the north pole.
South poles are aløo found to repel
J+-+p
ø
one another. From thiø it may be
!
stated that fiße poles repøf one another
( .)
(b)
Attraction
10. 2'ole SAeggth.—The force of
6.—Repuløion and attraeattraction (or repuløion) between two Fee.
DOD b&tA Bn
ŒgD łiC Ol 8.
given poles &found to be inreraely aø the square of the dă tance between the po1u, provided that the dimeæioæ of the poles are #mall compared with
the distance between them. Ã nail »iop»etic pofe is one OJ 8î É 8IYB
ÍĂHat ii placed at a di8 IWEOJOFF06ftI1 ÃY#H
6
DJBEPT C€/AAENf›S
ferce of
d#ix.
Pole strength is measured by the number of unit polea which, if
placed aide by side, would be equivalent to the pole in question.
The force J, existing between polea in air may be formulated aofollows:
J = p
2
dyneg
(1)
where m and ni’ are the respective pole strengths (in terma of a
unit pole) of two magnetic poles, placed a distance r cm. apart, aa
shown in Fig. 5. Thia force may be attraction or repulaion
according as the poles are unlike or like.
HzacpIe.—Two north poles, one having a strength of 600 units and the
other a strength of 1fi0 unita, are placed a distance of 4 inchea apart. What is
the force in grama acting between thve poles, and in what direction doea
4 ia. = 4
_ 500X 10
" (10.16)^
Y28 —0.741 gram.
981
2.54 —10.16 ca.
75,000 = 728 dynes
103.2
Poles repel each other.
«rna.
11. Lines of Porce.—Thus far the magnetic field has been
studied only with respect to the lif›eg of magnetism or induction.
lf a oingle north pole be placed in auch a field two edects will be
observed.
1. Thia pole will be wged along the lineo of inductioA.
2. The force urging thie pole will be greatest where the linea of
induction are the moat dense, and, moreover, the force will be
proportional to the number of linea per unit area taken perpendicular to the lineo in the field in which the pole findsitseh.
From theoe statements it can be been that !ines
similar
to lines of induction, can be drawn, to represent the forces at the
various points in the magnetic field. In much of the £teratwe on
the subject Uneo of induction and lineo of force are uaed indiscriminately. The fallacy of oo doing is immediately apparent upon
considering a aolid bar magnet. The lineo of induction paas
completely through the solid metal of the magnet, whereaa the
lineo of force terminate at the poles. To be sure, a magnetic force
does exiot within the magnet, but this force can be deter- mined
only by making a cavity in the magnet, and the force
MAI?NH1’ISM AN D MAGNHTS
acting under theae condition is quio distinct from that indicated by the number of ûneo of induction paasing through the
bar. In air, however, the ûneg of force and the ûneg of induction
coincide.
12. Field Intensité.—It haa been stated that the force acting
upoa a magnetic pole placed in a magnetic field is proportional to
the number of ûnea of inductio£f at that point. Vai› jtetd inieniri?;ç ie
&fined aa Ike fîèld atrenqth which uiiü ad upon a unit pok wifù o
Jorw oJ one d$ne. One true oJ Jorae perpendicular to and paooing
through a square centimeter represe te unit field iuoœity. Pield
inoœity is usually repreaeaod by the aymbol
V. It ia evident that ü a pole of c unita be placed in a field of
intensity Û, the force acting on thio pole il
/ = > x J2 dyueo
(2)
A pole jilaced ia such a field muot be of such amall magnitude
that it will have no appreciable disturbing eBect upoa the magnetic field.
13. Plux Density.—Flux density is the number of liaes of
induction per unit area, taken
Total Linee W
perpendicular to the induction.
Ia free space, 8ux density aad
field intensity are the oame,
numerically, but within magnetic
material the two are entirely
diBerent. The two ahould aot ggg¡q, p„¢S,y„
be con/used. The uait of 8ux
'•'°deuaity (one line per oq. cm.) ia
oftea called the potna, but the
expresaion “linea per square
centimeter” and “£aea per
aquare inch” are more ofoa
8.—Linea of force emanating
used in practical wora when **°from a unit N-pole.
apeaküig of 8ux denöty.
By definition the force exerted by a unit pole upoa another
uait pole at centimeter distance izi air io always oae dyae. The
field intensity on a spherical surface of oae centimeter radius must
thea be uaity aad can be repreaented by one liae per aquare
centimeter over the entire spherical surface as shown ia Fig. 6.
8
DIRECY CURRENTE
Since there are 4r square centimeters upon the surface of a
unit aphere, each unit pole muat have radiating from it 4r =
12.6 lineo of force. Fig. 6 repreaenta a portion of a spherical
surface of one centimeter radius and showo roughly the paaaage of
one £ne of force through each square centimeter of audaee, each
?ne originating in the unit north pole.
This alao explaina the
appearance of the 4r term ao often encountered in magnetic
formulae. A pole having a strength of c unita will radiate 4rc
lines of force.
Hsatnpte.—A total Bux of 2&,000 linea paaaea in air between two parallel
pole faces, each 8 cm. squnre. The field is uxiifomly diatributed. With what
force (grama) eill a pole, having a atrength of 100 unita, be acted upon if
placed in this fieldt
200,000
Flux denaity " 8 X 8 = 3,120 £nes per sq. cm. or 3,120 gauases. Being
X
in ak t1¡ia value of Bux deneity also equals the field intensity, J2.
/ = ni x H = 1& X 3,120 = 312,000 dynea
312,000
981
JsacpI#.—A pole having a strength of 400 unita ia placed at the center of a
sphere having a radius of 3 cm. What i8 the flux density at the sur- face of the
sphere and what force «ifl be exerted on a pole of 10 unite placed at the suHace
of the sphereP
Total lines emanating from pole = 400 X 4r — 5,020 lines.
Area of surface of 8phere =4a-r•=4•-9 —113sq. cm.
Flux deœity _ 5020 —44.4 gauosea.
" 113
Force upon pole of 10 units = 44.4
10
dynes.
4ng.
& a check, the force may alao be determined by the law of inverse squarea
(æe Par. 10).
»ini’ _ 400 X 10
= 444 dynes.
/
3X 3
r•
14. The Compass Needle. The compass conaigto of a hard- ened
steel needle or amall bar, permanently magnetized and
accwately balanced upon a aharp pivot. The north-aeeking end or
north pole pointo north, and the South-seeking end pointa South.
The north pole of the needle is uaually colored blue or given some
digtinguisNng mark. With the exception of a few uoed for lectwe
purposes, the needle is enclosed in an air-tight caae for mechanical
protection. Mariners’ compaooes are mounted carefully upon
gimbals, ao that they alwaya hang level. Upon steel ahips, heavy
iron balls placed near the compaaa
HXENETIEH XND ÆXGNETS
9
neceasary to compensate for the magnetic eBect *ofthe ahip
itaeh.
By means of the compass the polarity of a ma$net is
readily determined. The south pole of the compaaa points to
Eio. 7.—Compaan needle and bar magnet.
the nerlh pole of the magnet aa ahown in Pig. 7. Likeaiae, the nor
h pole of the compaaa points to the south pole of the magnet. Thie
action of the compaaa needle follows immediately from the law
that like polea repel and un?ke poles attract each other.
Fio. 8.—Exploring the field about a bar magnet with a compare.
This ia very useful ta practical work for it enablea one to determine the polarity of the varioua poleo of motoæ and generatora
and to ahoæ ü the exciting coila are correctly oonnected.
Further, the compaao needle always tendu to set iteeh in the
direction of the magnetic field in which it finds itæh, the north
end of the needle pointing in the direction of the linea of force or
magnetic lines. Thia ä illuatrated in Pig. 8. By placing a
10
BIAS:CP CYAA5iNf5
small compass at the various points in the region of a magnet, and
drawing an arrow at each point, the arrow pointing in the aame
direction aa the needle, the field around the magnet may be
mapped out ao ahown in Fig. 8. In mapping out a field in this way
it must be remembered that the earth’s field may exert
considerable influence on the compass needle in addition to the
esect of the field being studied.
lfi. Magnetic Pigures. If a card be placed over a magnet and
iron Oinge be sprinkled over the card, a magnetic figure is obtained. The Oinge at each point set themaelvea in the dñection
CIO. 8.—Magnetic figure, unlike poles adjacent.
of the £neg of force at that point, and the resultant figure shows in
very close detail the character of the magnetic field. Fig. 9 shown
the magnetic field due to two bar magnets placed side by side and
having unlike poles adjacent. On the other hand, Fig. 10 shows the
field due to these same bar magnets when like poles are adjacent. It
will be noted in Fig. 9 that the lineo of force seem like elastic banda
stretched from one pole to the other, acting to pull the unlike polea
together. In Fig. 10 the lines of force from the two like polea appear
to repel one another, indicaY ing a state of repulsion between the
poles. Fig. 11 shows the field obtained by placing the bar magnets
end to end, having the two north poles adjacent.
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DžR&C7 CURREW73
magnet ă brought near the iron a north pole ă similarly induced.
This iø illuøtrated in Fig. 12 (a). From the foregoing, the ability of
magnets to attract soft iron is readily undeætood. An oppœ site
pole to that of the magnet iø induced in the iron, and these two
po1e#being of unliko polarity then att rack d toward each other.
It å æmetimea noticed that ü a comparatively weak north pole
be brought into the vicinity of a strong north pole, attraction
between the two results, rather than the repulsion which might be
expected. Thiø å no violation of the laws governing the at-
SoSIron
CIO.12(o)— Polesproducedbyœ agneüc
induction.
F*o. 12 b)—Proper œehod of
"keeping" barœagneM.
traction and repuløion of magnetic polea, but comes from the fact
that the strong north pole induces a south pole which overpowerø
the exiøting weak north pole and results in at traction. In th& way
it & eaøy to reveæe the polarity of a compaøo needle by hold- ing
one end too cloæ to a strong magnetic pole of the same polarity.
For a similar ræвon, when two bar magnets are put away in a
box, the adjacent ends should be of opposio polarity, aø shown in
Fig. 12 (b). They will retain their magnetiam better under these
conditions. When a horseshoe magnet in not in we a "keeper" of
soft iron should be placed across the poles.
17. Iøw of the Magneëc Pield. fße mognełic @łd dwaę»
aüaiiœd. This o8eæ fwther explanation of the attraction of iron
to poles of magnets. The iron is drawn toward the magnet so that
the magnetic lines may utiûze it aø a part of their return
HXGNHYISH XND MXI2HHYS
path, since iron conducts theae Unes much better than the air.
This is illustrated in the horaeahoe magnet of Fig. 14. The
armature ia Oawn toward the polea ofthe magnet, and the retwn
Fin. 13.—Ring magneta.
path to ough the air é materially shortened, so that the number
of magnetic lines ia materia£y increaaed. The maximum 8ux
exiats when the armatwe é against the poles.
18. Other Forms of Magnets. The aimple bar magnet frequently iø not øuitable for practical
æork. For the øame amount of material,
other formø are more poæedul and more
compact. riø. 13 (o) shoæø a clæed ring
magnet. All the magnetic 8ux å
contained in the ring and £ttle external
eØect iø noted. Thiø type å not very
uøeful. &oæever, if the ring be cut aø
ahoæn in Fig. 13 (b), a north and a
æuth polo are obtained. A piece of æft
iron, if brought near thiø gap, ø8l be
strongly attracod and æill tend to be
draæn acroøø the gap and thuø øhorten
the lenQh ofthe &uxpath.
The horøe hæ magnet, hoæn in Fig.
E‘zo. 14.—Ef o zs e- s b o e
magnet attraeting a softiron armature.
14, å very uæful, for tæo reaøoæ. The tæo poleø being near each
other, a comparatively øtrong field exists. Further, if the function
of the magnet is to exert a pull upon an armature, each pole å
equafly eØective. Fig. 118, Chap. VII, page 130 shoæs a horøeøhæ
magnet øuch aø is used in Weston direct-current iætrumentø.
14
DIRHCY CURRBN YS
19. Iæxfiaated Oague&.—It å found that thin steel magnetø
are stronger in propoNion to their æeight than thick onoa. For a
given amount of maorial a magnet made up of æveral
lainiaatioes, aøshown in Pigø.
15 and 16, å more poæedul than
one made of a single piece
of metal.
Fig. 16 shoæs the
form of hoæe-shæ magnet
generaPy used for telephone
and igeition magnetoø.
20. Magnet Screens.—There
is no knoæn inøulator for magnetic 8ux. No appreciable
change in the 8ux or in the pull
of a magnet is noticed if glasø,
paper, æood, copper, or other
Fzo. 15.—Compound or laminated bar Fi«. =.—Compound h o rse - s h o e
magnet.
magnet used in magnetos.
such material be placed in the magnetic field. However, it is often
desirab le to shield galvanometerg and electrical measuring
inntrumentg from the earth’s field and from stray fieldn due to
a
Fin. 17.—Magnetie sereen.
generat ors, conductors carrying currents, etc. Thia is done by
surrounding the instrument with an iron shell aa shown in Fig.
17. This shell by-paasea practically the entire 8ux and thus
MASNHYISM AND MASNHY3
15
prevents it from aäecting the sensitive portions of th einstrument.
The smaßer the openingø ix› the shell, themoree8ectivethencreening becomes. Three or four sheßs, with air spaøes between, are
found to be more &ective than one øhell of t he same total
thickneæ. ßuch, however, are used only in connection with the
øcreeeing of the most sensitive galvanometeæ.
ż1. Magne‘tizigg.—A magnet may be magnetized by merely
rubbing it wit.h another magnet. The resulting polarity at any
point Ô oppoaite to that of the lvt pole which came in contact with this point. Therefore, it is weß to rub one end with the
north pole of the inducing magnet and the other end with the
æu t h pole. Thiø may be done simultaneously by the “divided touch”
method ahoæn in Fig. 18. It ă advisable to rub both 8ides of the bar.
Stronger magnets may be obtained
by placing them between the poles
Fin. 18.—Divided touch method of
magnetizing.
CIO. 19.—Magnetizing a horaøahoe magnet with an electro
magnet.
Fig. 19 shows this method
of a very powerful electromagnet.
An armature or “keeper”
of magnetizing a horseshoe magnet.
should be placed across the poles of the horseshoe magnet
before removing it from the electromagnet.
Magnetization may also be produced by inserting the magnet in a øuitable
exciting coil and allowing a heavy current to flow in the coü. A
few turns of low resistance wire may be wound around the magnet
and connect.ed in series with a fuse to the supply mains. Upon
closing the switch, an enormous cwrent paø8es temporarily, but
the fuse blows immediately and prevents damage to the electric
cñcuiÍ. The heavy rush of current is usually øuocient to leave the
steel in a strongly magnetized condition.
22. The £arth's Magueësm.—The earth behaves as a huge
bar magnet, the poles of which are not far from the geographical
16
DIRECY CURRBNY€
polæ. The north magnetic pole (corresponding to the south pole
of a magnet) ä situated in Bæthia Felix, about 1000 miles from
the geograp@cal north 9o1e. The sout h magnetic pole haa never
been located but experiment pointe to the existence of tæo south
poles. Llue to t he non-coincidence of the geographical and magnetic
poles and to the preænce of magnetic materials in the earth, the
compaaa pointa to the true north in oaly a feæ places on the
earth’s surface. The deviation from the true north è caEed the
decûnation, and magnetic maps are provided shoæ- ing the
decûnation at various parts of the earth. At Neæ York it è about
9º æest. The decûnation undergoes a gradual vaHa- tion from
year to year, caEed the variation change. A careful record è kept of
this secular vafiation and scientific measure- ments, such aa are
used in aatronomy, swveying, and naviga- tion, muat be corrected
correspondingly. The needle undergœa a very small daüy
variation and an annual vaÛation, due poaaibly to the inBuence of
the sun and the moon.
A freely suspended and balanced needle doea not take up a
position paraûel to the earth’s swface, æhen under the influence
of the earth’s magnet;ism alone, but assumer a position
some angle æith the horizontal. Thi8 angle ö called the dip
of the needle. At Neæ York it è about 70º North. The dip
undergœs changes simüar to those in the variation. The field
inteæity (total, not horizontal) of the earth’s field at Neæ York è
about 0.61 C.G.S. units, althoug h thia value changes slightly from
time to time.
CHAPTER TT
ż3. Hagoeäc Pield ßunounding a Conductor.—ït had ìong
been ønpected that some relation exŁted between electriвity and
magnetism, but it remained for Oerøted in 1819 to show that this
relation not only exÙted but that it was a dehnite relation.
Tf a compaeø be brought into the neighborhood of a øingle
conductor cariying an electric cument, the needle deßectø, thu e
indicating the presence of a magnetic field. It ă fWher obæmed
that the needle always tendø to set itøeh at right anglæ to the
conductor. When it is heìd above the conductor, the
ÛIO. S1.—Iănea of force surrounding
a cyûndücal e o ndu ctoт==eu r re n t
ioWard8.
%o. 22. Unea of force aurrounding a
eyûndxical e o n du cto т=-cu r re nt
outward8.
needle poinŁ in a direction opposite to tbat whlch it aøaumeø
when held beneath the conductor. FWher investigation shows t&t
the magnetio 8ux existø in cñcleø about the conductor (ü there
aæ no other conductoæ in the vicinity) aø øhown in
18
DJBF9P CYAAFNrfi
Fign. 20, 21 and 22.
Theae circles have their centers at the
center of the conductor and their planet are perpendicular to the
conductor. If the cwrent in the conductor be reversed, the
direction in which the compaaa needle is deflected aiP be seen to
reverse a&o, nhowing that the direction of thia magnetic field is
dependent upon the dñection of the current. The relation of the
two in shown in Fig. 20. The fact that the magnetic field exists in
cñcles perpendicular to the conductor explains the reversal of the
compaaa needle when moved from a point above the conductor to
a point beneath it, for the direction of the field above the
conductor must be oppoaite to that beneath the con- ductor. Thin
is Gugtrated ie Nga. 21 and 22.1
The experiment shown in Fig. 23 is illustrative of this concentric relation of the 8ux to the conductor. A conductor carrying
,q
a current io brought veNically
down through a horizontal sheet
of cardboard. Iron Oingn
sprinkled on the cardboard form
concentric circles. (A cwrent of
about 1& amperes is necea- oary
to obtain distinct figures.) If
four or more compares are
arranged aa ahoan in Ng. 23,
they »ill indicate, by the direction in which their needles
point, that the magnetic ?nea
are circles having the axis of the
wire as a center.
H. Relation of Magnetic
Field to Cuwent.—A definite relation existo between the direcCIO. 23.—Investigation of the magnetic
tion of tEe current in a conductor
field surrounding a conductor.
and the direction ofthe magnetic
field surrounding the conductor,
There are two oimple ruleo by
which this relation may be remembered.
' A circle having a cross inside (IB) indicates that the current ia 8o«ing into
the paper, and represents the feathered end of an arrow. A cñnle having a dot
at the center ('i7) indicates that the current is 8owing out of 4he paper, and
represents the approaching tip of an arrow.
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»/4XV3' C/?47¥E3‹zS
number of magnetic lines ä a maximum. The pulling together of
the conductor reduces the length of path abcd through æhich the
ûnes mwt pæo. The field due to each conductor separately Ô stül
cÙcular in form but the resultant magnetic ûnes are no longer
circular, as Ô shoæn in Fig. 25.
In Fig. 26 are shoæn the conditions æhich exèt æhen tæo
parallel conductor carry current in oppoaite direction. The
magnetic lines are circleg, but thèse circles are not concentric
either with one another or with the conductor. The lines are
crowded between the conductors and therefore tend to push the
conductor farther apart. Again, æhen the •conductors æparate, the area through which the flux passes is increased, so that
the magnetic cñcuit in this case also tends to so conform itælf
that the magnetic 8ux ä a maximum.
From the foregoing, the following rules may be formulated.
Conductors carrying current in the sam« direction Ynd to & dra»m
together; conductors cerryïng current io oppoÂk direäione tend fo
be repelled /roni each ot£er.
dJl electric eircuite tend lo tn£e eunh a poeitioa ce will mo£e
their currente poroIkI and ,flouñng in tÑeae«ne direction.
Thia e8ect Ô especially pronounced in modern large capacity
power systems. Bus-baæ
been ærenched from
clampa; transformer coûa
been pulled out of pl8ce
have
theû
have
and
transformers arecked by the
forces produced by the enormous
currents ariaing under shorY
c2cuit conditions.
28. Magneêc Field of a Single Tum. If a wire carrying a
cwrent be bent into a loop a
field gimilar to that shoæn in
Fig. 27 il obtained. Thä magFio. 27.- -Magnetic field produeed by
netic field has a north pole and a
a single turn.
aouth pole which pæseaa all the
properties of similar poles of a short bar magnet. A compaaa needle
placed in th& field angumes the direction shown, the north pole
pointing in the direction of the magnetic lines.
MhMC7ROMACWE77S36
21
fl7. The Solenóid.—An electfic conductor wound in the fom of
a helix aztd carryiog cwrent is called a solenoid. A simple solenoid
and the magnetic field produced within it when current 8ows
through the conductor is shown in Fig. 28. The solenoid may be
connidered as consisting of a large number of the twaa
Flo. 28.—Magnetic field produced by a hehx or solenoid.
ahown in Fig. 27 placed together. The solenoid winding may
coeoiot of aever& layera as ahown in Ng. 30.
The relation of the direction of the Bux within the solenoid to
the direction in which the cwrent 8owa in the helix may be
determined by the hand rule, or by the corkscrew rule of Par. 24.
Fin. 29.—&lation of magnetio pole to direction of exeiting current.
Another simple method, in shown in Fig. 29, where the a rrown at
the ends of the "N" and the "£" show the direction of current ie the
cofi. For example, when looking down upon a north pole the
current direction in the cofi wfil be counter-clockwise as nhown by
the " N ; " when looking down upon a south pole the direction of
the exciting current wG be clockwise as shown by the " 5 . "
23
DfAsCr*VARfwTf
$& The Commercial Solenoid. The soleñoid é ueed in practice
for tripping cñcuit breakera @ar. 237), for operating contactora
in automatic motor startera (Par. S19), for operating voltage
regulating devices (Par. S07), for arc lamp feeds (Ohap. XIII,
Vol. II), for operating valvea, and for numerous other purpoaea.
In practically all instances a aoft iron (or steel) plung-
er or armature is neceaaary to obtain the tractive pull required of
the solenoid. The operation of asolenoid and plungeris indicated
in Fig. 30. The flux due to the solenoid produced magnetic poles
on the plunger. The pole nearer the plunger will be of auch nign
that it will be urged along the Unes of force, (aee Par. 11) and in
auch a direction a8 to be drawn within the solenoid.
Fno. 31.—“Iron-elad”eolenoid and plunger with stop.
A position of equilibrium is reached when the center of the
plunger reaches the center of the solenoid (Fig. 30). Fig. 31 ahown
an “iron«lad” solenoid commonly uaed for traitive work. The
iron-clad feature increaaea the range of unsorm pull and produced
a very decided increaae of pull as the plunger
» « » D Æ « » « Æ
2 3
approacheø the end of the øtroke. When a stop “o” is uøed,
the solenoid becomeø a plunger ek4romognet. This changes
Dlstance fi- Inches
Fin. 32.—Pull of solenoid on plunger.
the characteråtics of the solenoid in that the maximum pull
noæ occura æhen the end of the plunger å near the stop.
Fig.
32 øhoæø the reøultø of solenoid testø
made by C. R. Underhill.' Curve (a) is the
pull upon the plunger of a øimple
olenoid like that of Ug. 30; cwve (b)
shoæs the pull when thiø solenoid å ironclad aø in Fig. 31 but without a
*tap; curve (c) shoæø the eØect of the
“stop” on the pull. It wfil be noted that
the iron-clad featwe and the stop have
but ?ttle e8ect except near the end of the
øtroke.
An important practical appUcation of
the solenoid occuæ in the braking of
elevatoæ and craneø. When the poæer is
removed from the lifting motor or
øhen the poæer iø interrupted due to a Fin. 33.—Plunger electrooperatinø a crane
broken æke or other accident, the brake magnet
brake.
muat be applied immediately.
One method of accomplå@ng this is shown iq Fig. 33. When
' “ Standard Handbæk, Section 5.”
the power, for any reaaon, è interrupted, the pluoger P of the
solenoid d drops, due partly to gravity and partly to the action of
the apônga £. The springa 5 immediately force the leveæ L
agaiæt the brake banda B, presaing theæ agaiæt the brake drum
A, thua e8ecting the braking action. When the poæer ä appûed to
the lifting motor, the plunger P è pulled up, thus releaaing the
brake. A plunger electromagnet ä most suitable for this‘ purpoae
becauae the atroke à short and the pull muat be positive.
H. The Bœnoeöoo Solenoid. The use of an armature m
connection æith solenoid è wefl illuatrated by the relay or the
sounder uaed in telegraphy, and alao by electric bells, buzzeæ, etc.
To increaae the e8ectiveneas of 8uCh devicea tæo ao1enoi&
are uaed, each being placed on one of the lega of a horseshoe or Ushaped magnet. When the coi& 9 (Ug. 34) become excited, the
iron armature d é attracted because of the tendency of the
magnetic lines to make their path of minimum len@h. Aa a rule,
the armatwe «'t is not allowed to cloae the magnetic cñcuit completely, for under these conditiona the magnetic linos still exist
after the excitation in removed, preventing rapid releaae of the
armature. The stop £’ preventa the armatwe making contaot
with the cores FY and thus completely clo8ing the magnetic
circuit. The contacts A close any secondary circuit that the relay
may be operating. The 8pring I drawa the armature back against
a atop d when the excitation is removed.
r I«. as.—Cutler-Stammer 38-inch magnet, handling heavy caøtingø.
26
o7Racz' ccrRRaæz'a
fi0. The Lifting Magnet.—Lifting magnetø are uøed commercially to handle iron and ateel in various forms. A very appreciable øaving of time and labor å e8ected by theiruae, becauøe
ehains and øUngo for holding the load are not necesøary. They
very uøeful for handling øteel b?lets in rolling millø, but
the billets cannot be picked up æhen red hot aø they ltæe their
magnetic propertieø at thiø temperatur. Magneta are eøpecially
uøeful in loading and unloading oteel railø, for an entire layer may
be picked up and laid doøn again æithout being dåarranged.
Lifting magnetø e8ect a very great øaving of labor æhen amaE
pieceø of iron, such aø scrap iron, are handled, for they %1 pick up
large quantitieø at every lift. Without a magnet each individual
piece æould have to be moved by hand. Fig. 35 shoæø in croga-
øection a typical Cutler-Hammer lkting magnet.
Ug. 36 øhoæa a lifting magnet in actual operation.
Formulæ for the holding force ofelectromagnetø are given in
Par. 149.
Fin. 37.—Magnetic øeparator.
It should be Understood that the magnet itseh does ?ttle or no
work in the lifting, but merely serveo ae a holding device. The
actual work is pedormed by the engine or motor which operates
the steel ropea or chaiaa attached to the magnet.
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ducoa, therefore, the amountol $uxpaaaing throughtbearmature.
Moreover, the 8ux in taking the abortest patb tends to crowd
through the upper hah ol the armature. Thä tenda to produce
unaatäfactory commutation.
The magnetic circuit ol a bi-po1ar generator ol modern design
is shown in Fig. 3ö. Because of the aymmetry of the magnetic
circuit the 8ux divides evealy through the two aides of the
armature. The long air path existing between the pole shoes
Pleld
TIO. 39.—Magnetic circuit and field «indings of a modern bi-polar generator.
reduees the magnetic leakage to a minimum. lt ö to be noted that
the flux in the cores divides æ it passes into the yoke. Ordinarily
the yoke need only be one-half the crosn-section of the field corea.
Directæurrent machines of the bi-polar type are made usually in
small unité.
Fig. 40 shows the more complex magnetic circuits of a multipolar generator having eight polen. lt is to be noted that the poles
are alternately north and noutb. Again the 8ux paæing through
the field cores divides, both upon reaching the yoke
and upon reaching the armature path and the crossæection of the