`
`PANASONIC EX1013, page 001
` IPR2021-01115
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`

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`
`
`
`
`
`
`PRINCIPLES 0F PHYSICS SERIES
`
`
`ELECTRICITY
`
`MAGNETISM
`
`53'
`
`FRANCIS WESTON SEARS
`
`Prafeuor of Playn'm
`
`Maude/awn” Inititut: of Teclmulogy
`
`I951
`
`ADDISON-WESLEY PRESS,
`CAMBRIDGE 42, MASS.
`
`INC.
`
`(CourtesyofGeneral!Elecrric)
`
`
`
`
`
`
`
`
` IOU-MillionvoItinductionelectronaccelerator.
`
`PANASONIC EX1013, page 002
` IPR2021-01115
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`I ‘u/vmm/Il 1.951
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`Printed in U. S. A.
`
`PREFACE
`
`This book is the second volume of a. series of texts written for the two-
`year course in General Physics at the Massachusetts Institute of Tech-
`nology. The time allotted to Electricity and Magnetism in this course
`covers approximately the first 20 of the 30 weeks of the second year. The
`remainder of the second year is devoted to Optics.
`Students using the book have completed, during their first year, a. course
`in Mechanics, Heat, and Sound. They have also studied Analytical
`Geometry and Calculus for a full year and are completing Calculus and
`Differential Equations during their second year. This thorough grounding
`in Mathematics and Physics makes it possible to develop the subject of
`Electricity and Magnetism on a. somewhat higher level than in the usual
`college course in General Physics.
`Except for brief mention of the electrostatic and electromagnetic systems,
`rationalized mks units are used throughout. The symbols and terminol-
`ogy, with a few exceptions, are those recommended by the Committee on
`Electric and Magnetic Units of
`the American Association of Physics
`Teachers in its report of June, 1938.
`The author wishes to express his gratitude to Dr. Charles W. Sheppard,
`who wrote the sections on chemical emf’s, and to Dr. Mark W. Zemansky
`for hls assistance In preparing the manuscript for publication. Acknowl—
`edgement Is also made to numerous contributors to the American Physms
`Teacher and the American Journal of Physics.
`The line drawings for all of the books in the series were made by Mrs.
`Jane A. Osgood, and the wash drawings by Mr. Joseph S. Banks. The
`entire staff of Addison-Wesley Press, and Mrs. Olga A. Crawford in
`particular, have been most co-operative in the task of seeing the series of
`texts through the press.
`
`Cambridge, Mass.
`March, 1946
`
`FRANCIS VVESTON SEARS.
`
`PANASONIC EX1013, page 003
` IPR2021-01115
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`

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`(TIIAPTER 1. COULOMB’S LAW .
`
`. ..........
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`CONTENTS
`
`PA 1
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`1
`
`ADDISON WI'IHIIICY PHYSICS SERIES
`.'
`1
`IIMM'IM \VMH’I‘UN SEARS Consulting Editor
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`MANUAL 01“ ELECTRICAL MEASUREMENTS
`1
`NDAMENTALS 0F ELECTRONICS
`Principles of Physics Series
`UND
`Smrs_uECHANICS HEAT AND So
`gears E ELECTRICITY AND MAGNETISM
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`Lonr/uu-Lz’flshttz — THE CLASSICAL THEORY OF FIELDS
`Goodman—INTRODUCTION To PILE THEORY
`(The Science and Engineering of Nuclear Power 1)
`Gomlman —APPLICATIONs or NUCLEAR ENERGY
`(The Science and Engineering of Nuclea1 Power, 11)
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`1-5 Verification of Coulomb’s law. Rutherford’s nuclear atom .
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`PANASONIC EX1013, page 004
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`vi
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`I 'I I \' 7+; \‘ 1-5
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`CONTENTS
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`PAGE
`101 CHAPTER 81 CAPACITANCE AND CAPACITORS 1
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`CHAPTER 91THE NIAGNETIC FIELD .
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`9-4 Orbits of charged particlesIn magnetic fields1
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`9—9 Force and torque on a complete c1rcu1t
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`CHAPTER 101 GALVANOMETERS, AMMETERS, AND VOLTMETERS.
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`CHAPTER 11. MAGNETIC FIELD OF A CURRENT AND OF A MOVING
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`176
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`187
`12-3 Lenz’s law .
`
`\IIIIII'II III
`I
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`
`PANASONIC EX1013, page 005
` IPR2021-01115
`
`

`

`
`
`vlll
`
`r '1 I \ I‘M 1's
`
`PAGE
`290
`___________ .
`11". In“... .1“, mm"...
`I'J a]
`291
`___________ _
`_
`lturllm-II u-ml m n Inlllllllu .0"
`HI II
`..... .
`....... 294
`I'll: nllurl IIIHI'IIl min-unlur
`Ill
`I
`“HUI-h lull lm-lllml all MOIIlll'lng magnetic flux ...... .
`.
`i
`295
`I“ H
`llfll‘fliumll m ulnmpum.
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`296
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`I“ Hi In“: I-mII-uln
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`l-"nHm M hum l'\\'r‘I-‘. .................... ‘ 302
`H I Hullml Inductance
`.
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`A
`‘
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`302
`H ul
`lh-Il
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`" " ”““"" °' “””“ in 3“ mm “”“” -
`-
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`:l: .“l
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`------ I
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`:33
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`DIM Him 14. MAGNETIC PROPERTIES OF MATTER ......... 316
`lt-l
`Introduction ....................... .
`316
`14-2 Origin of magnetic effects ............... .
`.
`r
`317
`14-3 Equivalent surface currents ...............
`‘
`320
`.
`14—4 Magnetic susceptibility, permeability, and magnetic intensity .
`.
`320
`14—5 Magnetization ..................... r
`.
`328
`CfigiTEgeiimfgizgfiAGfiéT‘Isi/I .‘ " _'
`'
`_'
`‘
`I
`'
`'
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`' ::: 33::
`15-2 The Curie temperature
`.
`. .............. .
`.
`.
`335
`15-3 Hysteresis
`.
`.
`.
`.‘ ................... '.
`.
`335
`15—4 The domain theory ................. .
`.
`.
`.
`339
`15-5 Magnetic poles ....................... 340
`15-6 The magnetic field of the earth .
`.
`. ............. 343
`15-7 General definition of magnetic intensity ............ 344
`15—8 Magnetization of a bar
`.
`.
`,
`i
`.
`.
`.
`.
`.
`.
`.
`.
`.
`l
`.
`.
`.
`.
`346
`15—9 Torque on a bar magnet
`.
`. ................ .
`347
`15—10 Magnetic moment. The magnetometer
`.
`.
`.
`_....... .
`l
`350
`15-11 The magnetic circuit .................... 352
`15-12 Derivation of magnetic circuit equation ......... _
`.
`.
`355
`15-13 Energy per unit volume in a magnetic field ........ r
`.
`.
`358
`
`CHAPTER 16. ALTERNATING CURRENTS .............. 362
`16-1 The alternating current series circuit
`.
`. ........ .
`.
`.
`362
`16-2 Root-mean-square or efi'ective values ............. 365
`16-3 Phase relations between voltage and current .......... 367
`16-4 Potential difference between points of an A. C. circuit
`.
`.
`.
`.
`.
`.
`368
`16—5 Rotating vector diagrams .................. 371
`16—6 Circuits in parallel ...................... 374
`
`16-7 Resonance ......................... 374
`
`16-8 Power in A. C. circuits .................. .
`16-9 The transformer ..................... r
`
`377
`381
`
`CONTENTS
`
`ix
`PAGE
`
`_
`392
`CHAPTER 17. ELECTRICAL OSCILLATIONS AND ELECTROMAGNETIC
`.
`392
`WAVES :
`.
`.
`'.
`.
`2 .................... ~.
`17"1 Eben-1°31 OSPIHaT’mnS """""""""""" 394
`17'2 Damged OSCIIlatlgnS '
`'
`'
`'
`'
`i ------------ 395
`17'3
`SUSt§1¥ed oscillations """"""" . """ 396
`1‘7'4 Radiatlon """ ,' """"""""""" 399
`17—5 Velocity of electromagnetic waves ---------------
`17—6 The Poynting vector .................... 405
`17—7 Reflection and refraction. Fresnel’s formulae .......... 407
`-
`C’iQ‘ZTEEIiienfiiiii‘ifiil‘e‘f
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`‘
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`18-2 Thermionic emission. The vacuum diode ........... 2;;
`.
`.
`.
`.
`,
`.
`.
`.
`.
`.
`.
`.
`.
`.
`.
`.
`18-3 Multi-electrode vacuum tubes
`18-4 ‘The cathode ray oscillograph ................. 425
`18-5 The photoelectric effect
`.
`.
`.
`.
`.
`.
`.
`.
`.
`1 ......... 426
`18-6 The x-ray tube ................... -.
`.
`.
`.
`429
`18-7 Conduction in gases ___________ . .........." 430
`PHYSICAL CONSTANTS
`TABLE OF SYMBOLS
`NATURAL TRIGONOMETRIC FUNCTIONS
`COMMON LOGARITHMS
`CONSTANTS AND CONVERSION FACTORS
`GREEK ALPHABET
`
`INDEX
`ANSWERS T0 PROBLEMS
`
`‘
`
`'
`
`PANASONIC EX1013, page 006
` IPR2021-01115
`
`

`

`4O
`
`’I'IIE ELECTRIC FIELD
`
`[CHAR 2
`
`2-8]
`
`APPLICATION OF GAUSS’S LAW
`
`41
`
`and in (-xprnumul in (Mlllllllll)H/lll()ll()['2.) Construct a gaussian surface as in
`Fig. 2-18. By the same reasoning
`as in the previous example,
`1
`EX21rTb=—Xa'X2-Irab,
`En
`
`
`
`1/
`FIG. 2-18. Gaussian surface for a.
`charged cylinder.
`
`long
`
`E =
`
`111'
`607‘
`
`(2—14)
`
`The charge per unit length of the
`cylinder is 21am Calling this A as
`before, we have
`
`)\ = 21raa,
`
`ya = )\/27r,
`
`and Eq. (2-14) becomes
`
`E = — —-
`
`(2-15)
`
`This is the same as the expression for the field around a “line” of
`charge. Hence the field outside a charged cylinder is the same as though
`the charge on the cylinder were concentrated along its axis, Of course
`the field inside the cylinder is zero, and Eqs (2—14) and (2-15) are true
`only for values of 7 equal to or greater than a.
`The field in the space between two oppositely charged coaxial cylin-
`ders, having equal charges per unit length,
`is also given by Eq.
`(2-15).
`The quantity )\ represents the charge per unit length on either cylinder.
`Field around a charged sphere.
`It will be left as an exercise to show
`by Gauss’s law that the field at a distance r from the center of a sphere
`of radius a, on which the surface density of charge is uniform and given
`by a, is
`
`l 0&2
`E = ——:
`60 T2
`
`where r is equal to or greater than a.
`Since the total charge g on the sphere is
`
`Eq. (2-16) can be written
`
`g = 41ra20',
`
`E _ n _
`
`(2-15)
`
`
`
`and the field outside a uniformly
`charged conducting sphere is the
`same as though all of the charge
`were concentrated at the center of
`the sphere. The field inside the
`sphere is zero.
`Eq. (2-16) also gives the electric
`intensity at points in the space be-
`tween two concentric spherical con—
`(luctors.
`
`plates.
`parallel
`between
`Field
`When two plane parallel conducting
`plates, having the size and spacing
`shown in Fig. 2—19, are given equal
`and opposite charges, the field be—
`tween and around them is approxi-
`mately as shown in Fig. 2-19(a).
`While most of the charge accumu-
`lates at the opposing faces of the
`plates, and the field is essentially
`uniform in the space between them,
`there is a small quantity of charge
`on the outer surfaces of the plates
`and a certain spreading or “fring—
`ing” of the field at the edges of the
`plates.
`As the plates are made larger
`and the distance between them di-
`minished, the fringing becomes rela—
`tively less. Such an arrangement
`of
`two oppositely charged plates
`separated by a distance small com-
`pared with their linear dimensions
`is encountered in many pieces of
`(electrical equipment, notably in ca—
`pacitors (see Sec. 8-3).
`In many
`instances the fringing is entirely neg-
`ligible, and even if its is not,
`it is
`usually neglected for simplicity in
`computation. We shall
`therefore
`
`
`
`l l
`
`IIIIIIIII)
`
`
`
`(a)
`
`FIG. 2-19. Electric field between oppo-
`
`PANASONIC EX1013, page 007
` IPR2021-01115
`
`

`

`
`
`THE MILLIKAN OIL DROP EXPERIMENT
`
`43
`
`THE ELECTRIC FIELD
`
`[CHAR 2
`
`2-9]
`
`oppositely charged plates is uniform as in Fig. 2-19(b), and that the charges
`are distributed uniformly over the opposing surfaces.
`The electric intensity at a point in the space between the plates can
`be computed from the definition
`E:
`
`
`1
`47r£0
`
`dq
`r2
`
`by performing a double integration over both plates, but it is much simpler
`to compute it from Gauss’s law. The small rectangle in Fig. 2—19(b) is
`a side View of a closed surface shaped like a pillbox.
`Its ends, of area
`dA, are perpendicular to the plane of the figure. One of them lies within
`the left conductor, the other in the field. Let E represent the (uniform)
`electric intensity between the plates, and o' the surface density of charge
`(charge per unit area) on either plate. Lines of force cross the surface
`of the pillbox only over the end in the space between the plates, since the
`field within the conductor is zero. The number of lines crossing this end
`is E dA. The charge» within the pillbox is a dA. Then from Gauss’s law
`1
`= *o‘dA,
`
`EdA
`
`(2-17)
`
`In practice, electric fields are much more commonly set up by charges
`distributed over parallel plates, than by some arrangement of point charges.
`If we had not. introduced the factor 47r in our original formulation of Cou—
`lomb’s law, we would have found it appearing in Eq.
`(2—17). The ra-
`tionalized system therefore relegates the.factor 47rd to equations which,
`while fundamental, are less frequently encountered.
`We have shown in Sec. 2—7 that the field just outside the surface of
`any charged conductor is at right angles to the surface.
`If a small pill-
`box is constructed as in Fig. 2-19(b)_, enclosing a small portion of any
`charged surface, it follows that the electric intensity just outside the sur-
`face is also given by Eq.
`(2—17).
`In general, of course, the field varies
`as one proceeds away from the surface.
`In the special case of two plane
`parallel plates, the field is the same at all points between the plates.
`Note that Eqs.
`(2—14) and (2-16) reduce to
`1= — a
`50
`
`
`
`Oil drop
`
`FIG. 2-20. Millikan’s oil drop experiment.
`
`2—9 The Millikan oil drop experiment. We have now developed the
`theory of electrostatics to a point where one of the classical experiments
`of all time can be described—the measurement of the charge of an indi-
`vidual electron by Robert Andrews Millikan.
`Millikan’s apparatus is shown in Fig 2-20. A and B are two accu-
`rately parallel horizontal metal plates. Oil
`is sprayed in fine droplets
`from an atomizer above the upper plate and a few of the droplets allowed
`to fall through a small hole in this plate. A beam of light is directed
`between the plates and a telescope set up with its axis transverse to the
`light beam. The oil drops,
`illuminated by the light beam, appear like
`tiny bright stars when viewed through the telescope, falling slowly under
`the combined influence of their weight, the buoyant force of the air, and
`the viscous force opposing their motion.
`It is found that the oil droplets in the spray from an atomizer are
`electrically charged, presumably because of
`frictional
`effects. This
`charge is usually negative, meaning that the drops have acquired one or
`more excess electrons.
`If now the upper plate is positively charged and
`the lower plate negatively charged, the region between the plates becomes
`a uniform electric field. By adjusting the electric intensity,
`the force
`
`PANASONIC EX1013, page 008
` IPR2021-01115
`
`

`

`
`
`_ 7-11
`
`INDUCED CHARGES
`
`171
`
`E
`
`CHAPTER 7
`PROPERTIES OF DIELECTRICS
`
`,
`
`
`
`
`
`
`
`
`i thductor, of course, immediately rearrange themselves as soon as the
`
`Wmnrluctor is placed in the field, but let us assume for the moment that
`”my do not. The field then penetrates the conductor. Under the in—
`fluence of this field, the free electrons in the conductor move toward its
`lift surface, leaving a positive charge on its right surface. This motion
`Iiitmtinues until at all points Within the conductor the field set up by the
`;|1_1y1'-,rs of surface charge 1s equal and oppos1te to the 011g1nal field. The
`
`'gg'mtion of charge then ceases. The xc :1: char 5 at th surfaces of the
`7-1 Induced Charges. When an UhChaTged hOdb' 0f any sort, a 00'"
`liillilllcllfll' are called induced charges. The net charge on the conductor
`ductor or a dielectric, is brought into an electric field, a rearrangement of
`'figllmins zero.
`the charges in the body always results.
`If the body is a conductor, 1le :
`The field set up by the induced charges is shown by dotted lines in
`WWW :
`
`3|!“ng 7- 1(0). The resultant field is Shown in Fig. 7-1 (CD-
`Inside the con«
`bodv a field—freeX eguipotential volume.
`If the body is a nonconduclor!
`the electrons and the positive nuclei in each molecule are displaced W _i_l1|1_ tor the field1s everywhere zero
`In the gap between the conductor and
`
`the fiEld bIlt 511109 they are 1101? free to move Indefinltely the 1nter1or '1'
`the plates the field1s the same as it was before the conductor was inserted.
`thebod——3W9111potentralreEWWW‘EGOHIW .Ml of the lines of force that originate on the positive plate terminate on
`
`bodyin either case remains zero (the conductor15 assumed to be insulalmil
`induced charges on the left face of the conductor. An equal number of
`from other bOdlCS from Wthh it might acquire a charge) hUt certain NEW“
`lilies originate at the induced positive charges on the right face of the con-
`Of the body acquire excess positive 01‘ negative charges called induct-'1!
`Elm-tor and terminate on the negative charges on the other plate. The
`charges.
`In this chapter we shall be concerned chiefly With the Ph‘”
`lmluced charges at the faces of the conductor are equal and opposite in
`nomena in a dielectric when it is in an external field, but by way of intro.
`flu“ to the original charges on the plates, and, as far as the interior of the
`duction let us consider first the charge distribution on an originally uns-
`immluctor is concerned,
`they effectively neutralize the charges on the
`charged conductor in the form of a flat slab or sheet when it is inserted in
`plums. Hence the field in the conductor is zero.
`the field between two plane parallel conductors having equal and Opposite
`charges.
`If fringing effects are neglected,
`the field is uniform in tlm
`region between the charged plates, as in Fig. 7—1(a).
`In Fig. 7—1(b) an uncharged conductor has been inserted in the field,
`without touching either of the charged plates. The free charges in tlu‘)
`
`
`
` (/1)
`
`
`
`
`
`
`FIG. 7-1.
`ductor.
`.
`
`(b) Introduction of a (1m-
`(a) Electric field between two chargedplates.
`. induced :-
`es and their field.
`(d) Rpesultant field when a conductor Ii
`
`
`
`“1117-2.
`
`(:1) A nonpelnr molecule becomes an induced Llipole 111 an external field.
`
`(r!)
`
`
`PANASONIC EX1013, page 009
` IPR2021-01115
`
`

`

` 172
`
`PROPERTIES OF DIELECTRICS
`[cum If.
`INDUCED CHARGES
`
`
`.WA-
`
`
`
`
`
`++++++++
`EIWAI
`
`
`
`:'W/fl'I.
`
`
`EWII
`I
`
`
`
`+
`
`:IW/IWJ
`:Ifir’fi
`:IW/WAZ.
`++IW/fl
`m
`(”J
`(c)
`(’1)
`It»
`(b) introduction of a
`(a) Electric field between two charged plates.
`. I'm. 7-3.
`(c) Induced surface charges and their field.
`(d) Resultant field when a
`electric.
`“Metric13 between Charge‘l Plates-
`
`I
`I
`.
`.
`-—.—i—I—I—i
`
`
`:
`I
`_
`I
`.
`I
`
`
`—
`'
`I
`'
`'
`.
`.-.
`
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`:
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`
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`-
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`:
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`Fl—lfl—l—li'
`
`
`
`
`
`
`F10 7—4
`
`(a) A conductingsphere in an external electric field.
`
`(b) The field due
`
`IiIIiI
`Consider the behaviour of a dielectric in the same electric field.
`our present purposes the molecules of a.dielectric may be classified [Ii
`either polar or nonpolar. A nonpolar molecule is one in which ll'u]
`“centers of gravity” of
`the protons and electrons normally coinI'iIliI},
`while a polar molecule is one in which they do not. Under the mamma-
`of an electric field the charges of a nonpolar molecule become diSpIIIIII.II'§l,'
`as in Fig. 7—2 (a). The molecule is said to become polarized by the field Inn]-
`is called an induced dipole, of dipole moment (see Sec. 2—3) equal to the.
`product of either charge and the distance between them. The effect of
`an electric field on a polar molecule is to orient it in the direction of LhI'I
`field as in Fig. 7-2 (b). The dipole moment may also be increased by tlIu
`field: A polar 11101801118 ls called a permanent (lipde'
`-
`._
`When 3' nonpolar 1110190119 becomes DOIarled; restoring forces """ll"
`into play on the displaced charges. These are the interparticle binIl‘III'g-
`forces which hold the molecule together. These forces are,
`in pail M.
`least, of electrical origin but, whatever their origin, we may think of them
`as elastic restoring forces pulling the displaced charges together much III!
`if they were connected by a spring. Under the influence of a given 11.“
`ternal field the charges separate until the binding force is equal and OppIIv
`site to the force exerted on the charges by the field. Naturally the biIIIh .
`ing forces vary in magnitude from one kind of molecule to another, wil.l'I
`corresponding differences in the dipole moments developed by a given field
`Whether the polarization is induced or due to the alignment of pernma
`nent dipoles, the arrangement of charges within the molecules of a dielI‘IIu
`trio in an external field will be as shown in Fig. 7-2 (c). The entire dicleu.
`tric, as well as its individual molecules, is said to be polarized. Within
`the two extremely thin surface layers indicated by dotted lines there in
`an excess charge, negative in one layer and positive in the other.
`Them,»
`layers constitute the induced surface charges. The charges are not fI'I'II'I,
`however, but each is bound to an atom lying in or near the surface. Within
`the remainder of the dielectric the net charge remains zero. The internal
`state of a polarized dielectric is therefore characterized not by an excumi
`charge but by the relative displacement of the charges within it.
`The four parts of Fig. 7-3, which should be compared carefully with
`those of Fig. 7—1, illustrate the behaviour of a sheet of dielectric when in.
`serted in the field between a pair of oppositely charged plane parallel
`plates. Fig. 7-3 (a) shows the original field. Fig. 7-3 (b) is the situation
`after the dielectric has been inserted but before any rearrangement of
`charges has occurred.
`Fig. 7—3 (0) shows by dotted lines the field set I”)
`in the dielectric by its induced surface charges. As in Fig. 7—1(c), this fichl
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`PANASONIC EX1013, page 010
` IPR2021-01115
`
`

`

` 175
`
`174
`
`PROPERTIES OF DIELECTRICS
`
`INDUCED CHARGES ON SPHERES
`
`
`
`[Cmr “
`
`
`A dielectric sphere in an originally uniform field is shown in Fig. 7—6.
`not free to move indefinitely, their displacement does not proceed to mifilj-
`in Fig. 7-3, the induced surface charges weaken the field in the sphere
`an extent that the induced field is equal in magnitude to the original Holt-l,-
`I. do not reduce it to zero.
`The field extends inside as well as outside
`The field in the dielectric is therefore weakened, but not reduced to zero.
`
`The resultant field is shown in Fig. 7—3 (d). Some of the lines of Tunis?
`Hence the surface of the sphere is not an equipo-
`llliu dielectric sphere.
`
`Min] and the lines of force do not intersect it at right angles.
`leaving the positive plate penetrate the dielectric; others terminate iti‘i
`
`
`the‘induced charges on the faces of the dielectric.
`The charges induced on the surface of a dielectric sphere in an exter-
`
`nal field afford an explanation of the
`attraction of an uncharged pith ball
`or hit of paper by a charged rod of
`rubber or glass.
`In Fig. 7-6, where
`the external field is uniform, the net
`force on the sphere is zero since the
`forces on the positive and negative
`induced charges are equal and oppo—
`site. However,
`if the field is non—
`uniform the induced charges are in
`regions where the electric intensity
`is different and the force in one direc-
`tion is not equal to that in the other.
`Fig. 7-7 shows an uncharged di-
`electric sphere B in the radial field of
`a positive charge A. The induced
`positive charges on B experience a
`force toward the right while the force
`on the negative charges is toward
`
`It is of some interest to consider
`7-2 Induced charges on spheres.
`the induced charges on a spherical conductor or insulator when inserliiijf
`in an originally uniform field. The conducting sphere is illustrated ll},
`Fig. 7—4. As in Fig. 7-1,
`the free charges within the sphere rearrurmi
`themselves in such a way as to make the field zero at internal points.
`'l'l'u's
`field of the induced charges is shown by dotted lines in Fig. 7-4 (h) and the]
`resultant of this field and the original field in Fig. 74(0). Traces of a low
`equipotential surfaces, of which the surface of the sphere is one, are Ill-e
`shown.
`Since lines of force and equipotential surfaces are orthogonal,
`the lines of force intersect the surface of the sphere at right angles.
`The same physical principles are involved whatever the shape of ai_
`conductor, but the mathematical expressions for the field and charge (ll-3»
`tribution are extremely complex except for spheres and ellipsoids. Thug
`if two conducting spheres in contact are placed in a field, one acquires ml
`excess positive and the other an excess negative charge, the charge (luau
`tribution being such as to bring both spheres to the same potential ltlltl
`reduce the field Within them to zero.
`If slightly separated while still In
`the field and then removed from it, the induced charges become “trapped”
`on the spheres and may readily be detected by an electroscope.
`Sm).
`Fig. 7-5.
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`((1)
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`(lil
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`(Cl
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`I’IG. 7-6. A dielectric sphere in an
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`Q
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`x
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`PANASONIC EX1013, page 011
` IPR2021-01115
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`

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`CAPACITANCE AND CAPACITORS
`
`[(lnu'
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`9-.
`
` 198
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` ll! THE PARALLEL PLATE CAPACITOR
` 199
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`
`
`Since 60, A, and d are constants for a given capacitor, the capacitance
`The term “condenser” has long been used for the piece of apparulni:
`Ii n constant independent of the charge on the capacitor, and is directly
`we have described as a “capacitor.” But “capacitor” is to be prel‘vrrr-tl,
`both because nothing is actually “condensed” in a “condenser,” and ulefil‘.
`microlmrtional to the area of the plates and inversely proportional to their
`
`.
`'- mration.
`(The simple form of Eq.
`(8—5) results from the introduction
`because of the corresponding usage of the terms resistance and rcslHlmr.
`_ii_l
`lllc factor 47r in the proportionality constant in Coulomb’s law. Had
`That is, a resistor is a device that has resistance, and a capacitor is a (lm urg-
`that has capacitance.
`.{tlliH l‘uctor not been written explicitly in this law it would have appeared
`‘1]:
`l‘iq.
`(8-5).
`Since in practice the latter equation is used much more
`llrmluently than is Coulomb’s law, there is an advantage in transferring
`the l'actor 47r to Coulomb’s law.)
`If mks units are used, A is to be expressed in square meters and d in
`hwlcrs. The capacitance C will then be in farads.
`ICq.
`(8—5)
`indicates an alternate combination of units in which per—
`nultivity can be expressed.
`If we solve this equation for so we obtain
`
`8-3 The parallel plate capacitor. The most common type of capnrlluii
`consists of two conducting plates parallel to one another and separnlgag‘l,
`by a distance which is small compared with the linear dimensions of lluif
`plates.
`See Fig. 8-1. Practically the entire field of such a capacitor in“
`localized in the region between the plates as shown. There is a slight:
`“fringing” of the field at its outer boundary, but the fringing become;-
`relatively less as the plates are brou