wj hooper news horions motional e fields

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William J. HOOPER

Motional Electric Field

New Horizons In Electric, Magnetic & Gravitational

Field Theory

by

William J. Hooper

(B.A., M.A., Ph. D. (University of California Berkeley! President " Dire#tor of

$esear#h, %le#trodynami# &ravity, In#.! Professor of Physi#s %merit's, Prin#iia

Colle)e.

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Table of Contents

Preface

Introdction! "e# Hori$ons in Field theor%

Chapter &! Fndamental Fields

Chapter '! The Electroma(netic Force E)ation

Chapter *! Experimental Confirmations b% Electrostatic +hieldin(

Chapter ,! The Motional Ma(netic Field

Chapter -! ra/itation

Chapter 0! 1nti2ra/it% 3 Electrical Po#er

Chapter 4! +ome Confirmin( Experiments

1ppendix

+his book is dedi#ated to Mr. And Mrs. arren . &ibson, -ho have made it ossible

finan#ially to #arry on the last t-o years of fr'itf'l exerimental -ork. +he devotion

and dedi#ation of Mrs. &ibson (ran to this ro/e#t, servin) as se#retary and $esear#h

Assistant, has rovided a flame -hi#h has ket it a)lo- to its resent stat's.

0It aears to me, that the st'dy of ele#troma)netism in all its ase#ts has no- be#ome

of the first imortan#e as a means of romotin) the ro)ress of s#ien#e.0 (1ames Clerk

Max-ell2 Treatise on Electricity & Magnetism, 3ol. 4, Pref., . vii.

Preface

5early everyone believes that )ravity is a for#e emanatin) from matter, b't /'st ho-,

/'st -hy, nobody seems to kno-6 In the s#ien#e of hysi#s m'#h is kno-n abo't

ele#tri#ity and ma)netism, b't of )ravity, nothin) really, -ith the ex#etion of the

inverse s7'are la- of 8ir Isaa# 5e-ton, -hi#h -e kno- )ravity obeys.

+his treatise resents ne-ly dis#overed 'ni7'e and startlin) roerties of one of o'r

ind'#ed ele#tri# fields. It )ives this field a ne- stat's amon) o'r field for#es. Its 'n's'al

roerties are ossessed only by )ravity. hile it is too early to #laim #omlete

identifi#ation of this field and the )ravitational field, the similarities are ama9in)ly

alike.

%le#tri#ity and Ma)netism -ere on#e t-o searate s#ien#es. In 4:;


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#ond'#tor. +his dis#overy served to 'nite the t-o s#ien#es of %le#tri#ity and Ma)netism

into one, that of %le#troma)netism.

D'rin) orld ar II the -riter, -orkin) on an invention for a 0drift and )ro'nd seed

meter for air#raft0, arrived at a lan for 'tili9in) the verti#al #omonent of the earth?s

ma)neti# field. If the volta)e ind'#ed bet-een the ends of t-o oriented linear

#ond'#tors travelin) hori9ontally a#ross the verti#al #omonent #o'ld be meas'red-ithin an air#raft, a self>#ontained meter, indeendent of )ro'nd instr'mentalities,

-o'ld be forth#omin). +he lan -as revie-ed by the U.8. B'rea' of 8tandards, and its

-orkability #onfirmed 'nder a #ertain restri#tion. It -as stated that the devi#e -o'ld be

inoerable -ithin a #ond'#tin) #avity s'#h as a metal>#lad air#raft. ='r textbbooks have

ta')ht 's that -hen a linear #ond'#tor moves -ith a velo#ity 3 a#ross a ma)neti# fl'x

of intensity B, an ele#tri# field of ve#tor intensity 3xB is ind'#ed -ithin the -ire and

)ives rise to a volta)e at its terminals. +his ele#troma)neti#ally ind'#ed ele#tri# field,

often #alled a motional ele#tri# field, -e have been ta')ht, -o'ld be ele#trostati# in

#hara#ter, that is, identi#al and indistin)'ishable from an ele#tri# field arisin) from

#har)es of ele#tri#ity. e kno- that radio t'bes, silvered on the inside, shield the

interior from stray ele#trostati# fields. In the same -ay, it -as exlained, s'#h a driftand )ro'nd seed meter -ithin a metal>#lad air#raft -o'ld be shielded from the ele#tri#

field ind'#ed in a #ond'#tor by motion a#ross the verti#al #omonent of the earth?s

ma)neti# field. +his exlanation -as a /olt to the -riter. Ho- #o'ld -e kno-, -itho't

exerimental eviden#e, that s'#h -o'ld be the #ase@ +his resented a )reat #hallen)e6

8ome of the foremost thinkers in hysi#s -ere #ons'lted. It -as dis#overed that there

-as no exerimental eviden#e to s'ort the o'lar belief held by hysi#ists that the

motionally ind'#ed 3 x B field -as ele#trostati# in its f'ndamental #hara#ter and

therefore s'b/e#t to shieldin). It -ill be sho-n ho-, ste by ste, the -riter has been

)'ided over a eriod of ;< years to exerimental means -hi#h at last reveal

exerimentally, beyond all do'bt, the bea'tif'l 'ni7'e roerties of the motional

ele#tri# field. It is not ele#trostati#6 Its imm'nity to shieldin), ma)neti# or ele#trostati#,

is the ex#itin) roerty -hi#h it shares -ith the )ravitational field and thereby indi#ates

their kinshi. By a )eneral theorem in ele#tri# field theory -e kno- that a non>'niform

B x 3 field m'st also a#t attra#tively on matter6 +h's the motional ele#tri# field has

a#7'ired a stat's -hi#h makes it 7'ite 'ni7'e.

&'ided by theory the inventor has b'ilt a )enerator of the B x 3 field -hi#h ro/e#ts its

field into the s'rro'ndin) sa#e. +he -riter #alls this artifi#ially )enerated field

%le#trodynami# &ravity be#a'se it sim'lates )ravity. Altho')h 'tili9in) rin#iles of

ma)neti# field s'erosition and ele#troma)neti# ind'#tion, the rod'#t field, B x 3,

like the )ravitational field dislays no eviden#e that ma)netism lays a art in its)eneration. ike-ise it is free of ele#trostati# #hara#teristi#s. Altho')h ma)neti# fl'x is

moved by the )enerator, there are no me#hani#ally movin) arts.

+he )'idin) #on#et emloyed by the inventor -as first set forth in 4 by %. &.

C'll-i#k ( Electromagnetism & Relativity, . ;E, on)sman &reen " Co.. His

resear#h had led him to the #onvi#tion that the ma)neti# fl'x loos dis#overed by

=ersted -ere a#t'ally in motion alon) the linear #ond'#tor in the dire#tion of the

ele#tron #'rrent )ivin) rise to it, and moved -ith the ele#tron drift velo#ity. ='r

motional ele#tri# field )enerator demonstrates the #orre#tness of the fore)oin)

redi#tion. Its oeration makes 'se of this movement of fl'x to )enerate the B x 3 field

in sa#e abo't the )enerator. +his #onfirmation of C'll-i#k?s redi#tion is anexerimental #ontrib'tion to modern ele#troni# theory and it has all the earmarks of

bein) the -eldin) link -hi#h ties )ravitation to ele#tri#ity and ma)netism. +he oersted


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fl'x, first its dis#overy, and no- the dis#overy that it moves -ith the ele#tron drift

velo#ity )ivin) rise to it, th's holds a 'ni7'e role in the ro#ess of -eldin) the three

s#ien#es into one.

+he ne- )enerator affords 'sef'l instr'mentation for dire#tly meas'rin) ele#tron drift

velo#ities in metals, as -ell as exerimentally determinin) the n'mber of ele#trons

available at vario's temerat'res. +h's, it rovides a ne- exerimental method finvesti)ation into the realm dealt -ith by the ermi>Dira# statisti#s. +heoreti#ally, this

devi#e holds ex#itin) ossibilities of )reat 'tility at very lo- temerat'res. If

s'ffi#iently intense fields #an be obtained by the 'se of s'er#ond'#tin) -ire in o'r

)enerator at lo- temerat'res, as -e have )ood reason to believe is ossible, the

henomenon of attra#tion and olari9ation of materials by this field #an be st'died. +his

-o'ld immediately brin) into the realm of ossible exerimental demonstration s'#h

effe#ts as -ei)htlessness, artifi#ial )ravity, and anti>)ravitational effe#ts. +his

a#hievement, the -riter believes, -ill be no more diffi#'lt of attainment than that -hi#h

has already been demonstrated exerimentally.

8ho'ld s'##ess follo- the forth#omin) lanned #ryo)eni# (lo- temerat'reexeriments and -e find that very intense B x 3 fields #an be )enerated and identified

-ith the )ravitational field, the romise of 'tility to h'manity -o'ld be beyond all

des#rition. ree ele#tri# o-er from the earth?s )ravitational field -o'ld be obtainable

any-here, 'nder the sea, on earth or nei)hborin) sa#e, on the moon or the lanets6

&ravity>free laboratories on earth, and artifi#ial )ravity in sa#e#raft >>> these are some

of the ossibilities6 ith s'#h romises on the hori9on it is diffi#'lt for the -riter to rest

on his oars for one min'te. +his treatise therefore )oes forth -ith 0&reat %xe#tations60

8arasota, (De#ember 4F

Introdction

"e# Hori$ons In Field Theor%

orty years have assed sin#e Max Mason and arren eever -rote in their #elebrated

book, The Electromagnetic Field (4 G . xii, Univ. of Chi#a)o Press, 4;2

0+he )reat s#ientifi# task of the next < years is the develoment of a ne-

ele#troma)neti# theory. It is imossible to fore#ast the form s'#h a theory -ill take, so)reatly are -e re/'di#ed by o'r resent vie-s. It -ill, ho-ever, do'btless be based on

a 7'antitative des#rition of the individ'al behavior of #har)es0

+he ne- hysi#s 'nder the leadershi of s'#h men as %instein, Plan#k, Heisenber),

8#hrodin)er, and Brid)man, has rod'#ed a series of kaleidos#oi# #han)es in #lassi#al

#on#ets. +he #ontrib'tions of the first fo'r of these five men have been -ell

in#ororated into o'r modern textbooks. It is the -ork of Brid)man, his hilosohy as

embodied in 0+he o)i# of Modern Physi#s0 (; G Ma#Millan Co., 4;:, and

arahrased as 0+he =erational 3ie-oint0, -hi#h has to a lar)e extent insired this

treatise, and rovided a bea#on of ill'minated thinkin) to )'ide #ontemorary hysi#ists

in the develoment of ne- ideas. hat Brid)man has done is to sho- 's ho- theadvent of relativity theory has made it ne#essary to take #o)ni9an#e of the fat that ne-

henomena srin) into existen#e as the res'lt of introd'#in) into an exeriment nothin)


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more than motion or a #han)e in motion. e m'st be a-are of ass'min) that be#a'se of

the fa#t that similarities exist bet-een old and ne- henomena that they are ne#essarily

e7'ivalent. +o be se#ifi#, let 's a)ain t'rn to Mason and eaver2

0It #annot be 'r)ed that it has been sho-n exerimentally that movin) arti#les and

#han)in) #'rrents are ri)oro'sly e7'ivalent as re)ards ind'#ed ele#troma)neti# for#es.

It is very easy to let the notation #arry the b'rden of the ar)'ment and to hold that theval'e of #'rl % s related to the rate of #han)e of B in every #ase in the -ay stated by the

e7'ation (#'rl % >@B@t. It is very imortant to oint o't, ho-ever, that by doin) so

one may be overlookin) somethin) of f'ndamental hysi#al imortan#e.0 (J G ibid., .

;

It is this 0somethin) of f'ndamental hysi#al imortan#e0 -hi#h is overlooked -hen the

so>#alled 0rin#ile of e7'ivalen#e0 is alied -itho't ri)oro's examination and

analysis. +his is the very essen#e of Brid)man?s thesis.

+here is no eviden#e that the s'b/e#t matter of ele#troma)netism, sin#e its earliest

in#etion, has ever been )iven the Brid)man treatment. If -e desire to kee o'r f't're)ro-th on solid s#ientifi# )ro'nd, -e are fa#ed -ith the ne#essity of revie- and

revision of old and ne- #on#ets -hi#h dominate thinkin) in the dire#tion of its

inevitable exansion. e need m'#h to learn ho- 0)reatly are -e re/'di#ed by o'r

resent vie-s0. In order to make -ay for the next )reat breakthro')h in hysi#s -e

m'st first #ome fa#e to fa#e -ith fa#ts that reveal ho- )reatly o'r resent #on#et of

fields is restri#tin) o'r thinkin) and limitin) o'r a#hievements.

An examle of one of the )reatest blind sots in #'rrent o'lar field theory -ill

ill'strate this oint. +his blind sot, d'e to an ass'med #on#et, has been 'held by

some of o'r most brilliant mathemati#al hysi#ists. 8o do)mati# and #omletely #ertain

of the a##'ra#y of his osition -as one that he #ontrib'ted the follo-in) /in)le -ith

-hi#h to s'ort his #onvi#tion2

0+here is b't one &od Allah, And Mohammed is his rohet6 +here is b't one ele#tri#

field %, and Max-ell is its rohet60 (E G 1. 8teian, 0%le#trostati# or

%le#troma)neti#ally Ind'#ed %le#tri# ield@0! Scientific Paper 4E4, estin)ho'se

$esear#h aboratory, >4E>E

+hat nat're has rovided 's -ith b't one field a)en#y -hi#h a##elerates ele#trons, one

ele#tri# field, and that one ele#trostati# in its f'ndamental #hara#ter, is erhas the

)reatest of all o'r #'rrent re/'di#ed and erroneo's vie-s. 5one of araday?s famo'sexeriments sho- or rove the existen#e of b't one ele#tri# field in nat're. It is

Max-ell?s translation of these exeriments into the lan)'a)e of mathemati#s that bear

the ta#it ass'mtion of only one s'#h field. B't araday left 's a -ord of -arnin)2

0and #onsiderin) the #onstant tenden#y of the mind to rest on an ass'mtion, and, -hen

it ans-ers every resent 'rose, to for)et that it is an ass'mtion, -e o')ht to

remember that, in s'#h #ases, it be#omes a re/'di#e, and inevitably interferes, more or

less, -ith #learsi)hted /'d)ment.0 ( G Phil.Mag ., 4:EE

It -ill be sho-n -ith exerimental and theoreti#al roof that this ass'med and

re/'di#ed vie- is in#orre#t. Indeed, it is as obsolete as the #on#et of the atom as bein)a sin)le indivisible arti#le, and as obsolete as the #on#et of a sin)le atom for ea#h

element. It is as 'nrealisti# as -ere the ar)'ments of the famo's Professor 8imon


6/56

5e-#omb, re#iient of honorary de)rees from ten %'roean and seven Ameri#an

'niversities, -ho -as demonstratin) mathemati#ally that man #o'ld not fly, -hile the

ri)ht brothers -ere assemblin) their air#raft at Kitty ha-k. 8imly be#a'se it #an be

sho-n mathemati#ally that an ele#trified arti#le -ill tra#e identi#al tra/e#tories in ea#h

of t-o tyes of fields, is no roof that these fields, these a##eleratin) a)en#ies, are

e7'ivalent and identi#al. Penetratin) roerties of fields, renderin) them imm'ne to

shieldin), ossessed by some and not by others, have no mathemati#al reresentation ins'#h so>#alled roofs, hen#e the roof is not ri)oro's be#a'se it does not in#l'de all the

field roerties.

A se#ond modern re/'di#e, an ass'med #on#et, -hi#h has )ained #onsiderable

o'larity, is one -hi#h states 0the -hole #on#et of a ma)neti# field is a fi#tion.0 (F G

P. Moon " D.%. 8en#er2 0%le#troma)netism itho't Ma)netism2 An Histori#al

8ket#h0! Amer. J. Phys., vol. ;;, . 4;>> therefore the

field e7'ation and the for#e e7'ation be#ome identi#al in form -ith the e7'ations

obtained on the ass'mtion that only ele#tri# #har)e exists in nat're. +here is no

exerimental eviden#e, therefore, to /'stify the #ommon ass'mtion that only ele#tri#

#har)es and no ma)neti# #har)es are resent in the -orld of exerien#e. If the reverse

-ere tr'e, or if ele#tri# and ma)neti# #har)es o##'rred #ombined in any fixed ratio, allele#troma)neti# henomena -o'ld take la#e in exa#tly the same -ay. 5o

ele#troma)neti# exeriment -o'ld reveal the roortions in -hi#h the t-o tyes of


7/56

#har)e mi)ht exist.0 ( G ei)h Pa)e " 5orman Adams2 Electrodynamics, . ;4;44,

3an 5ostrand " Co, 4E


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-ay o't of them. It -ill reveal a vista of ne- oort'nities for resear#h. It is #onfidently

believed that as a res'lt of the #larified i#t're th's attained, ne- hori9ons in field

theory are in the offin). A )limse of these hori9ons, to)ether -ith an ele#troma)neti#

theory of )ravitation leadin) ' to the derivation of 5e-ton?s Inverse 87'are a-, -ill

be resented -ith exerimental roosals for its verifi#ation. inally the s'b/e#t of

anti)ravity -ill be dis#'ssed and, in the li)ht of this thesis, ho- a ra#ti#al aroa#h to

this roblem is #learly indi#ated -ith its thrillin) ossibilities.

Chapter &

Fndamental Fields

ebster defines s#ien#e as 0kno-led)e #lassified and made available in the sear#h for

tr'th0. A #orre#t #lassifi#ation of kno-led)e th's be#omes the basi# fo'ndation of a

s#ien#e. +he -ord #lassifi#ation has been 'nderlined by the -riter, be#a'se of its )reat

imortan#e. A -ron) #lassifi#ation of anythin) #an res'lt in )reatly imedin) the ro)ress of the bran#h of s#ien#e in -hi#h it exists. +h's )reat treas'res in s#ien#e #an

be hidden and obs#'red for a)es 'ntil some rose#tor #omes alon) and reveals its tr'e

nat're. A #riti#al s'rvey of the resent stat's if ele#trodynami#s reveals a #onsiderable

n'mber of ele#tri# and ma)neti# fields -hi#h are bro')ht into bein) by oerations

-hi#h are 'ni7'e and seemin)ly 'nrelated. 8o entren#hed is the resent ta#it ass'mtion

of hysi#ists that nat're has rovide nat're -ith one and only one ele#tri# field and one

and only one ma)neti# field that no ioneer has as yet attemted to serio'sly enetrate

this re/'di#e and vent're into the ossibilities of #lassifi#ation -hi#h mi)ht brin) la-

and order to some of o'r #'rrent roblems.

+he advent of relativity theory -as instr'mental in for#in) hysi#ists to reexamine andalter many of their most #herished and f'ndamental #on#ets in hysi#s. Consdier, for

instan#e, the #on#et of time. 5one other than the )reat 8ir Isaa# 5e-ton has defined

time, in his Principia, in the follo-in) manner2

0Absol'te, +r'e, and Mathemati#al +ime, of itself, and from its o-n nat're flo-s

e7'ably -itho't re)ard to anythin) external, and by another name is #alled D'ration.0

Brid)man oints o't -ith )reat #larity that f -e examine the definition of absol'te time

in the li)ht of exeriment, -e find nothin) in nat're -ith s'#h roerties. By examle

after examle he oints o't that many of the st'mblin) blo#ks -hi#h have #lo))ed the ro)ress of hysi#s, and then he does somethin) abo't it. He has #ontrib'ted -hat is

#alled the =erational 3ie-oint as a )'idin) bea#on to enable 's to avoid makin)

these kinds of mistakes in the f't're. In brief, he tells 's -hat -e sho'ld define and

#lassify o'r #on#ets in terms of the oerations -hi#h are ne#essary in order to dete#t

and meas're them, and not in terms -hi#h have no #o'nterart reality in nat're, no

dire#t exerimental eviden#e to s'ort them. =nly as -e do this, he oints o't, #an -e

avoid trea#hero's itfalls and embarrassments in the f't're )ro-th of o'r s#ien#e. He

states, 0It is evident that if -e adot this oint of vie- to-ard #on#ets, namely that the

roer definition of a #on#et is not in terms of its roerties b't in terms of a#t'al

oerations, -e need r'n no dan)er of havin) to revise o'r attit'de to-ard nat're. or if

exerien#e is al-ays des#ribed in terms of exerien#e, there m'st al-ays be#orresonden#e bet-een exerien#e and des#rition of it, and -e need never be

embarrassed, as -e -ere in attemtin) to find in nat're the rototye of 5e-ton?s


9/56

absol'te time0 (4J G Brid)man, o. #it., . F. hile statin) that 0oerational thinkin)

-ill at first rove to be an 'nso#ial virt'e0, he nevertheless redi#ts that, 0In this self>

#ons#io's sear#h for henomena -hi#h in#rease he n'mber of oerationally

indeendent #on#ets, -e exe#t to find a o-erf'l systemati# method dire#tin) the

dis#overy of ne- and essentially imortant hysi#al fa#ts0 (4E G ibid., . ;;E.

+he -riter has #lassified oerationally the three most rominent ele#tri# and the threemost rominent ma)neti# fields -hi#h -e find in nat're. +hey are as follo-s2

'ndamental %le#tri# " Ma)neti# ields (m.k.s. 'nits

(4 %# LrE i eor J

+he ele#trostati# or Co'lomb field arisin) from the resen#e of #har)es

(; %m v x Bs

+he motional ele#tri# field -hi#h a#ts on #har)es travelin) -ith velo#ity 3 a#ross ama)neti# ind'#tion Bs. +his field is rod'#ed by fl'x #'ttin) and sho'ld not be

#onf'sed -ith %t arisin) from fl'x linkin)

(J C'rl %t @B@t

or %t @A@t

+he ele#tri# field %t, in this form'la arises from fl'x linkin), or transformer

ele#troma)neti# ind'#tion dis#overed by Henry and araday. In this field B #han)es

intrinsi#ally -ith time. A is the ma)neti# ve#tor otential.

(E C'rl Hs 1

+his ma)netostati# field H arisin) from a #ond'#tion #'rrent density 1 -ithin a

#ond'#tin) medi'm -as first dis#overed by =ersted. It is at rest -ith rese#t to the

#'rrent #ir#'it so'r#e rod'#in) it.

( Hm >v x D#

+he motional ma)neti# field arisin) from relative velo#ity v -ith rese#t to ele#tri#

#har)es rod'#in) the ele#tri# ind'#tion D#.

(F C'rl H$ @D#@t

+he ma)neti# field H$ s'rro'ndin) a #han)in) ele#tri# ind'#tion #alled a disla#ement

#'rrent. +his ma)neti# field lays a rominent art in the rod'#tion of ele#troma)neti#

radiation. It -as first theoreti#ally redi#ted by Clerk Max-ell.

Parti#'larly ill'minatin) is the analysis of C'll-i#k -ith rese#t to the salient


10/56


11/56

the resent state of o'r kno-led)e, and afford ne- oort'nities for resear#h, ne-

ossibilities in alied hysi#s and ne- hori9ons for a 'nified field theory. An analysis

of the roerties of these fields -ill next be #onsidered so that their 'ni7'e roerties

may be aarent.

+able 4 has been reared to sho- the o'tstandin) differen#es in the roerties of ea#h

of the first three oerationally different ele#tri# fields. +he re#o)nition of the 'ni7'enessof ea#h field is aided by a #omarative st'dy of these roerties. +he roerties of the

ele#trostati# field are -ell kno-n and need no elaboration in this treatise. 8#ientifi#

literat're dealin) -ith this field is relete -ith its -ell>kno-n #hara#teristi#s.

Table &! Field Properties

ield Proerties2 (4 8atially distrib'ted ener)y! (; % ds ! (J C'rl % ! (E @ab % ds

! ( % d3ds Potential f'n#tion ! (F Behavior -ith rese#t to shieldin)! (Div. % ! (: Poisson?s f'ndamental la- -ith rese#t to the interior of #ond'#tors! ( In

#ond'#tors #arryin) #'rrent! (4>>.

The motionally ind"ced electric field 2 %m 3 x B G (4 5o satially distrib'ted ener)y!

(; < in )eneral! (J v x (v x B < in )eneral! (E In a erfe#tly 'niform B the val'eof the inte)ral bet-een ; oints a and # -ill not be deendent on the ath, -ill be

indeendent of it, b't in )eneral this -ill not be tr'e! ( May or may not be a otential

f'n#tion! (F Imm'ne to shieldin)! ( < al-ays! (: 5ot obeyed! ( Can drive a

#'rrent -itho't a otential dro alon) the -ire! (4


12/56


13/56

In the araday )enerator there is no time rate of #han)e in the ma)neti# ind'#tion B,

sin#e it ori)inates from a ermanent ma)net and is #onstant. +he #ir#'it #an even be

made so as to link -ith no fl'x -hatsoever. In any #ase, there is no #han)e of B -ith

time. +his very fa#t that all #ontemorary a'thorities (4: G 8later " rank2

Electromagnetism, . :F, M#&ra->Hill, 4E on this s'b/e#t have fo'nd it ne#essary to

add the fl'x #'ttin) la- to the famo's Max-ell e7'ations in order to satisfa#torily

exlain all #ases of ele#troma)neti# ind'#tion is itself indi#ative of the 'ni7'eness of

the ele#tri# field so rod'#ed.

Many of my #ollea)'es have said that it -as not diffi#'lt for them to distin)'ish

f'ndamental differen#es in the Co'lomb field %# and the ma)neti#ally ind'#ed fields %t

and %m, b't they -ere 'nable to see any #learly defined differen#e bet-een the % t and

the %m field. et 's, therefore, dis#'ss some of the most o'tstandin) differen#es

bet-een these t-o fields.

hat is o'r #on#et of an ele#tri# field@ Most hysi#ists -ill rely that it is a for#e

-hi#h a#ts 'on an ele#tri# #har)e and tends to a##elerate it in a definite dire#tion

termed the dire#tion of the field. ith this #on#et in mind, let 's analy9e the t-o

ele#tri# fields %t and %m.

In i)'re ; belo- is sho-n a #ross>se#tion of a lon) strai)ht solenoid in -hi#h a

)rad'ally in#reasin) #'rrent is flo-in) #o'nter#lo#k-ise.

Fi(re '

+he 'niformly distrib'ted ma)neti# fl'x density B -ithin this area is therefore

in#reasin) -ith time and a##ordin) to araday?s la- of %le#troma)neti# Ind'#tion, the


14/56

emf aro'nd any #losed #ir#'it la#ed -holly -ithin the area sho-n in i)'re ; -o'ld be

)iven by2 emf d5dt @L%t>ds -here 5 e7'als the total fl'x linkin) the #ir#'it.

='r interest #enters on %t, the ele#tri# field -ithin the #ond'#tor of s'#h a #ir#'it, )ivin)

rise to the emf. =bvio'sly, araday?s a- )ives 's absol'tely no information abo't this

field %t other than to say that the line inte)ral of this field aro'nd the #losed #ir#'it -ill

)ive 's a val'e of the emf ind'#ed in it. If this #losed #ir#'it A lies in the lane of the

area, i)'re ;, then at oint P in this #ir#'it, it is obvio's that % t is dire#ted to-ard the

bottom of the aer. If, ho-ever, -e sele#t the #ir#'it B instead of A, then at this same

oint P the ele#tri# field %t is dire#ted hori9ontally to the ri)ht. If -e sele#t #ir#'it C

instead of B, -e then find %t dire#ted to-ard the to of the aer at P exa#tly the

oosite dire#tion from that in #ir#'it A. And if -e sele#t #ir#'it D then %t at P is

dire#ted hori9ontally to the left, in exa#tly the oosite dire#tion that it had in #ir#'it B.

+hat an ele#tri# field %t exists in this area there seems to be no do'bt sin#e an emf arises

-ithin ea#h of these #ir#'its. B't this field %t is very e#'liar, sin#e it is imossible to

define it at the oint P 'nless -e first sele#t a arti#'lar #ir#'it thro')h P -hi#h -ill

then enable 's to determine its dire#tion at P.

5o- let 's remove the #ond'#tin) #ir#'its from -ithin the area of i)'re ;, and la#e a

stationary free #har)ed arti#le L at the oint P. ill it move@ If so, in -hat dire#tion

-ill it move@ If it remains stationary, and is free to move, then does an ele#tri# field

exist at this oint@ Certainly the ma)neti# fl'x density exists there and is #han)in) -ith

time, b't -e have no ass'ran#e -hatsoever that it -ill a#t 'on a stationary #har)e, nor

is the dire#tion in -hi#h it -ill a#t 'nless it is first )iven an initial velo#ity, or 'nless it

is #onfined -ithin the #ond'#tin) medi'm of a #losed #ir#'it. 5o other ele#tri# field has

this 'ni7'e oerational rere7'isite, -hi#h in this #ase aears to re7'ire that the

#har)ed arti#le 'on -hi#h it a#ts m'st either have an initial velo#ity -ithin the

ele#tri# field, or that it m'st exist -ithin a #ond'#tin) #ir#'it before it -ill make itselfmanifest. A free stationary #har)ed arti#le la#ed -ithin an %m or %# field -ill be

immediately a#ted 'on in both ma)nit'de and definite dire#tion. Abo't all that -e #an

say in a des#ritive manner of %t at a oint P, s'#h as sho-n in i)'re ;, is that this

transformer tye field has #'rl at that oint, as sho-n by Max-ell?s form'la. or a

#larifyin) #on#etion of /'st -hat #'rl means one -ill find it helf'l to st'dy 8killin)?s

treatment of it -here he defines it as the limitin) val'e of #ir#'lation er 'nit area (4 G

H. H. 8killin)2 F"ndamentals of Electric %aves, ;nd %d., . E4! 1. iley " 8ons, In#,

4E:. +his means simly, as alied to i)'re ;, that if a small #ond'#tin) disk of ink,

say a dot made -ith India ink, -ere la#ed at oint P, ne)ative ele#trons -o'ld #ir#'late

in this dot in a #o'nter#lo#k-ise dire#tion. +he dot of ink -o'ld be every-here at the

same otential, and therefore 'n#har)ed. C'rl is one of the most o'tstandin)#hara#teristi#s of the %t field -hi#h may or may not be ossessed by the %m field, b't

never by %#. 5o- la#e this same dot of India ink in a 'niform %m field and it -ill

be#ome an ele#tri# diole. +he a#tion of a 'niform %t field on this dot is therefore very

m'#h different from that of an %m 'niform field.

ith the ex#etion of mason and eaver?s text, little literat're aears to exist -hi#h

dire#ts attention to the ambi)'o's nat're of the #on#et of the satial distrib'tion of

ener)y as #on#erns the t-o ele#troma)neti#ally ind'#ed ele#tri# fields. +hat the ele#tri#

field ind'#ed by a ma)neti# fl'x intensity -hi#h is #han)in) -ith time has a satial

distrib'tion of ener)y, -hereas the motionally ind'#e ele#tri# field does not have any

s'#h identi#al distrib'tion of ele#tri# field in sa#e is one of the most #r'#ial of the

f'ndamental differen#es in their roerties. 8in#e the establishment of this fa#t that

these t-o fields differ radi#ally in their relation to field ener)y is all>imortant to the


15/56

ob/e#tives of this treatise, let 's no- take ' a di)ression at this oint.

Insofar as this -riter is informed, no one 7'estions the a#t'ality of the se#ial

distrib'tion of ener)y in the #ase of the ele#trostati# field or the % t field, d'e to a

ma)neti# ve#tor otential intensity varyin) -ith time (;< G +he transformer la- is

's'ally stated in terms of the ne)ative time ration of #han)e of ma)neti# fl'x linkin)

-ith the #ir#'it and this )ives the total ind'#ed emf. +he ele#tri# field rod'#ed by thistye of ind'#tion is most #onveniently desi)nated by the time rate of #han)e of the

ma)neti# ve#tor otential.. Cal#'lations involvin) field ener)y in the ele#trostati# #ase

have lon) been made -itho't diffi#'lty, and the transfer of ener)y bet-een the rimary

and se#ondary #oils of a transformer -itho't any movement of its #omonent arts )ive

dire#t eviden#e that ele#tri# ener)y is distrib'ted in the sa#e o##'ied by the % t field.

+he very nat're of this ele#tri# field re7'ires the #on#et of the satial distrib'tion of

field ener)y.

An analysis of the nat're of the motional ele#tri# field -ill reveal, on the other hand,

that this #on#et of satially distrib'ted ele#tri# field ener)y, is not only re7'ired for a

satisfyin) 'nderstandin) of henomena -here this field is involved, b't it a#t'allyind'#es basi# ambi)'ities and imossible #on#etions.

et 's no- examine the ori)in and basi# nat're of the motional ele#tri# field -ith its

'n's'al roerty.

%m 3 x B. +his ve#tor field e7'ation -as derived by orent9 from the emiri#al for#e

form'la of Biot and 8avart. +his is the ele#tri# field -hi#h is resent in the movin)

-ires #onstit'tin) the armat're #oils of an ele#tri# )enerator. It #a'ses an emf to exist in

a #ond'#tor by virt'e of motion a#ross ma)neti# fl'x. 8'#h ind'#tion is #alled a

motionally ind'#ed emf or fl'x #'ttin) emf. As -e shall see, this field has some of the

most 'n's'al and interestin) roerties #on#eivable. Pa)e and Adams have emhasi9ed

one of these 'ni7'e roerties. +hey oint o't in the #ase of the )enerator -ith a

rotatin) armat're #oil that this field, 0exists only in the movin) #ond'#tor0 >>> -here

movin) ele#tri# #har)es are resent >>> 0sin#e no ele#tri# field is resent in the

observer?s referen#e frame0 (;4 G Pa)e " Adams, o. #it., . 4F. et 's examine this

ase#t of the field more #losely, for neither the ele#trostati# field nor the % t field

ossesses this roerty, for these fields #an exist in an observer?s referen#e frame,

-hether a #ond'#tin) #ir#'it, or #ond'#tor, or #har)e is at hand or not.

+hree essential oerational in)redients are ne#essary to brin) this %m field into

existen#e2 (4 A #onstant ma)neti# ind'#tion B, (; an ele#tri#ally #har)ed arti#le e (;;G the #har)ed arti#le may be an ele#tron in a ie#e of matter, or free as in a )as, a

relative velo#ity v bet-een the arti#le and the referen#e frame of the ma)neti# so'r#e

rod'#in) B. A defle#tin) for#e -ill a#t 'on the arti#le -herever it moves a#ross

ma)neti# fl'x lines. As vie-ed from the referen#e frame of the arti#le, this for#e (v x

B has many ase#ts of a real ele#tri# field and in fa#t it is termed a motionally ind'#ed

ele#tri# field havin) an intensity (v x B er 'nit #har)e. In the referen#e frame of the

ma)neti# so'r#e )ivin) rise to B only a ma)neti# field is resent. =ne observes that the

movin) #har)e is a#ted 'on by a for#e -hi#h to all aearan#es is -holly ma)neti# in

nat're. hether -e think of it as a defle#tin) ma)neti# for#e or an ele#tri# field, it is

obvio's that it exists only at the oints in sa#e -here movin) #har)es, either free or in

matter, are resent, for stationary ele#tri# #har)es are 'naffe#ted. In a va#''m, or insa#e bet-een movin) ele#tri# #har)es, no %m field or defle#tin) ma)neti# for#e exists.

Hen#e it m'st ne#essarily have a sotty, or dis#ontin'o's nat're. Ho- #an this be


16/56

ossible@

et 's ro#eed as Mason and eaver have s'))ested by #onsiderin) 0a 7'antitative

des#rition of the individ'al behavior of #har)es0. et a ositively #har)ed arti#le -ith

mass m and #har)e e be ro/e#ted into a va#''m #hamber -ith 'niform velo#ity vo at

ri)ht an)les to the dire#tion of 'niform ma)neti# fl'x B. +he arti#le has initial kineti#

ener)y + 4; m vo;. By Amere?s a-, the movin) arti#le (or #'rrent element iss'rro'nded by a #on#entri# distrib'tion of ma)neti# fl'x.

Fi(re *

It -ill be a#ted 'on by a me#hani#al defle#tin) for#e e v o x B.

It -ill also be readily seen that this for#e on the #har)ed arti#le exists only -hen there

is a ma)neti# field abo't the arti#le. +he for#e is a#t'ally the for#e of lateral re'lsion

bet-een t-o ma)neti# fields. itho't the resen#e of both ma)neti# fields, no s'#h

for#e exists, hen#e the existen#e of f re7'ires the sim'ltaneo's resen#e of all three of

its essential #omonents, e, v and B. +he a#t'al a#tion on the #har)ed arti#le is

ma)neti# in #hara#ter, rather than ele#tri#al.

et 's next observe that the for#e f al-ays a#ts at ri)ht an)les to both v and B. 8in#e the

disla#ement of the arti#le is al-ays in a dire#tion at ri)ht an)les to the for#e, thisfor#e #an do no -ork on the #har)ed arti#le 'on -hi#h it a#ts, and no ener)y is

extra#ted from B. +his for#e, arisin) from the ma)neti# re'lsion bet-een t-o ma)neti#

fields, one d'e to the movin) arti#le, and the other d'e to the alied B, a#ts like a

#ir#'lar defle#tin) #onstraint or baffle, -hi#h only #han)es the dire#tion b't not the

ma)nit'de of the velo#ity of the arti#le. +he seed of the arti#le and hen#e its kineti#

ener)y remain 'n#han)ed. It is -ell kno-n that s'#h for#e -ill #a'se the arti#le to

travel in a #ir#'lar ath, the radi's of -hi#h is readily obtained by e7'atin) the for#e

Bevo to the #entrif')al for#e mvo;r and solvin) for r , r mvoeB. +he arti#le is th's

traed by the ma)neti# field, -hi#h -ill hold it to a #ir#'lar ath 'ntil its ori)inal

kineti# ener)y is dissiated by #ollisions -ith nei)hborin) arti#les, or by radiation.

It is of arti#'lar imortan#e to this dis#'ssion and is a)ain reeated, that sin#e the

defle#tin) for#e is al-ays at ri)ht an)les to the relative velo#ity vo of the arti#le and

also to B, no -ork is done on the arti#le by the defle#tin) for#e.

hether the arti#le is #onfined -ithin the bo'ndaries of a -ire or not, (v x B -ill

al-ays be at ri)ht an)les to v and B. or #larifi#ation let 's s'ose the arti#le is

en#losed -ithin a fri#tionless t'be the axis of -hi#h is at ri)ht an)les to vo and to B.

e- f'rther imose the #ondition the velo#ity vo of the t'be be ket #onstant in

ma)nit'de and dire#tion. et 's examine the behavior of the arti#le -ithin it. As the

t'be moves for-ard, the arti#le is revented from movin) in a #ir#'lar ath by the-alls of the t'be, b't it #an and -ill be)in to move alon) the axis of the t'be 'nder the

defle#tin) a#tion of the ma)neti# field. +o maintain the ori)inal for-ard #omonent of


17/56


18/56

the v x B henomenon has not hitherto been exosed in detail and hen#e is to a lar)e

extent #'rrently ta')ht and believed to be of an ele#trostati# nat're by theoreti#al

hysi#ists, it -ill be -orth o'r -hile to )o into some of the s'btle ase#ts it resents

-hen it is so #on#eived.

et 's #onsider the o'lar vie- of this henomenon as resented by most interreters

of relativity theory. +he 8e#ial +heory of $elativity as alied to ele#trodynami#sstates that if -e have a 'niform ele#tri# field of intensity %, d'e to #har)es, and a

'niform ma)neti# ind'#tion B, d'e to ma)nets, both at rest in a referen#e frame 8, then

in frame 8? movin) -ith 'niform velo#ity v -ith rese#t to 8 an observer -ill find an

ele#tri# intensity %?, and a ma)neti# ind'#tion B? )iven in ve#tor notation in absol'te

)a'ssian (#.).s. 'nits by2

(%7. E %? @ S% > (4# v x BT

(%7. B? @ SB > (4# v x %T

-here @ 4@ 4 > (v#;

and

# J x 4


19/56

#ir#'it. 5oti#e also the (v x B does not exist in the absen#e of movin) #har)es, be#a'se

it is the ma)neti# for#e on the #har)es movin) -ith the -ire -hi#h sets ' the ele#tri#

field intensity0 (; G $alh P. in#h2 Electricity & Magnetism, . JF! Prenti#e " Hall,

In#., 4.

5ot-ithstandin) s'#h rono'n#ements, the -riter has dis#'ssed the s'b/e#t -ith many

exonents of relativity theory -ho are 7'ite insistent that all the terms in %7'ation (Em'st be #onsidered identi#al to, and indistin)'ishable from, an ele#trostati# field. A

ersonal letter from a #ollea)'e at o'r 5ational B'rea' of 8tandards also takes this

osition, as -ell a several 5obel a'reates -ith -hom he has #ons'lted. And this stand

is taken admittedly by these hysi#ists -itho't a sin)le iota of dire#t exerimental

eviden#e -ith -hi#h to s'ort it6

D'rin) the early sta)es of the -ork on this ro/e#t, I #alled on several 5obel a'reates

to dis#'ss the -orth-hileness of this endeavor, one of -hom -as the distin)'ished

hysi#ist and a'thority in the field of ele#trodynami#s, %nri#o ermi, -ho had delivered

a le#t're at the 4EE P'bli# Affairs Conferen#e at Prin#iia Colle)e. Amon) the

7'estions asked, t-o -ill be of interest to the reader. (4 0If it -ere ever dis#overed thatthe motional ele#tri# field v x B# -as 'ni7'e and not identi#al to, and indistin)'ishable

from, an ele#trostati# field, -o'ld this dis#overy be of any )reat val'e to o'r s#ientifi#

kno-led)e@0 His ans-er in s'bstan#e -as2 It -o'ld indeed be of very )reat si)nifi#an#e

and #onse7'en#e. (; 0+o yo'r kno-led)e, do yo' kno- of the existen#e of any dire#t

exerimental eviden#e -hi#h #onfirms the belief that the motional ele#tri# field and the

ele#trostati# field are identi#al in nat're@0 After #onsiderable tho')ht, his rely -as,

0Come to think of it, I #an re#all of no s'#h existent eviden#e.0

It -ill no- be sho-n that the relativity e7'ations themselves rovide a means for

obtainin) a f'ller 'nderstandin) of the hysi#al nat're of the terms they #ontain. It is

imortant to observe mathemati#ally that in the )eneral #ase every term of both of these

e7'ations (E and ( is a f'n#tion of B -here B v#. By a binomial exansion it #an

be readily sho-n that2

(%7. F @ l (l ; @; (J@ @E OQ

8'bstit'tion in the t-o ri)ht hand terms of %7'ation (E yields

(%7. %s @ l (l ; ';Q %

(%7. : %?m @ v x B#Q l (l ; ';Q (v x B# 'Bn

-here v and B are taken at ri)ht an)les to ea#h other and n is a 'nit ve#tor at ri)ht

an)les to both v and B and terms of hi)her de)rees that '; have been droed.

%7'ations ( and (: reresent rese#tively the ele#trostati#, and the motional ele#tri#,field #omonents of the res'ltant ele#tri# intensity %? in the referen#e frame 8? movin)

-ith 'niform velo#ity v -ith rese#t to 8. If no- % and B in referen#e frame 8 are


20/56

ad/'sted so that they are both erendi#'lar to v and to ea#h other and their intensities

fixed at #onstant val'es s'#h that2

%?s >%?m <

+hen these t-o ele#tri# field intensities -ill be e7'al in ma)nit'de and oosite in

dire#tion (; G +-o lar)e, similar, re#tan)'lar, arallel, and verti#al lates searated bya distan#e d #o'ld be oositely #har)ed and ele#tri#ally isolated in s. Above and belo-

the air sa#e bet-een the #ondenser lates t-o lar)e #ir#'lar hori9ontal Helmholt9 #oils

#o'ld next be fastened so that -hen #onne#ted in series a #onstant #'rrent thro')h them

-o'ld rod'#e a 'niform verti#al ma)neti# ind'#tion B in the sa#e bet-een the

#ondenser lates. et 8? be a frame of referen#e movin) hori9ontally thro')h this sa#e

-ith velo#ity v at ri)ht an)les to both % and B.

A stationary ele#tron in 8? -ill therefore exerien#e no for#e a#tin) 'on it be#a'se the

res'ltant ele#tri# intensity in this frame is 9ero. Most relativists #laim that 'nder this

sit'ation there -ill be #omlete #an#ellation of ele#tri# fields. It -ill be observed that

%?s and %?m are araboli# and linear f'n#tions of ' rese#tively. It -ill at on#e beevident that altho')h %?s and %?m #an be made e7'al to ea#h other in ma)nit'de and

oosite in dire#tion for any one referen#e frame 8?, movin) -ith an assi)ned val'e of v

and a fixed roer ad/'stment of % and B in frame 8, s'#h that v #%B, nevertheless

s'#h e7'ality of %?s and %?m -o'ld be ossible for only t-o frames at the most, for a

strai)ht line #an #'t a arabola in not more than t-o oints. It is th's self>evident that in

the )eneral #ase it -o'ld not be ossible to make these t-o oositely dire#ted fields

#ontin'o'sly e7'al in more than t-o ossible referen#e frames at the most, by assi)nin)

fixed val'es to % and B in 8. +his is a #lear>#'t #ase of the simle s'erosition of t-o

distin#t tyes of fields. If the %?m term reresented an ele#tri# field -hi#h is identi#al to

and indistin)'ishable from an ele#trostati# field, then it -o'ld have to behave like one,

-hi#h -o'ld re7'ire that it vary araboli#ally -ith @ instead of linearly. Ho- #o'ld

there be #omlete #an#ellation of fields in a arti#'lar frame if there is a real differen#e

in their intensities manifest in the referen#e frames havin) both )reater and lesser

velo#ities than this arti#'lar frame@ 8'rely s'#h a sit'ation #alls for fields -hi#h are

distin#t and 'ni7'e, balan#ed a)ainst ea#h other -ith a 9ero res'ltant in one (or ossibly

t-o arti#'lar frames, b't not in nei)hborin) frames of referen#e.

+he (v x B# term most #learly sim'lates the #hara#teristi#s of an ele#trostati# field

-hen it is isolated by itself, -itho't the resen#e of a res'ltant ma)neti# ind'#tion6 It is

this #ase -hi#h has been mostly resonsible for the o'lar belief that the t-o fields are

identi#al in nat're. +o simlify the i#t're, let 's first ass'me a verti#al 'niformma)neti# ind'#tion B in frame 8 and no ele#trostati# field resent. In the referen#e

frame 8?, movin) -ith 'niform hori9ontal velo#ity v, -ith rese#t to 8, an observer -ill

dis#over a hori9ontal ele#tri#al field, (v x B# and a verti#al ma)neti# ind'#tion B? B

(ass'min) velo#ities small -ith rese#t to #, the ath of a free ele#trified arti#le in

frame 8? 'nder the a#tion of the t-o fields -hi#h are at ri)ht an)les to ea#h other -ill be

that of a #y#loid tra#ed on a hori9ontal lane. +he ath of the arti#le as seen in frame 8

-o'ld be #ir#'lar, as revio'sly sho-n. +his motion ro/e#ted on frame 8? movin) -ith

velo#ity v, is that of a oint on the #ir#'mferen#e of a #ir#le rollin) in a hori9ontal lane

alon) a line in the dire#tion of >v. If -e no- s'erimose a 'niform ma)neti# ind'#tion

B0 e7'al in ma)nit'de and oosite in dire#tion to B?, in frame 8?, then in this frame -e

-ill have only the isolated ele#tri# field v x B#, -ith the res'ltant verti#al ma)neti#ind'#tion of 9ero intensity. 5o- this ele#tri# field very )reatly sim'lates that of an

ele#trostati# field, and it is readily 'nderstandable that many hysi#ists have so


21/56

interreted it. +he ath of the arti#le in this field is no- re#tilinearly in the dire#tion of

v x B# in 8?, and araboli# as seen from 8. 'rthermore, sin#e the #'rl and diver)en#e

of v x B# in 8? are both 9ero, as they are in the #ase of a 'niform ele#trostati# field,

mathemati#ians #an #all 'on -hat is kno-n as the identity theorem as a roof that the

%m field is identi#al to an indistin)'ishable from an ele#trostati# field. +his roof

amo'nts to nothin) more than sayin) that the dynami# behavior of a #har)ed arti#le

-ill be the same in both fields. In the follo-in) #haters -e -ill sho- exerimentallythat this is not al-ays tr'e. Also analysis sho-s that a rime mover is re7'ired for

movin) the so'r#e of B0 and s'lies ener)y to the arti#le #ontin'o'sly.

et 's a)ain analy9e this #ase #aref'lly be#a'se of its )reat imortan#e. Kineti# ener)y

is imarted to a free #har)ed arti#le and )ives it a velo#ity v o -ith rese#t to frame 8.

At the #ommen#ement of its motion the arti#le is at rest in frame 8?, -hi#h is movin)

-ith the same velo#ity. It aears to an observer in this frame that the arti#le starts

from rest and be)ins to move in the dire#tion of (vo x B#. If the ma)neti# ind'#tion is

8? is only that d'e to B, then its motion v? -ith rese#t to 8? -ill rod'#e a ne-

defle#tin) intensity v? x B?# in frame 8? in the dire#tion of >v o. If, ho-ever, the e7'al

and oosite ma)neti# ind'#tion B0 is introd'#ed in this frame, the effe#t -o'ld be to rod'#e another defle#tin) intensity v? x B?# -hi#h -o'ld be e7'al and oosite in

dire#tion to the intensity v? x B0#. At this oint one needs to think #aref'lly. +he

defle#tin) intensity v x B?# in 8? dire#ted a)ainst the for-ard motion of the arti#le

arises by virt'e of en9?s a-. +he for#e on the arti#le d'e to this intensity -ill a#t

#ontin'o'sly as lon) as the arti#le moves at ri)ht an)les to vo. +o enable the arti#le to

maintain #onstantly it ori)inal for-ard velo#ity vo, the kineti# ener)y -hi#h is bein)

#hanneled at ri)ht an)les to vo m'st be #ontin'o'sly rela#ed. +o do this, -ork m'st be

done #ontin'o'sly 'on the ma)net )ivin) rise to B0 in 8?, be#a'se the a#tion of B0 on

the arti#le is to assist its for-ard motion -ith rese#t to 8 in exa#tly the same amo'nt

that v x B?# deresses it. +-o ma)nets are involved in this a#tion. (4 +he ma)net

)ivin) rise to B? in 8? and -hi#h is at rest in 8. (; +he ma)net )ivin) rise to B0 in 8? and

-hi#h m'st be #ontin'o'sly s'lied -ith ener)y from a rime mover.

+he arti#le #an th's be made to travel re#tilinearly in 8?, in the dire#tion of (vo x B#

rovided ener)y is #ontin'o'sly )iven to it via the role layed by B0. +his is the

sit'ation -hi#h aears on first inse#tion to be exa#tly like an ele#trostati# field. A free

ele#tron ori)inally at rest in 8? -ill be a##elerated re#tilinearly in 8? at ri)ht an)les to vo.

+he ele#tron is seemin)ly -itho't #onta#t -ith any material body, hen#e the ele#tri#

field (vo x B# aears to be the only so'r#e of its steadily a##'m'latin) kineti# ener)y.

+he ener)y -o'ld aear to have #ome from a satial distrib'tion also as in the

ele#trostati# #ase, sin#e (vo x B# is the only ele#tri# field resent in 8?, and theres'ltant ma)neti# ind'#tion is 9ero. +his aearan#e is ex#eedin)ly de#etive and is

the basis of this #'rrent false ass'mtion -ith rese#t to the motional ele#tri# field. 5o

rime mover is re7'ired in the ele#trostati# #ase6 +he ener)y in this #ase #omes from the

field itself.

In the first la#e, -e m'st remember that an ele#tri# field of the tye (v x B# #annot of

itself imart ener)y to the ele#tron be#a'se its line of a#tion is al-ays normal to the

velo#ity of the ele#tron -ith rese#t to 8, and to the dire#tion of B. e -ill remember in

one of o'r revio's dis#'ssions, that this defle#tin) intensity -as sho-n to #hannel the

kineti# ener)y of the arti#le do-n a t'be -itho't itself imartin) ener)y. +he f'n#tion

of the t'be a#t'ated by a rime mover -as to #ontin'o'sly s'ly to the arti#le theener)y to so #hannel and revent the arti#le from takin) ' a #ir#'lar ath in 8 or a

#y#loidal ath in 8?. e no- dis#over that the s'erosition of a ma)neti# ind'#tion B0


22/56

in 8? a##omlishes the same thin) that the t'be did. B't this a##omlishment #an only

be a#hieved by feedin) ener)y to the arti#le #ontin'o'sly in the for-ard dire#tion as

the t'be did and this is done by a rime mover a#tin) on the ma)net )ivin) rise to

B0.+his ma)neti# ind'#tion B0 intera#ts -ith the ma)neti# field aro'nd the #har)ed

arti#le so as to #ontin'o'sly 'sh the arti#le in the for-ard dire#tion vo, th's

rela#in) #ontin'o'sly the kineti# ener)y #hanneled at ri)ht an)les by (vo x B# and

th's keein) the velo#ity of the arti#le in this for-ard dire#tion #onstant, therebymakin) its ath in 8? one that is -holly at ri)ht an)les to vo. A rime mover )ives

kineti# ener)y to a ma)net, and its ma)neti# field 'shes on the ma)neti# field aro'nd

the arti#le, and th's does -ork #ontin'o'sly, -hi#h in frame 8? aears as in#reasin)

kineti# ener)y of the re#tilinear motion of the #har)ed arti#le. 5o ma)neti# field

ener)y is 'sed ' in this transfer of ener)y to the arti#le. +he ma)neti# field of the

ma)net is a hysi#al art of the ma)net -hi#h 'shes a)ainst the ma)neti# arti#le -ith

exa#tly the same for#e that the t'be did in o'r earlier des#rition. It erforms the same

f'n#tion as that of the t'be. +here is no real ele#tri# field involved in this i#t're ex#et

that aro'nd the #har)ed arti#le, -hi#h -hen movin) (by Amere?s a- )ives rise to

the ma)neti# field aro'nd it. +h's the -hole a#tion of an isolated (v x B# field on a

#har)ed arti#le, instead of bein) ele#trostati# has a des#rition -hi#h is essentially thedire#t transfer of me#hani#al kineti# ener)y from rime movers to the arti#le. 5o

satially distrib'ted motional ele#tri# field ener)y enters the i#t're of this field. +he

'niform and relative motion of t-o ma)nets -ith e7'al and oositely dire#ted fields

and the resen#e of an ele#tri# #har)e released -ith kineti# ener)y from its osition of

rest in the referen#e frame of one of the ma)nets rod'#es a #ombination of 'shin) and

defle#tin) ma)neti# for#es -hi#h #a'ses the arti#le to behave as tho')h it -ere in an

ele#trostati# field. +his sho'ld not s'rrise 's. hat sho'ld s'rrise is that hysi#ists

sho'ld have ass'med, -itho't dire#t exerimental eviden#e, that these #ombined

ma)neti# for#es #o'ld be identi#al to and indistin)'ishable from an ele#trostati# field. A

monkey and a man are t-o distin#tly different a)en#ies (-e hoe6 +hey #an, ho-ever,

exert identi#al for#es on one and the same ob/e#t, and if oositely dire#ted hold the

ob/e#t in e7'ilibri'm. B't s'rely no one -ill 'se s'#h an ar)'ment as eviden#e that a

monkey is a man, or that a man is a monkey6 8'#h, ho-ever, aears to be the nat're of

some ar)'ments that (v x B# is intrinsi#ally ele#trostati#. Ca/ori states2 0+he

'ns#ientifi# hysi#al se#'lations of Aristotle held the -orld bo'nd -ithin their )ras

for t-o tho'sand years! the 'nfort'nate #or's#'lar theory of 5e-ton #ontrolled

s#ientifi# tho')ht for over a #ent'ry0 (;: G lorian Ca/ori2 A (istory of Physics, . 4si)hted /'d)ment.

Chapter '

The Electroma(netic Force E)ation

+hree o'tstandin) ele#tri# field intensities -hen added to)ether ve#torially, #onstit'te

-hat has been termed the ele#troma)neti# for#e e7'ations (in kms 'nts2

(%7. % %# %m %t CrE@eor J (B x 3 > @A@t (; G C'll-i#k, o. #it., .


23/56

;:

In their A )e* Electrodynamics, Moon and 8en#er derive a ne- form'lation for thise7'ation based entirely on the for#e bet-een t-o #har)ed arti#le L4 and L; (J< G

Moon " 8en#er, o. #it., . JF. +hese a'thors sho- that all ossible ele#tri#

intensities #an be exerted by #har)e L4 and L; d'e to (a #onstant L4, no relative

motion, (b #onstant L4, 'niform relative velo#ity, and (# #onstant L4, a##elerated

motion, -hen added be#ome rese#tively2

(%7. 4J; #os;@Q >aa

L4E@eo#;r dvdt

5ote that the Co'lomb intensity %# is the same in ( and (4


24/56


25/56

dire#t exerimental eviden#e -hi#h #onfirms the #laim resented in this thesis that the

isolated motional ele#tri# field is note and #annot be ele#trostati# in #hara#ter. As -e

have seen, nevertheless, this field had de#etive ase#ts -hi#h #a'se it to resemble in

many -ays the ele#trostati# field.

In order that the #ase may be transarently 'nderstood, let 's #onsider a very simle

#ase of relative motion. et 's ass'me that -e have an inertial system 8 -hi#h has onlya 'niform do-n-ard ma)netostati# ind'#tion B, and no ele#trostati# field is resent. In

the inertial system 8?, -hi#h is movin) -ith 'niform hori9ontal velo#ity v -ith rese#t

to 8, the transformation e7'ations (E and ( yield2

(%7. 4; %? @ (v x B#

(%7. 4J B? @ B

or #onvenien#e, let 's think of the system 8? as a #omletely #losed re#tan)'larly

shaed #oa#h, made of al'min'm, travelin) d'e 5orth -ith velo#ity v. et 's think of B

as the ma)neti# ind'#tion d'e to the earth?s ma)neti# field (res'med verti#al. +he

transformation e7'ations (4; and (4J inform 's that an observer ridin) in his #ar

-o'ld find a verti#al ma)netostati# ind'#tion B?, both inside and o'tside the #ar, -hi#h

for ordinary seeds -o'ld be identi#al to B. +his ind'#tion -o'ld be red'#ed to 9ero by

b'ildin) aro'nd and atta#hed to the #ar a lar)e Helmholt9 #oil -hi#h -o'ld rod'#e

-ithin and thro')ho't the #ar an e7'al b't oositely dire#ted ind'#tion B0. By doin)

so -e isolate the ele#tri# field %? -ithin the #ar. An observer -o'ld find o'tside the #ar a

'niform ele#tri# field %?, dire#ted from %ast to est, )iven by (4;. ithin the #ar,

ho-ever, -e kno- from exerien#e that an ordinary ele#tri# field intensity robe -o'ldre)ister 9ero, or no res'ltant ele#tri# field intensity. A##ordin) to most interreters of the

8e#ial +heory of $elativity, this is exa#tly -hat sho'ld be exe#ted, sin#e they #laim @

(v x B# is identi#al to, and indistin)'ishable from, an ele#trostati# field, and it m'st,

therefore, behave similarly -ith rese#t to shieldin). Hen#e, a##ordin) to this vie-, the

al'min'm #oa#h, bein) a )ood #ond'#tor, has rod'#ed -ithin it in a##ordan#e -ith the

f'ndamental la- of ele#trostati#s a s'rfa#e redistrib'tion of #har)e -hi#h brin)s abo't

the #omlete #an#ellation of all ele#tri# field -ithin the #ar so that no #har)e or ele#tri#

field -hatsoever exists inside the exterior bo'ndin) s'rfa#e of the #ar.

An entirely lo)i#al and different #on#l'sion may no- be arrived at by reasonin) based

'on o'r kno-n la-s of ele#troma)netism. +he #ar is movin) a#ross a ma)neti#ind'#tion B dire#ted verti#ally do-n-ard. +herefore every free ele#tron -ithin the

al'min'm shield -ill exerien#e a for#e d'e to the ele#troma)neti#ally ind'#ed field @(v

x B# 'r)in) it to-ard the ri)ht hand side of the #ar. Under the infl'en#e of this field a

redistrib'tion of #har)e th's takes la#e 'ntil an ele#trostati# field %s dire#ted

hori9ontally a#ross the inside of the #ar from the est -all to the %ast -all, e7'al in

intensity and oositely dire#ted to the ind'#in) field is established. hen e7'ilibri'm

is th's established, there -ill be -ithin the #ar t-o oositely dire#ted #otermino's

ele#tri# fields, of tyes %# and %m, in balan#e s'#h as to rod'#e a 9ero res'ltant ele#tri#

intensity.

+he 7'estion before 's no- is, -hi#h i#t're is #orre#t@ Can it be that % s and %m are

a#t'ally identi#al in nat're and #omlete #an#ellation -ithin the #ar takes la#e@

%xerimental eviden#e m'st ans-er this 7'estion, and it does, #learly and de#isively.


26/56

Before resentin) this ans-er, ho-ever, it -ill be of interest to note some of the

#omments made by hysi#ists -ith rese#t to this 7'estion and the dense fo) -hi#h has

s'rro'nded it. A #ollea)'e at the 5ational B'rea' of 8tandards, )ivin) a vie- in

harmony -ith most interreters of relativity theory, has, in a letter, -ritten -ith rese#t

to the inside of the shield2

0If it is ass'med that ma)neti# ind'#tion has a #ertain roerty not in #onfli#t -ithanythin) observed exerimentally, it follo-s that there are t-o ele#tri# fields -hi#h at

every oint are e7'al and oosite in dire#tion. =ne of these fields res'lts from

ele#troma)neti# ind'#tion and the other from ele#tri# #har)es.

0If it is ass'med that ma)neti# ind'#tion has another roerty, not in #onfli#t -ith

anythin) observed exerimentally, it follo-s that at no oint is there an ele#tri# field

and on no element of s'rfa#e is there an ele#tri# #har)e. +herefore, any redi#tion not in

a##ord -ith both of these ass'mtions sho'ld be #onsidered as la#kin) an exerimental

basis.

8mythe, in #ommentin) 'on the roblem of meas'rin) )ro'nd seed in an air#raft bymeas'rin) the emf ind'#ed in a devi#e by translation a#ross the verti#al #omonent of

the earth?s ma)neti# field, states2

0+he 7'estion arises as to -hether the effe#t disaears if the aarat's is ele#tri#ally

shielded in the airlane. e kno- that the ma)neti# field -ill enetrate nonma)neti#

metalli# #ond'#tors, b't -e also kno- that the ind'#ed ele#tromotive for#es in the

shields -ill set ' ele#tri# fields tendin) to #o'ntera#t the fields ind'#ed inside.0 (JJ G

illiam $. 8mythe, Static & ynamic Electricity, .


27/56

+hree ele#tri#al #ir#'its -ere emloyed, all lyin) in hori9ontal lanes, arallel to a lar)elaboratory le#t're table. +he test #ir#'it #onsisted of a #oil of 4tire -heels so that it #o'ld be 'lled at a 'niform 5orth>8o'th velo#ity

alon) the le#t're table by an ele#tri# motor #o'led to a red'#tion )ar. +he re#ise

velo#ity -as #al#'lated -ith the 'se of a meter sti#k and an ele#tri# timer. 8'rro'ndin)

the for-ard end of the test #oil, a se#ond #ir#'it -as -o'nd on a ly-ood extension

#onsistin) of a sin)le strand of V4F B"8 #oer -ire held at a #onstant t-o>in#h

distan#e from the test #ir#'it, and #arried a 'niform dire#t #'rrent so ad/'sted that thema)neti# fl'x B0 s'rro'ndin) it -o'ld exa#tly #an#el o't the verti#al #omonent B of

the earth?s ma)neti# field at the lo#ation of the test #ir#'it. +he third #ir#'it -as a

lar)ely a##'rately #onstr'#ted Helmholt9 #oil so mo'nted in the laboratory and ad/'sted

that the trailin) end of the test #ir#'it moved hori9ontally in the #entral re)ion (bet-een

the t-o #oils in -hi#h the verti#al #omonent of the earth?s field -as #omletely

#an#elled. +he entire test #ir#'it in#l'din) the mi#rovoltmeter -as ele#trostati#ally

shielded. A very heavy #oat of a7'ada) -as alied over the test #oil and the to and

bottom of the s'ortin) ly-ood frame. In addition, al'min'm foil -as -raed

aro'nd the for-ard semi#ir#'lar art of the test #oil, and finally 't over the entire front

ortion of the aarat's. hen moved 'niformly alon) the table, the shielded -ires of

the test #oil alon) the t-o sides of the frame move hori9ontally in the earth?s ma)neti#

meridian and therefore #annot #'t any fl'x. +he trailin) ed)e of the test #oil in the

#entral re)ion of the Helmholt9 #oil like-ise #an #'t no fl'x. +he for-ard end of the

test #oil alone #'ts the verti#al #omonent of the earth?s field, and is not at rest -ith

rese#t to the #an#elin) fl'x B0 of the se#ondary #ir#'it. +he shield, -ith the ex#etion

of the ortion -ithin the Helmholt9 #oil, like-ise #'ts the verti#al #omonent of the

earth?s ma)neti# field. e no- have a erfe#t set>' -ith -hi#h to test exerimentally

-hether or not the 'niform isolated motional ele#tri# field is e7'ivalent and identi#al to

the ele#trostati# field. +he -alls of the shield have ind'#ed in them an emf -hi#h drives

ele#trons to the -est side and leaves a ositive #har)e on the east side of the shield. e

kno- that these #har)es -ill b'ild ' 'ntil the ele#trostati# field #a'sed by thissearation of #har)e -ill be every-here -ithin the shield e7'al and oosite to the

intensity of the motional ele#tri# field )ivin) rise to it. If they are e7'ivalent and

identi#al in nat're, they -ill #omletely #an#el ea#h other o't and the leadin) -ires of

the test #oil -ill be in a field>free sa#e. If a volta)e is ind'#ed in the test #oil, it -ill be

be#a'se these t-o fields do not #an#el ea#h other, be#a'se they are 'ni7'e and different

in their f'ndamental hysi#al nat'res. +able II )ives the res'lts of 4 different velo#ities

-hi#h -ere #aref'lly meas'red2

Table II

Trial 6 7istance 8cm9 6 Time 8sec9 6 :elocit% 8cm;sec9 6 Micro: 8obser/ed9 6

Micro: 8theor%9


28/56

4 ;:. EF.4 .F;F 4


29/56

#ir#'it, and this exeriment involved s'#h a time rate of #han)e and, therefore, the

res'lts sho'ld have been exe#ted, for it is kno-n that shieldin) is not effe#tive in

transformer #ases in -hi#h this la- is ali#able. +his ar)'ment is not valid for the

follo-in) reason. e have sho-n in Chater 4 that the fl'x linkin) a #losed #ir#'it #an

be #han)ed in only three ossible -ays2 (4 fl'x #'ttin), (; the )ro-th and death of

fl'x as in transformer henomena, (J se#ial s-it#hin) arran)ements. Items (; and (J

-ere obvio'sly not involved in this exeriment. +herefore there #an be no aeal totransformer henomena. +he fl'x density B is #onstant thro')ho't the exeriment and

therefore Max-ell?s e7'ation C'rl % @B@t, -hi#h is his interretation of araday?s

a-, #annot be invoked. +he exeriment is so desi)ned that the only ossible seat of

ind'#ed emf -o'ld have to be in the al'min'm shielded leadin) -ires of the test #oil.

+he motional ele#tri# field alone is involved.

A brief a##o'nt of t-o other shieldin) exeriments #arried o't in the -riter?s laboratory

to rovide interestin) 7'alitative demonstration e7'iment -ill no- be des#ribed.

The Trape$e Experiment

+he trae9e bar -as made of six one>meter len)th ie#es of soft iron ie teles#oed

-ithin the other. A sin)le strand of ins'lated and ele#trostati#ally shielded -ire -as

threaded thro')h the innermost ie of the bar and fastened at t-o la#es in the #eilin)

of the laboratory in s'#h a manner as to ermit the trae9e to s-in) hori9ontally in a

5orth>8o'th dire#tion -hile the s'ortin) -ires on ea#h side moved in the ma)neti#

meridian and therefore #o'ld #'t no ma)neti# fl'x. +he shielded -ire -as #onne#ted to

a sensitive -all )alvanometer -hi#h -as also shielded. Here a)ain -e have only the

isolated motional ele#tri# field involved, for it is -ell kno-n that the iron ie -o'ld

#omletely s#reen o't the earth?s ma)neti# field from the interior. ith this simle

aarat's, it #a be readily demonstrated that any small hori9ontal movement of the bar

#a'ses a defle#tion of the )alvanometer dire#tly roortional to its velo#ity. 5o

meas'rable ma)neti# fl'x exists -ithin the innermost ie, b't the ele#tri# field 3x B is

resent -itho't dimin'tion, and 'n#an#elled by the e7'al and oositely dire#ted

ele#trostati# field set ' by the searation of #har)e in the shield. +he -ire in the ie

#'t the verti#al #omonent of the earth?s ma)neti# field, b't -as at rest -ith rese#t to

the bar. +he defle#tions of the -all )alvanometer for a )iven seed -ere identi#al -ith

or -itho't the iron ie and ele#trostati# shieldin) aro'nd the -ire in the trae9e bar.

The 1lminm 5ox Experiment

In this exeriment the entire aarat's -as #ontained in a #losed al'min'm box -hi#h-as moved hori9ontally in a 5orth>8o'th dire#tion on a laboratory table. +he test #oil

-as re#tan)'lar in shae, made ' of many t'rns of fine, flexible, ins'lated #oer -ire.

+he 5orth and 8o'th sides of the re#tan)'lar #oil -ere ri)idi9ed and s'orted in the

same hori9ontal lane -ithin the box. +he 8o'th side -as fastened to the inside 8o'th

-all of the al'min'm box and the terminals of the #oil -ere #onne#ted to a sensitive

ortable )alvanometer also mo'nted on this -all so that the ointer #o'ld be read

thro')h an oenin) in the box. +he 5orth side of the #oil -as s'orted in a fixed

osition by t-o lasti# rods -hi#h -ere #lamed to fixed verti#al s'ort rods on the

table, and extended hori9ontally thro')h holes in the al'min'm box. +he flexible %ast

and est sides of the test #oil h'n) in the ma)neti# meridian of the earth?s field. Any

movement 5orth or 8o'th of the box th's #a'sed these -ires to either sa) or be#ometa't rese#tively. +he resen#e of the 'n#an#elled motional ele#tri# field #an be

demonstrated to be existent in the test #oil -hen the box is #omletely #losed and


30/56

moved -ith vario's seed, 5orth or 8o'th, a#ross the earth?s verti#al ma)neti# field

#omonent. +he defle#tions of the )alvanometer -ith vario's seeds of the box are

identi#al -ith those obtained -hen the shielded box is eliminated from the exeriment

and /'st the so'th side of the #oils and the )alvanometer -ere moved as before.

+mmar%

et 's make a brief s'mmary of -hat -e have th's far resented -ith rese#t to the

motional ele#tri# field. Mathemati#al, oerational, theoreti#al and exerimental

eviden#e #onvin#in)ly #onfirm the #on#et of the motional ele#tri# field as hysi#ally

real and distin#tly 'ni7'e. Its ma)nit'de varies -ith referen#e frames in a manner 'nlike

the ele#trostati# field. +he #r'x of the theoreti#al ar)'ment involvin) this field

amo'nted to the fa#t that the dire#t transfer of kineti# ener)y from a rime mover to a

#har)ed arti#le #an be lo)i#ally tra#ed in detail and in a##ordan#e -ith kno-n la-s,

and f'lly a##o'nts for all ener)y transfer, -hereas the #on#etion of motional ele#tri#

field ener)y existin) at all and bein) distrib'ted satially, in addition to bein) #aable of

transfer, is next to imossible. +he #r'#ial eviden#e of 'ni7'eness is exerimental and it

has been sho-n that this field does not obey Poisson?s 'ndamental a- of%le#trostati#s -ith rese#t to shieldin). If the ma)neti# field has no hysi#al reality,

then -hen the motional ele#tri# field -as balan#ed a)ainst an e7'al and oosite

ele#trostati# field, the ma)nit'de of the t-o terms in %7'ation ( of the 05e-

%le#trodynami#s0 -o'ld have been identi#ally e7'al and oosite and their al)ebrai#

s'm e7'al to 9ero. +he fore)oin) exerimental eviden#e re7'ires a #on#et of

somethin) real to a##o'nt for the real differen#e exerimentally meas'red. +he

ma)neti# field and the motional ele#tri# field #on#ets #onstit'te that 0somethin) of

f'ndamental hysi#al si)nifi#an#e0 -hi#h -as intentionally b't ill>advisedly omitted in

the ne- form'lation in terms of arti#le ele#trodynami#s.

Uon the fore)oin) eviden#e -e rest o'r #ase that this motional field is 'ne7'ivo#ally a

'ni7'e ele#tri# field ossessin) its o-n nat're, behavior and roerties. e have asked

nat're a 7'estion and the rely is #lear and 'ne7'ivo#al. L'antitative and 7'alitative

exerimental eviden#e s'#h as has been #aref'lly obtained in this #ase al-ays has the

last -ord. It #loses the door on #ontroversy and oens it -ide to-ard the da-n of ne-

hori9ons. 5at're herself has )iven the ans-er -hi#h, in the -ords of %nri#o ermi,

sho'ld 0indeed be of )reat si)nifi#an#e and #onse7'en#e0 to o'r s#ientifi# kno-led)e.

+he imli#ations and #onse7'en#es of this dis#overy -ill be dis#'ssed more f'lly later.

+hey do, ho-ever, lead 's immediately to the ne#essity for makin) in7'iry into the

basi# nat're of the analo)o's motional 3 x %# ma)neti# field. +his -e -ill do in the

next #hater.

Chapter ,

The Motional Ma(netic Field

+he #lassi#al belief that nat're has rovide 's -ith one and only one ma)neti# field has

so bef'ddled reason that hysi#ists have so')ht to eliminate the ma)neti# field #on#et

entirely. +o ill'strate the ambi)'ity, the ma)neti# field arisin) from t-o oerationally

different so'r#es -ill be des#ribed. +he imossibility of these t-o fields bein)sidenti#ally the same be#omes aarent 'on #omarison2


31/56

(4 +he ma)neti# fl'x arisin) from the steady flo- of ele#tri#ity in a solenoid #an be

meas'red in intensity and in satial ener)y #ontent at any oint in the s'rro'ndin) sa#e

by an observer, either at rest or in motion -ith rese#t to the solenoid.

(; +he se#ond so'r#e #an best be des#ribed by a 7'otation from 8ir Arth'r %ddin)ton2

0Consider an ele#tri#ally #har)ed body at rest on the earth. 8in#e it is at rest, it )ives anele#tri# field, b't no ma)neti# field. B't for the neb'lar hysi#ist it is a #har)ed body

movin) at 4


32/56

same kinds of ma)neti# field, be#a'se they behave differently -ith #han)e in referen#e

frames.

Be#a'se Hm 3 x %# is a ma)neti# ve#tor dire#ted at ri)ht an)les both to 3 and % #, the

ele#tri# field %# #an do no -ork, sin#e any disla#ement of a ma)neti# arti#le -ill be a

defle#tion at ri)ht an)les to this field. +he Hs ma)neti# field, ho-ever, #an imart

ener)y dire#tly to a ma)neti# arti#le from its field ener)y.

+he t-o tyes of ma)neti# fields des#ribed above have s'#h obvio's dissimilarities that

the only ossibility of a #onsistent satisfyin) i#t're of them is obtained by the

ali#ation of Brid)man?s =erational 3ie-oint. hen this is done -e see these fields

as 'ni7'e. +he first tye Hs is analo)o's to the Co'lomb ele#tri#al field %# in that it has

hysi#al reality, and has a satial distrib'tion of ma)neti# ener)y @H;:@

er)s#mJ . +he motional ma)neti# field Hm is analo)o's to the %m field in

that it too disaears -hen there is no relative velo#ity.

+he intimate relationshi and 'nity bet-een ele#tri#ity and ma)netism is seen in these

t-o fields. +he motional ele#tri# field #an be des#ribed as a ma)neti# defle#tion

henomenon rod'#ed on movin) #har)es, and the motional ma)neti# field #an be

vie-ed as an ele#tri# field defle#tion -hi#h -ill a#t on movin) ma)neti# oles.

=ne of the thrills of this resear#h ro/e#t -as redi#ted by Brid)man -hen he -rote, 0In

this self>#ons#io's sear#h for henomena -hi#h in#rease the n'mber of oerationally

indeendent #on#ets, -e may exe#t to find a o-erf'l systemati# method dire#tin)

the dis#overy of ne- and essentially imortant hysi#al fa#ts.0 (JF G ibid., .;;E

It is -orth o'r -hile to note that -e have six s'#h 'ni7'e field #on#ets sho-n on a)e

44 instead of the #lassi#al t-o, or the modern arti#le dynami#s -ith none6 +hese ne-field #on#ets -hen 'nderstood in #onne#tion -ith the e7'ations of modern

ele#trodynami#s #omletely eliminate the aradoxes and ambi)'ities -hi#h have

la)'ed this s'b/e#t for years and exlain ele#troma)neti# ind'#tion -hi#h arti#le

ele#trodynami#s #annot handle. Most of all, they oen ' ne- hori9ons for the

'nifi#ation of the three )reat fields of ele#tri#ity, ma)netism and )ravitation

Chapter -

ra/itation

0In the limited nat're of the mathemati#ally existent simle fields and the simle

e7'ations ossible bet-een them, lies the theorists? hoe of )rasin) the real in all its

deths.0 (J G Albert %instein2 Essays in Science, . 44

4JE

0It may -ell be that the aroa#h of a ne- theory #annot be)in 'ntil the mathemati#al

nat're of the old ones is #learly 'nderstood.0 (J: G reeman 1. Dyson2 Scientific

American, 8etember 4:

In the revio's #hater -e have sho-n ho- Brid)man?s =erational 3ie-oint aliedto o'r 0existent simle fields and the simle e7'ations ossible bet-een them0 has

enabled 's to )ain an 'nderstandin) of 0the mathemati#al nat're of the old0 #lassi#al


33/56


34/56

shielded from a re)ion of sa#e by a #ond'#tin) shell and that it does not ossess the

roerties of an ele#trostati# field, as has been ta#itly ass'med by theoreti#al hysi#ists

-itho't exerimental eviden#e to s'ort it, -e are bro')ht fa#e to fa#e -ith the fa#t

that this 3 x B field is really somethin) entirely different than it has been hitherto

tho')ht to be, in site of the fa#t that it is the )eneratin) field so a#tive in o'r ele#tri#al

o-er lants. Indeed it -ill be sho-n that this field sho'ld behave in a manner that is

identi#al to )ravity.

et 's remember that this 3xB field is an ele#tri# field, that is, it -ill exert a for#e on,

and -ill #a'se the a##eleration of ele#tri# #har)es. In this rese#t it is similar to an

ele#trostati# field. B't an ele#tri#ally ne'tral #ond'#tor la#es in a 3xB field is a#ted

'on differently than -hen it is la#es in an ele#trostati# field. In the latter field only an

o'tside s'rfa#e redistrib'tion of #har)e and field take la#e -hereas in a 3xB field the

ne'tral #ond'#tor exerien#es an internal redistrib'tion of #har)e thro')ho't its entire

interior -ith t-o tyes of ele#tri# fields existent -ithin the interior, balan#ed a)ainst

ea#h other in the e7'ilibri'm state. +his state of affairs has been exerimentally verified

in the -riter?s laboratory and this eviden#e is the #r'#ial blo- -hi#h overthro-s the

o'lar vie- that the 3xB field is ele#trostati# in nat're. In the ele#trostati# #ase thefield is entirely on the o'tside of the #ond'#tor, -hereas in the 3xB #ase, this field

exists both -ithin and -itho't the #ond'#tor.

ithin a #ond'#tin) en#los're -hi#h is la#ed in an ele#trostati# field, this field is -ell

kno-n to be self>#an#elled, -hereas -hen la#ed in a motional ele#tri# field, this field

)ives rise to -hat has been tho')ht to be a #an#elin) ele#trostati# field e7'al in

ma)nit'de and oositely dire#ted, b't #ontrary to o'lar belief this motional ele#tri#

field is 'n#an#elled by this ind'#ed ele#trostati# field and remains 'ndiminished in

intensity and in balan#e -ith it. +his imm'nity to #an#ellation by shieldin) is the

roerty -hi#h it has in #ommon -ith )ravity.

It is the enetratin) roerty of the B x 3 field -hi#h 7'alifies it to lay the role of a

)ravitational field (EJ G +he term B x 3 is 'se -hen one refers to a so'r#e -hi#h #a'ses

a ma)neti# fl'x B to move -ith a velo#ity 3 as -o'ld be the #ase -hen the field

ori)inates in atoms of matter. Mathemati#ally, 3 x B >B x 3. +his field #an rea#h to

every art of atomi# str'#t're and in and thro')ho't the n'#le's. Ma)neti# shieldin)

#annot revent it be#a'se B x 3 exists, re)ardless of the resen#e of a res'ltant B,

-hi#h may or may not be 9ero. It seems in#redible that this enetratin) nat're -as

dis#overed even in the days of araday and yet so little attention has been )iven to it.

In des#ribin) the -ork of araday on ele#troma)neti# ind'#tion, Max-ell stated that theintensity of the ind'#ed ele#tri# field 0is entirely indeendent of the nat're of the

s'bstan#e of the #ond'#tor in -hi#h it a#ts0 (EE G Clerk Max-ell2 Electricity &

Magnetism, vol. 44, . 4:4. +his -as also later fo'nd to be tr'e for diele#tri#

s'bstan#es as -ell as #ond'#tors.

Matter, as -e kno- it, #onsists of ele#trons, rotons and ne'trons. +he a#t'al nat're of

the ne'tron is not kno-n -ith #ertainty. +his -e do kno-, that a ne'tron does emit a

beta arti#le, an ele#tron. e also kno- that a roton #an by ele#tron #at're t'rn into a

ne'tron. hile the resent tenden#y is a)ainst the belief that the ne'tron #onsists of a

roton and an ele#tron in #lose bond, this thesis ass'mes that it does have an internal

str'#t're #omosed of oosite ele#tri#al #har)es. e so kno- that it has a ma)neti#moment. If ma)netism is d'e to #har)es in motion, then -e #annot be far -ron) in this

ass'mtion. %le#trons and rotons also have ma)neti# moments. In other -ords, ea#h of


35/56

the elementary arti#les -hi#h make ' ordinary matter has asso#iated -ith it a

ma)neti# moment, ele#tri# #har)e, or #har)es. In the exeriments of 8tern and &erla#h,

ma)neti# moments -ere meas'red by #a'sin) a beam of arti#les to ass thro')h a

-ed)e>shaed ma)neti# field -hi#h defle#ted them.

et 's #onsider a solid #ylindri#al bar ma)net of #ir#'lar #ross se#tion raidly rotated

abo't its lon)it'dinal axis. hile it is -ell kno-n that in this #ase the ma)neti# fielddoes not rotate -ith the ma)net, let 's ass'me for #onvenien#e that it does rotate -ith

the ma)net. If the axis of this ma)net is verti#al -ith the 5orth ole 'ermost, then in

the e7'atorial lane mid-ay bet-een the oles of the ma)net -e -ill have a ma)neti#

field every-here dire#ted verti#ally do-n-ard, and the motion of this field -ill be

to-ard the observer on one side and a-ay from the observer on the other side of the

ma)net. In this e7'atorial lane there -ill also be a radial hori9ontal Bx3 ele#tri# field.

+his field -ill be #onver)ent or diver)ent deendin) on the dire#tion of rotation of the

ma)net.

et 's #onsider -hat -o'ld haen if an atom of any kind of matter is la#ed in a

#onver)ent or diver)ent Bx3 ele#tri# field. +he lanetary ele#trons -ill all exerien#e afor#e -hi#h -ill shift their orbits sli)htly, say a-ay from the axis, -hereas the n'#le's

-o'ld be 'lled to-ard it. +here -ill be a very small differential in the ma)nit'de of

these t-o for#es d'e to the sli)ht shift in the osition of the #enter of mass of the

ele#trons -ith rese#t to the osition of the n'#le's. In this #ase, the 'sh on the

ele#trons -ill be less than the 'll on the n'#le's. +he net effe#t of this -ill be a small

attra#tive for#e -hi#h -ill tend to move the atom to-ard the axis of the ma)net. %ven a

sin)le ne'tron la#ed in a #onver)ent Bx3 ele#tri# field mi)ht exerien#e this attra#tive

for#e if its #onstit'ents are oositely #har)ed attra#tive arti#les. 8'#h a field mi)ht be

emloyed to investi)ate the #omosition of the ne'tron6 +he #r'x of this aer is that it

rooses that )ravitational for#e is none other than the differen#e bet-een the 'll and

the 'sh of a #onver)ent or diver)ent Bx3 ele#tri# field a#tin) on the ele#tri#al

#onstit'ents of atoms.

+he #onse7'en#es of this roosal -o'ld mean that the henomenon of mass is

indeendent of -ei)ht. An ele#tron alone in s'#h a field mi)ht be reelled -hile a

roton -o'ld be attra#ted. +his is a sta))erin) tho')ht, b't -e kno- of a #ertainty that

an ele#tron or a roton by itself a#t'ally has -ei)ht@ Mi)ht not the ne)ative #har)e

-hi#h the earth is kno-n to ossess be d'e to a radi#al #onver)ent Bx3 field emanatin)

from the atoms #omosin) the earth@ If all ne'tral matter #onsists of e7'al n'mbers of

oositely #har)ed ele#tri#al arti#les then the total mass of a body -o'ld be

roortional to the total #har)e of one si)n #ontained -ithin it. It is here roosed thatthe earth?s )ravitational field mi)ht -ell be a #onver)ent Bx3 field. e kno- that s'#h

a radial field is 'ni7'ely 7'alified to enetrate all sa#e o##'ied by matter and rod'#e

a differential attra#tive for#e to-ard the earth?s #enter of )ravity by searatin)

elementary #har)es of oosite si)n only a trifle from their normal mean ositions and

th's makin) the 'llin) for#e on the ositive #har)es sli)htly )reater than the 'shin)

for#e on the ne)ative #har)es.

%a#h of the elementary arti#les of -hi#h all matter is #omosed is also an elementary

ma)net. +he atom of today is a dynami# model. %a#h of these ma)nets has motion of

some kind >>> orbital, vibrational, re#essional. In addition to ossessin) a ma)neti#

moment d'e to sin, lanetary ele#trons orbitin) n'#lei )enerate ma)neti# fields. +hesemotions of the elementary ma)nets rod'#e Bx3 fields -hi#h extend into sa#e o'tside

the atom. 5o-here in modern theory is an a##o'nt )iven of these s'er>imosed Bx3


36/56

fields emanatin) from all matter. =n mi)ht think that in ordinary nonma)neti# matter

they -o'ld all #an#el o't sin#e this is -hat haens -ith the ma)neti# fields in s'#h

matter. +he ele#trons are aired in the vario's ener)y shells (of most atoms in s'#h a

-ay as to effe#t this #an#ellation of ma)neti# fields o'tside the atom. +heory sho-s that

if t-o s'#h aired lanetary ele#trons revolve in oosite dire#tions, one #lo#k-ise and

the other #o'nter>#lo#k-ise, their ma)neti# fields d'e to sin at a oint o'tside the atom

#an #an#el ea#h other o't and that their Bx3 fields #an #onstr'#tively reinfor#e ea#hother. +he #aital theoreti#al dis#overy, ho-ever, #omes from a st'dy of the ma)neti#

field )enerated by the orbital motion of the lanetary ele#trons. +he ne)ative ele#tron,

revolvin) abo't a ositive n'#le's, #lo#k-ise or #o'nter>#lo#k-ise, )ives rise to a Bx3

field -hi#h is, in either #ase, al-ays dire#ted radially in-ard to-ard the n'#le's from

oints o'tside of atoms. +he ma)neti# fields of t-o s'#h oositely revolvin) ele#trons

-ill #an#el, b't the Bx3 fields reinfor#e ea#h other. +hat these fields are dire#ted

radially in-ard makes it ossible for them to a##o'nt for the kno-n drift of ositive

ions in the atmoshere do-n to-ard the earth and the oosite movement of ne)ative

ions '-ard. Be#a'se of its romisin) otentialities let 's no- take ' an analysis of

the ma)neti# field and motional ele#tri# field arisin) from orbitin) lanetary ele#trons.

et 's take for o'r model the simlest ossible examle, the Bohr Hydro)en Atom.

Consider the n'#lear roton at rest and the ne)ative ele#tron as revolvin) in a #ir#'lar

orbit of radi's r o abo't it -ith an)'lar velo#ity v. +he Amere>Biot>8avart exression

for the ma)neti# field B )enerated abo't a #har)e / movin) -ith velo#ity v is in mks

'nits2

(%7. 4F B 7 v x rrJ

-here r is the radi's ve#tor from 7 to a oint P -here B is meas'red. If the ele#troni#

#har)e >7 is movin) thro')h free sa#e -itho't asso#iation -ith nei)hborin) #har)es

then -e kno- that B aears as a motional ma)neti# field d'e to relative velo#ity of the

ele#tri# field of the #har)e -ith rese#t to the observer at P. In this #ase, if the observer

moves -ith the same velo#ity v as the #har)e, then the ma)neti# field at P disaears.

=n the other hand, if >7 is movin) in a linear #ond'#tor -ith relative velo#ity v, then an

observer at the oint P -ill observe a ma)neti# ener)y field B, -hether or not he is

stationary or movin). +he a#t'al val'e of B -ill of #o'rse be altered if the observer

takes on relativisti# velo#ities. B't B -ill be observed in any frame of referen#e movin)

thro')h, or stationary at, the oint P. e no- in7'ire -ith re)ard to the stat's of B at a

oint P -hen the lanetary ele#tron is revolvin) abo't the roton in a Bohr atom. 8in#e

-e kno- this field is )enerated by #ooerative a#tion -ith the ositive n'#le's and that

lanetary ele#trons in ma)nets #ontrib'te #omonents of orbital ma)neti# moment, -ekno- that B m'st be an ener)y tye ma)neti# field. +he Amere>Biot>8avant form'la

re7'ires that at any instant the maxim'm val'es of B -ill be fo'nd at oints alon) a

rotatin) radi's ve#tor dra-n from the roton thro')h >7 to the oint. +his means that the

ma)neti# field ener)y of B is movin) in a #on#entri# orbit -ith the ele#tron, -ith a

tan)ential velo#ity 3 (r o r- at any oint a distan#e r from >7. If the ma)neti# field

-hi#h the ele#tron #arries abo't it as it revolves in its orbit -ere of the motional

ma)neti# field tye %s x 3 )enerated solely by the relative motion of a sin)le ele#tri#

#har)e and an observer, then one #o'ld hardly im'te motion to it. Ho-ever, in this #ase

-e kno- the ma)neti# ener)y is itself a hysi#al reality by virt'e of its kno-n tye.

+his toroidal>like band of ener)y obvio'sly holds a fixed relative osition -ith rese#t

to the orbitin) ele#tron, and hen#e moves -ith it.

+his movin) ma)neti# field, -e kno-, -ill in t'rn )ive rise to a motional ele#tri# field


37/56

B x 3. +his is ill'strated in the a##omanyin) i)'re .

Fi(re -

hen the ele#tron has a #o'nter>#lo#k-ise motion in its orbit, it -ill )ive rise to a B at

oint P -hi#h -ill be dire#ted ' o't of the a)e. 3 -ill have the same dire#tion as v,

and B x 3 -ill be dire#ted radially in-ard to-ard the roton. e -ill #all this a

#onver)ent motional ele#tri# field. et 's no- #al#'late the val'e of this fie

wj hooper news horions motional e fields

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