condensed intro tesla coils

8/10/2019 Condensed Intro Tesla Coils

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PRIMARY AND SECONDARY COILS Experimental Unit at Bolinas,

California, 1!1DISCLAIMER"#$is material %as %ritten earl& in t$e pro'e(t an) is innee) of extensi*e re*ision+ Paes 1-1. res/lt fromexperimental in*estiations an) t$eoreti(al (onsi)era-tions %$ile at m& la0 in t$e Mar(oni ireless B/il)in2R+C+A+3, at Bolinas, California, from 1!4-1!1+ Paes55-56 are ta7en from referen(e 253 an) a)apte) forrelation to #esla Coil %a*es+ Paes 56-81 are ta7en fromreferen(e 283 an) ser*e as an ill/stration of $o% t$e#esla Manif&in #ransmitter (an extra(t ener& from t$e

Eart$9s resonant ele(tri( fiel)+Eri( P+ Dollar) Mar($ 55, 1!.


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P.O. BOX 429 GARBERVILLE, CA 95440-0429 U.S.A.

#:E #ESLA #RANS;ORMERAt t$e t/rn of t$e (ent/r& #esla %as in t$e pro(ess of)e*isin a means of %ireless po%er transmission+ #$etransmission in*ol*e) t$e eneration of lonit/)inalet$er %a*es+ $et$er #esla a((omplis$e)t$is is not 7no%n, 0/t t$e i)ea %as (onsi)ere) 0& ot$ernota0les< s/($ as =el*in an) Max%ell+ =el*in (onsi)ere) itpossi0le toenerate >lonit/)inal %a*es in t$e l/minifero/s et$er>

t$r/ t$e p$enomena of )ispla(ement (/rrent 2(apa(it&

(/rrent 3+ :e oes on to in)i(ate $is feelin t$att$ese %a*es m/st 0e faster t$an li$t, as t$elonit/)inal %a*es in a steel ro) mo*e %it$ m/($ reater*elo(it& t$an t$e trans*erse %a*es+ #esla (laims t$at

t$e %a*es from $is transformer propaate at t$e*elo(it& of li$t+ It is interestin to note t$at t$e

*elo(it& meas/re) on t$e #esla (oil is also reatert$an t$e *elo(it& of" li$t, 0/t t$is )oes appear to 0e ap$ase *elo(it& rat$er t$an a ro/p *elo(it&+In $is %ritins #esla in)i(ates some seeminl& impossi0lep$enomena s/rro/n) t$e emanations from t$e sp$eri(alterminal (apa(it&, an) I $a*e )etermine) t$ese to 0e tr/e0& experiment+ One is t$at t$e po%er ra)ient 2po&ntin*e(tor3 is in t$e same axis as t$e )iele(tri( fl/xra)ient+ #$e ot$er is t$e slo% formation of a(on)/(ti*e area s/rro/n)in t$e sp$ere t$at is not ioni(in nat/re 2in ot$er %or)s is not a spar7 or lo%)is($are3+Contrar& to pop/lar relief, t$e #esla transformer is nota


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Be(a/se t$e )issipation of t$e transformer is for allpra(ti(al p/rposes nelii0le, t$e ener& 7eepsin(reasin at a linear rate per (&(le of os(illation,t$ere0& a((/m/latin a ianti( ?/antit& of ele(tri(alener&+ 2A form of laser a(tion ma& 0e possi0le+3

In or)er for t$e transformer to resonate %it$ t$e planett$e ener& storae in t$e a(ti*e reion t$at ro%s aro/n)t$e sp$ere terminal m/st e?/al t$e (on'/ate ener&storae of t$e eart$, a stiff re?/irement+It is interestin to note t$at )iele(tri( 0rea7)o%n int$is a(ti*e reion ro% into a lo perio)i( form 0ase) on5-1 as t$e lo 0ase+ #$is %ill 0e re(onise) as t$etran(en)ental P:I or t$e ol)en Ratio+ In lo%)is($ares t$e ions of metalli( elements form sta0lesp$eres of )iameter in*erse to t$e atomi( %ei$t of t$eelement in*ol*e)+

#$e transformer9s prin(ipals of operation are as follo%s"#$e first re?/irement is t$e s/))en (ollapse of an ener&fiel) t$ere0& pro)/(in a s/))en imp/lse of ener&,se(on) is t$e


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transformin properties of t$e o)) $armoni( or)ere) sinle%ire )ela& line 2(oil3 %$i($ allo% for t$e pro)/(tion ofenormo/s E+M+;+ an) M+M+;+, an) t$ir), t$e )iele(tri(p$enomena s/rro/n)in t$e free spa(e (apa(it& terminal+13 #$e formation of t$e ener& imp/lse in*ol*es t$e)is($are of a (apa(itor %it$ t$e $i$est pra(ti(al store)ener& into an impe)an(e 2in)/(ti*e3 of t$e lo%est pra(ti(al*al/e, an) t$e )is($are pat$ is (o/ple) to an ener& s/ppl&t$ro/$ a neati*e resistan(e )e*i(e+ #$is neati*eresistan(e is (lassi(all& a spar7 )is($are, 0/t a s/periorplasma )e*i(e nee)s to 0e )e*elope) to en$an(e effi(ien(&+


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Un)er optimal (on)itions t$e exponent of os(illation amplit/)e%ill 0e positi*e o*er a s/staine) perio) of time+#$e net res/lt of t$is s&stem is t$e pro)/(tion of an extreme

imp/lse of M+M+;+ of reat + An alternate met$o) is t$e)is($are of an in)/(tor of t$e $i$est pra(ti(al store)

ener& into a (ir(/it of t$e lo%erst pra(ti(al a)mittan(e,

t$ere0& pro)/(in an enormo/s imp/lse of E+M+;+ of reat53 #$e ener& imp/lse enerate) 0& t$e aforementione)met$o)s is t$en (o/ple) into a pair of sinle %iretransmission s&stems+ #$ro/$ in)/(tion a stron tra*ellin%a*e is forme)+ D/e to t$e impe)an(e transformin properties

of t$e o)) 2 , et(3 or)er line, t$e E+M+;+ of t$e %a*eis (on*erte) into li$tnin manit/)es, still retainin t$eextreme ))t of t$e initial )is($are+#$e (apa(iti*e )is($are met$o) of imp/lse eneration is

#esla9s fa*orite, 0/t Steinmet@ s$o%s t$at in)/(ti*e)is($ares %ill also %or7+

#$e (apa(itor (ontains t$e initial ener& of t$eos(illatin s&stem+ #$e 0/ss from t$e (apa(itors to t$eprimar& loop s$o/l) $a*e a nelii0le transientimpe)an(e+ #$e (apa(itors s$o/l) 0e of t$e 0olt on*a(//m t&pe, $o%e*er, t$e /ni?/e )iele(tri( properties of%ater mi$t 0e of a)*antae as (apa(itor plates+ #$e(apa(itors m/st 0e in s&mmetri(al arranement %it$ t$eprimar& (oil+ #$e primar& m/st 0e of one t/rn onl& an)ex$i0it t$e lo%est pra(ti(al imp/lse rea(tan(e

+ #esla in)i(ates t$e proper lent$

of t$e primar& (on)/(tor to 0e , %$ere n is a$armoni( n/m0er (on*enient for t$e si@e of t$e /nit an) =is /nspe(ifie)+ Also /nspe(ifie) is if t$is *al/e isfree os(+ )is(onne(te) from t$e (apa(itors or is LC)epen)ent+

#$e transmission net%or7 (onsists of t%o sinle %iretransmission s&stems of nelii0le ra)iation loss+ #$efirst of t$ese is (alle) t$e se(on)ar& (oil+ #$e next is

(alle) t$e >extra (oil> 0& #esla, 0/t $en(efort$ %ill 0e(alle) t$e >#esla Coil>+ #$is net%or7 or line ist&pi(all& a0sent in most /nits p/rportin to 0e #eslatransformers+#$e se(on)ar& (oil ser*es as a mat($in net%or7 0et%eent$e %a*e eneratin primar& loop an) t$e #esla (oil+ #$emaneti( (o/plin fa(tor >7> 0et%een t$e PRI an) SEC(oils is t&pi(all& 54+ Nelii0le maneti( (o/plins$o/l) exist 0et%een t$e se(on)ar& an) #esla (oils+#$e f/n(tion of t$e se(on)ar& is t$ree fol)+ #$e firstis t$e transformin of t$e primar& M+M+;+ p/lse into an

a0r/pt tra*ellin ele(tri( %a*e+ Se(on), to pro*i)e a(onstant potential (onstant (/rrent transformation for


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oo) *oltae re/lation at t$e o/tp/t terminal of t$e#esla (oil, an) t$ir) is to mat($ t$e )ri*e impe)an(e oft$e #esla (oil to t$e )ri*e impe)an(e of t$e eart$+


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FIG 26


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14#$is is a($ie*e) 0& (on(entri( (onfi/ration %it$ t$eprimar& se(on)ar& s&stem t$ere0& en(losin its)iele(tri( fl/x+#$e potential ra)ient alon t$e #esla (oil isapproximatel& a step f/n(tion )/e to t$e p$ase)ispla(ement of t$e inp/t imp/lse9s $armoni(s, $o%e*er,t$e *elo(it& of t$e $i$er or)ere) o*ertones 0e(omeproportionate to fre?/en(& if t$e self (apa(it& 0e(omessinifi(ant, t$ere0& )istortin t$is ra)ient %$i($

ass/mes e?/al *elo(it& for all o*ertones+Consi)er t$e ta0le+ ;re?/en(& Coil Lent$ in DereesInp/t P/lse Derees

;o 4 4

8;O 5J4 2-43 4

6;4 H64 2K43 4

J;4 .84 2-43 4#$e $armoni(s of t$e time f/n(tion imp/lse are all inp$ase, $o%e*er, t$e $armoni(s of t$e spa(e f/n(tion areall o/t of p$ase an) is t$erefore a step f/n(tion+ #$e

(oil (an 0e (onsi)ere) a form of )ifferentiator+:en(e t$e ra)ient alon t$e (oil is a0r/pt at t$e lastfe% )erees of (oil lent$ 0/t small else%$ere alon (oil2see ;i+ 53 + #$e last t/rns of t$e (oil m/st 0eins/late) a((or)inl&, it %o/l) seem possi0le t$era)ient to (ontin/e to in(rease 0e&on) t$e )iele(tri(terminal


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in(rease as t$e %a*e penetrates t$e eart$+ :en(e t$e 6se(tions of t$e #esla transformer"1+ Eart$5+ Primar& s&stem po%er s/ppl&8+ Se(on)ar& %a*e (oil

H+ #esla or manifi(ation (oil6+ Diele(tri( antennaIt s$o/l) 0e+ 0orn in min) t$at #esla )esine) t$iss&stem fort$e transmission of ele(tri( %a*es+< #$is is $ar)l&)esira0le forla0 %or7 as se*ere )amae to /nprote(te) apparat/s an)ele(tri(al interferen(e (an res/lt+ #o (onfine t$e ener&an imae (oil 21!4 s$ift3 m/st 0e (onne(te) to t$e eart$terminal+ Ma7in t$is arranement in a $orses$oe(onfi/ration pro)/(es intense )iele(tri( fl/x an)

)ispla(ement (/rrent t$at is ?/ite /sef/l for plasma%or7+D/e to t$e immense )iffi(/lties s/rro/n)in t$e spar7)e*i(e, a simple met$o) an) one of m/($ reater (ontrolis s$/nt fee) of t$e primar& net%or7 0& an A+M+ ra)iotransmitter of spe(ial )esin s/($ as t$e /nit at0/il)in n/m0er one+ D/e to t$e $i$ impe)an(eet$ertensions>+

FIG 3


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FIG 4offere) 0& t$e primar& resonator t$e impe)an(e effe(ti*eof t$e t/0es m/st 0e $i$ an) t$erefore m/st operate at$i$ ano)e *oltaes+ #$e ele(tron emission $o%e*er, m/stalso 0e $i$, ne(essitates lare (at$o)es an)

temperat/res+ :i$ ano)e an) lare ele(tron emissionare /s/all& of in*erse relation in a*aila0le *a(//mt/0es+ Spe(ial p/lse mo)/lator *a(//m t/0es m/st 0e/se)+ :&)roen t$&ratrons mi$t operate satisfa(toril&


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at lo% fre?/en(ies %$ere t$e 1 mi(rose(on) )eioni@ationtime %ill not $in)er (omm/tation+ #$e most effe(ti*e)e*i(e for s$/nt fee) ma& 0e t$e m/ltipa(tor t/0e )/e toits stron neati*e resistan(e effe(ts, 0/t it is not(lear if it %ill operate 0elo% 1444=C %it$ m/($

effi(ien(&+B& t$e /tili@ation of t$e aforementione) )e*i(es a m/($impro*e) fiel) is )e*elope) at t$e transformer o/tp/t%it$ rear) to sta0ilit&+ #$is I $a*e fo/n) )esira0le fort$e pro)/(tion of sta0le plasma formations+:o%e*er, I $a*e not noti(e) t$e >'ammin toet$er ofele(trons> /nless t$e spar7 met$o) is /se) as t$e rate ofrise of EM; is m/($ reater 0& t$e spar7 met$o)+ Per$apst$e m/ltipa(tor %ill operate (omparati*el& 0/t stronimp/lses )o not seem possi0le %it$ s$/nt met$o)s+;or sta0ilit& of (ertain plasma effe(ts A;C ma& 0e

re?/ire)+ 2See ;i+ 63 #$e imae (oil s&stem ex$i0itsstron )is(riminator effe(ts an) t$ere0& fa(ilitates t$eformation of an error sinal to t$e +C+O+As to p$&si(al (onstr/(tion t$e primar& s$o/l) 0e s$eet(opper of reat (on)/(tor %i)t$ an) lare loop area+Lare s/rfa(e is re?/ire) as t$e s7in effe(t is total%it$ imp/lses+ Lare %i)t$ also minimi@es in)/(tan(eallo%in for larer (apa(itors an) more


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Fig 5

- Setup for plasma work -

SCOPESHOWSSIZEOFP!S"!WI#H$ESPEC##O #I"E%rapi) )is($are an) $en(e $i$ imp/lse strent$+ Inopposition to t$is re?/ire) in)/(ti*e re)/(tion is t$enee) for a lare area )/e to t$e flas$o*er an) (o/plin

re?/irements+ :en(e a 0alan(e $as to 0e esta0lis$e)0et%een t$e nee) for minim/m in)/(tan(e for rapi))is($are an) for a lare maneti( fiel), res/ltin inlare in)/(tan(e+ #$e form/la for in)/(tan(e2rationali@e)3 is Larea%i)t$+#esla in)i(ates t$at t$e (opper %ei$t of t$e se(on)ar&m/st e?/al t$at of t$e primar& for maxim/m effi(ien(&+#$is of (o/rse oes alon %it$ stan)ar) transformert$eor& 0/t it m/st 0e remem0ere) t$at t$e )ept$ ofpenetration of %a*es into (on)/(tors is mi(ros(opi( forimp/lses+ #$is (opper re?/irement m/st 0e mo)ifie) to

e?/al s/rfa(e area rat$er t$an %ei$t+ As to t$e /se of%ater for (apa(itor (on)/(tors #esla i*es no reason+ It%o/l) seem t$at t$is is )one for t$e sa7e of simpli(it&an)or is a $ol)o*er from t$e Le&)en 'ar+ 2Remem0er $e0ean t$is in 1!43+ :o%e*er, %ater $as man& (/rio/s)iele(tri( properties t$at ma& 0e essential in operation+B& t$eor&, for maxim/m )is($are *elo(it& t$e )iele(tri(m/st 0e a *a(//m+Anal&sis 2See ;i+ .3#$e os(illatin (oil )iffers from t$e transmission lineon a((o/nt of t/rn to t/rn (apa(it& an) )istri0/te)

m/t/al in)/(tion+#$e presen(e of series (apa(it& (a/ses t$e (oil to


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respon) as a (apa(itor net%or7 2%it$ no in)/(ti*e effe(t3to%ar)s a0r/pt imp/lses an) an/lar *elo(ities reatert$an t$e an/lar *elo(it& of free os(illation+

Fig 6#$e *oltae )istri0/tion alon t$e (oil at t$e first

instant )epen)s on t$e fa(tor + C (apa(it& toro/n), Cs(apa(it& from en) to en)+#$e reater a,t$e reater t$e (on(entration of *oltae att$e fee) en) of t$e (oil+ #$e maxim/m *oltae per /nitlent$ is e?/al to atimes t$e *oltae of /niform)istri0/tion+ a is a small fra(tional *al/e %it$ #esla(oils+

#$e reater t$e ))t or t$e reater t$e ra)ient of


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*oltae+If t$e imp/lse $as a lon tail t$e p$enomena %ill 0e as)es(ri0e) 0/t follo%e) 0& a )ampe) os(illation+ 2OSC3B& impressin a s/staine) os(illation, an) if t$e (oil$as a small )issipation (onstant /, t$e *oltae %ill

(ontin/e to in(rease in)efinitel&+ Initiall& t$e (oila(ts as a (apa(itor la))er net%or7 2See ;i+ J3+ #$e(apa(it& elements are ($are) to nearl& t%i(e t$e applie)

E+M+;+ #$e effe(ti*e (apa(it& 0ein ($are) is +Be(a/se t$is net%or7 (ontains impe)an(e elements of onl&one t&pe t$e *oltae )istri0/tion is $&per0oli( rat$ert$an perio)i(+ If )istan(etotal lent$ an) e is*oltae to ro/n) at t$e parti(/lar )istan(e,

+ ;or #esla (oils t$is )istri0/tion s$o/l)0e aslinear as possi0le 2small a3+As t$e )istri0/tion oes from initial to final t$e*oltae (an 0e anal&@e) into a (omplex series of)e(remental %a*es at *ario/s fre?/en(ies an) %a*elent$s+#$is is a((omplis$e) 0& anal&@in t$e initial)istri0/tion 2$&per0oli(3 into spa(e $armoni(s %it$respe(t to t$e final 2DC3 )istri0/tion+ If a is(onsi)era0le, no linear relation exists 0et%een fre?/en(&an) %a*e lent$+ 2See ;i+ !3

$en an os(illatin %a*e follo%s t$e initial imp/lse 2asis t$e;I J1

= 1 Cs Darafs


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InitialResponse

Distri0/tion alon (oil

;i !;inalResponse

54(ase %it$ t$e #esla transformer3 t$e alternate positi*ean) neati*e *oltaes (a/se (ontin/o/s in(rease in*oltae an) ener&+ #$e effe(t of t$e alternations is toin(rease t$e amplit/)e of t$e %a*e 0& t%i(e t$e applie)*oltae for ea($ alternation+ Example - os(illatin

*oltae is 1+5H times applie) *oltae+ 2initial3 At ea($(&(le t$is is m/ltiplie) 0& t%i(e Ea, (a/sin E to ro/n)to in(rease in step+ At se(on) (&(le E is H+J5, at t$ir)E is J+54, et(+ #$is effe(t is re)/(e) or s/ppresse) 0&lare / or a+#$e a(tion of t$e spar7 ap $as a m/ltipli(ati*e effe(talso+ Consi)er Steinmet@9 anal&sis+ >Contin/al or(/m/lati*e os(illations in*ol*e an ener& s/ppl& to t$es&stem+ If t$e ener& s/ppl& is less t$an ener&)issipation t$e OSC+ )amps as a transient %it$ re)/(e) /+If t$e s/ppl& e?/als t$e )issipation t$e OSC is

(ontin/o/s+ If s/ppl& is reater t$e OSC is (/m/lati*e+#$e OSC represent ener& an) fre?/en(& transformation


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from t$e L+;+ or D+C+ s/ppl& to t$e :+;+ OSC s&stem+#$is transfer ma& - 0e 0ro/$t a0o/t 0& t$e transient ofener& rea)'/stment res/ltin from a ($ane in (ir(/it(on)itions, pro)/(in aain a ($ane in (ir(/it(on)itions an) t$ere0& an ener& a)'/stment 0& transient,

et(+, et(+ + +Re(/rrent os(illations ten) to r/n into ea($ ot$er an)form (ontin/o/s OSC+ $en s/((essi*e transients r/n in toea($ ot$er t$e& ten) to s&n($+:o%e*er, t$e formation of (ontin/o/s OSC is not t$e mereo*erlap or r/nnin toet$er of s/((essi*e %a*es+ #$ere(/rrent OSC (annot start /ntil t$e pre(e)in OSC $as)ie) o/t, an) s/ffi(ient ($are time $as elapse) for nextar( o*er of ap+ it$ o*erlap no )ea) perio) o((/rs)/rin %$i($ normal or s/ppl& fre?/en(& is s/pplie)+Ener& t$en m/st 0e s/pplie) 0& a p$ase )ispla(ement

%it$in ar(

FIG - 9Line elemental dx


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During oscillation, which gives a negative energy cycleor a reversed hysteresis loop. For continuous oscillationthen, a hysteresis loop must be formed by the lag ofeffect before cause." (This is negative resistance or the

formation rather than the dissipation of energy.) "Forthe cumulative oscillation, the area of the loop mustdepend on and increase with the stored volt amps of theoscillating system."Mathematic analysis (ee Fig. !) (ee reference )e # $ to ground es# $ gradient ($%inch)&y 'irchoffs aw

(*a)

et # space operator

et # time operator

ThenDifferentiation of (*a) in tine gives

(*b)These, (*a) + (*b) are independent of initial and final

distribution of $MF.$uation (*b) must be e-pressed in one variable. n


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terms of voltage and current, the current density incapacity to ground is / per inch of coil times the rateof change of e to ground.

(0)and

25J31elating sand voltagesin capacity between turns euals capacity per inch times thetime rate of voltage gradient.

(2)

(!)1elating . and voltage3The relation between magneti4ing current and 5is comple- anddefies analysis. (ee Fig. 56). For the fundamentaldistribution (5%7 wave) the effective inductance of the coilis the space integral of the 5%7 cosine wave of current ofM.M.F. and is euivalent to % times the normal totalinductance. For the third harmonic, *%7 cosine wave of currentor M.M.F. the inductance of 5%* of the coil opposes theremaining inductance resulting in diminishment of selfinduction depending on the mutual inductance of the buc8ingsection to the rest of the coil. The process progresses

similarly for the rest of the harmonic series (9F, :F, !F,etc.). This results in surge impedance for each harmonic buteffects tend to cancel for wave length. /apacitance of thecoil behaves in a similar fashion and may be voltage dependentgiving the coil voltage gain under the proper conditions.(;arametric amplification)Denoting this residual inductance as lea8age inductance , and


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FIG 10

Magnetic Distribution

(*6b) i*es t$e *al/e of , %$ile 258a3 in*ol*es

+If %e )ifferentiate t$e former %it$ respe(t to x an) t$elatter %it$ respe(t to t, s/0stit/tion 0e(omes possi0le+

28132813, 253 an) 25J3 express in terms of *olts t$e t$reeterms of 25803 :en(e, t$e eneral e?/ations

2883 #$ise?/ation nele(ts losses+Anal&sis of t$e intera(tion 0et%een t$e eart$ an) *ario/s(oils is possi0le 0& t$e /se of *elo(it& meas/re+ #$is in

eneral is a (omplex ?/antit& (onsistin of real an)imainar& parts+


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B& t$e relation %ell 7no%n"

28H3%$ere * is t$e *elo(it& of t$e %a*e+ #$en *elo(it& is t$eratio of time to spa(e+ Lettin t$is *elo(it& 0e of /nit

*al/e, time an) spa(e f/n(tions 0e(ome e?/i*alent,

+ Steinmet@ i*es t$e follo%in instr/(tions fora((omplis$in t$is++>Line (onstants are t&pi(all& i*en per /nit lent$, asper (entimetre, mile, 1444 feet, et(+#$emost (on*enient /nit of lent$, %$en )ealin %it$transients in )istri0/te) (ir(/its, is t$e *elo(it& /nit*+#$at is, ($oosin as /nit lent$ t$e )istan(e of

propaation in /nit time, or 8 times 1414

(mse( fortrans*erse %a*es in air, t$is i*es * 1 an) t$erefore

LC 1 C L-1G L C-1

#$at is, t$e (apa(it& per /nit of lent$, in *elo(it&meas/re,

is in*ersel& proportional to t$e in)/(tan(e+ In t$is*elo(it&

/nit of lent$, )istan(e %ill 0e represente) 0& +>

S/0stit/tin 1

#ime anle Distan(e anle

Anal&sis of t$e tra*ellin %a*e alon #esla (oildimensionall(, a 'ield o' bi>dimensional radiation /as that occurring in thecase o' long c(lindrical terminal sur'aces1 here+ as in this instance, the bul4 o' the energ( o' the 'ieldis to be 'ound near the smaller ore o' the to terminal sur'aces,In igure , I ha2e shon a 'ield ith concentric terminal sur'aces /either s)herical or c(lindrical1+ and

ha2e increased the sco)e o' the 'ield b( reducing the si?e o' the smaller terminal sur'ace ithout+hoe2er+ changing either the total number o' 'ield lines or the larger terminal sur'ace, As the linealenerg( densit( is 2er( great near the smaller terminal sur'ace+ such addition o' the 'ield at that )ointmust ha2e materiall( increased the energ( o' the 'ield and the change in ca)acit( to be ex)ected shouldbe considerable, In 'act+ a considerable change in ca)acit( o' a s)here is obtained b( a change o' itsdiameter,

I', in igure the larger terminal sur'ace alone is changed+2%

e2en materiall(+ the total energ( o' the 'ield ill be increased 2er( slightl( onl(= due to the

'act+ as e ha2e seen+ that the energ( densit( near the larger terminal sur'ace is 2er( small,Such a small change in energ(> corres)onds to onl( a small change in the ca)acit( o' the

'ield+ 'rom hich e conclude


32/37

In ,0 'ield ha2ing to terminal sur'aces o' greatl( di''erent si?e+ a change o' the smaller

sur'ace )roduces a great change in ca)acit(+ hereas a change o' the larger terminal sur'ace

a''ects the ca)acit( o' the 'ield onl( 2er( slightl(, The ca)acit( o' a 'ield is+ there'ore+ almost

entirel( determined b( the sha)e o' the smaller terminal sur'ace,

That is h( e ma( ith correctness s)ea4 o' the ca)acit( o' a s)here+ or an( other bod(+

ithout mentioning the si?e and sha)e o' the other terminal sur'ace+ as long as the assum)tion

is correct that such other terminal sur'ace is o' greatl( larger dimensions,

It ma( not le amiss to call (our attention to the 'act that the increase o' 'ield energ( as

illustrated in igure is accom)anied b( a decrease in ca)acit(, This relation ma( easil( be

deduced 'rom )h(sical considerations+ as ell as, 'rom consideration o' the mathematical

ex)ression 'or the ca)acit(

herein the ca)acit( is ex)ressed as a )ro)ert( o' the 'ield alone, I am tem)ted to introduce

here the reci)rocal 2alue o' ca)acit( and a))l( to it the term .sti''ness o' the 'ield+. as an

increase o' energ( ould he 'olloed b( an increase o' sti''ness, I am+22

hoe2er+ loath to mar an( additional insight hich ma( be gained 'rom these ex)lanations b(de2iation 'rom so 'amiliar a term as ca)acit(,

or a better conce)tion o' the slight change o' ca)acit( caused b( a considerable increase o'

the larger terminal sur'ace+ I re'er to igure + here the di''erence o' ca)acit( is onl( 0 )er

cent in s)ite o' the diameter o' the larger terminal sur'ace being increased 0:: )er cent, It

a))ears+ there'ore+ that that )art o' the ca)acit( o' an antenna hich is due to the 'lat to) is

not materiall( changed b( its height abo2e ground,

%hile considering the ca)acit( o' a 'lat to) antenna to ground+ it must ha2e occurred to man(

engineers+ as it did to me+ that the statement to be 'ound in man( text boo4s on electrostatics

is rather misleading .That the 'ree ca)acit( o' a bod( considered alone in s)ace must not be

con'ounded ith the ca)acit( the bod( ma( ha2e against another bod( considered as a )late

condenser,. This statement is uite erroneous, As the strength and direction in an( )oint o' a

'ield is o' single and de'inite 2alue+ onl( one electric 'ield can exist in a gi2en s)ace at a gi2enmoment+ and+ there'ore+ onl( one 2alue o' ca)acit(, It is incorrect+ there'ore+ to distinguish

beteen 'ree ca)acit( and condenser ca)acit(, This clari'(ing statement is deemed ad2isable+

or at least )ermissible+ in 2ie o' the uoted errors,

B( s)ea4ing o' the ca)acit( o' the 'ield instead o' that o' the bod(+ no such erroneous thought

is )ossible+ and it is clear that b( 'ree ca)acit( o' a bod( is meant the ca)acit( o' the 'ield

hose smaller terminal sur'ace is the gi2en bod( and hose larger terminal sur'ace is one o'

2astl( greater dimensions, It is not essential that this greater terminal sur'ace be located at

in'inite distance+ because o' the 'act that e2en i' construed as o' ten times the lineal

dimensions o' the small sur'ace the change caused b( remo2ing it to an in'inite distance

ould result in a change in ca)acit( o' not more than one>tenth o' 0 )er cent,

At a time hen I had not reali?ed the singl( determined 2alue o' a 'ield ca)acit(+ I considered

a com)arison beteen 'ree and )late ca)acit( as shon in igure 9+ herein to an u))er

disc /o' hich the 'ree ca)acit( is /3FPI1*r1, as added another loer

disc+ thereb( 'orming a )late condenser, The )roblem arose in rn( mind to determine the

distance o' se)aration o' the to )lates so that the )late ca)acit( ould eual the 'ree

ca)acit( o' the single disc, rom the ell>4non 'ormulas 'or the disc23


33/37

?E&

ca)acit( and )late ca)acit(+ it ould a))ear that the to ere eual at a distance eual to dG

/PIF91r+ and I must con'ess that

I had uite a struggle to decide hether in s)ea4ing o' the ca)acit( o' the u))er )late I ould

not ha2e to add the to ca)acities, %hile such a mista4e need hardl( be called to the attention

o' the ma7orit( o' engineers+ I do not hesitate to ma4e mention o' it 'or the bene'it o' e2en the

'e students ho might gain there'rom,

The ad2ent o' the aero)lane has o)ened another 'ield+ 'or radio communication, %hereas in

the static 'ield o' an antenna+ one terminal sur'ace is arti'icial and the other )ro2ided b( the

surrounding ground+ both terminal sur'aces in an aero)lane out'it ha2e to be arti'icial and are+there'ore+ o)en to design, The uestion arises in such a radio oscillator as to ho much ma(

be gained in energ( 'or each single charge b( increasing that one o' the to terminal sur'aces

hich consists o' a dro))ed ire, The arrangement is shon in igure 5, It is e2ident that?E924

as long as the dro))ed ire is o' smaller dimensions than the electrostatic counter)oise

)ro2ided on the aero)lane+ an increase in length o' such dro))ed ire ill materiall( increase

the ca)acit( o' the 'ield and+ there'ore+ the energ( )er charge /as e ma( conclude b( analog(

'rom igure 1, As soon+ hoe2er+ as the dro))ed ire is materiall( longer than the conductor

on the aero)lane it assumes the role o' the larger terminal sur'ace o' the 'ield+ and an( 'urther

increase o' its length ill not materiall( contribute to an increase o' electrostatic ca)acit( nor

o' the energ( )er unit charge,

igure 0: shos the 'unction o' the 2olumetric and lineal energ( densit( in a 'ield hose

smaller terminal sur'ace is a long c(linder, Such a 'ield+ radiating bi>dimensionall( onl(+

shos an energ( concentration not so accentuated as that 'ound in the

?E%(


34/37

tri>dimensionall( radiating 'ield= but considering the larger terminal sur'ace o' a diameter ten

times that o' the smaller sur'ace+ the ca)acit( ould onl( be changed 0 )er cent b( increasing

the larger terminal sur'ace in'initel(,

In all cases+ there'ore+ here the larger terminal sur'ace does not come closer at an( )oint

than /sa(1 ten times the corres)onding dimension o' the smaller terminal sur'ace+ e need not

be concerned ith the actual sha)e o' the larger terminal sur'ace hen e determine the seat

o' energ(+ the ca)acit( and the con'iguration o' the 'ield lines emanating 'rom the smaller

sur'ace, It ill be seen+ there'ore+ that 'rom the 'lat to) o' an antenna+ lines emanate almost

s(mmetricall( both u)ards and, donards as though the larger terminal sur'ace ere

one2@

surrounding the antenna s(mmetricall( on all sides+ in s)ite o' the 'act that the ground is

located entirel( at the bottom o' the antenna, This is clearl( illustrated in igure 00,

B( integrating the lineal energ( densit( o' a three>dimen>sionall( radiating 'ield beteen the

radius o' the smaller s)here

?E%%


35/37

3r.&i4ola Tesla+ and / epect to come bac4 to the beha2ior o' a sphere as a conductor o'

radio 'reuenc( currents at some later date,

The stud( o' ca)acities o' com)osite bodies is most instructi2eand conduci2e to a clear

conce)tion o' ca)acit(, Let, as in igure 08, a number o' small s)heres o' radius be so

arranged as to co2er com)letel( the sur'ace o' the larger s)here+ the radius R o' hich

be 0::, I' each one o' the

,%!1(( smaller s)heres could be counted at its 'ull 2alue o' ca)acit(+ the capacity o' the

com)osite bod( ould be 80+;::= as a matter o' 'act+ hoe2er+ it is not more than radiusR o'

the larger s)here+ that is 0::, Indeed+ the con'iguration o' the electric 'ieldF could not ha2e

changed materiall( b( the arrangement o' the small s)heres+ and the ca)acit( clearl( presentsitsel' as a )ro)ert( o' the con'iguration o' the 'ield l(ing outside o' the en2elo)ing sur'ace o'

the com)osite structure.27

Ca)acit( ma( )la( a )art in the conduction o' electricit( thru liuids and gases, Let us assume

a series o' s)heres in lineal arrangement as shon on igure 0;,

As long as the distance beteen the s)heres is great com)ared to the diameter o' the s)heres+

each s)here ill retain its 'ull ca)acit( as gi2en b( its radius, B( decreasing the distance

beteen s)heres the indi2idual ca)acities o' the s)heres decrease+ because o' the negati2e

ca)acit( coe''icients, I' such a))roximation be carried to the )oint o' contact beteen the

s)heres+ the ca)acit( o' each indi2idual s)here ould be reduced to a))roximatel( > o' the

original ca)acit(, I' such a ro o' s)heres

ere concei2ed as 'reel( mo2able+ so as to enable each s)here to ma4e contact ith a )late P,

hich is 4e)t charged to a certain )otential+ then the charges carried aa( b( the s)heres a'ter

contact ith the )late ould be )ro)ortional to the 'ull ca)acit( o' each s)here as long as the

s)heres are 'ar a)art+ and ouldbo onl( 0Fs G 0F3,09 th )art o' such maximum charge hen the s)heres are in contact, As e


36/37

assumed the )late P to be maintained at a certain )otential b( an outside source o' electricit(+

the con2ention current re)resented b( the de)arting charges o' the s)heres ould 2ar(

a))roximatel( in a ratio+ o' 3,0 to 0,

In the )assage o' electricit( thru an electrol(te+ the molecular conducti2it( has been 'ound to

be the same 'or all electrol(tes+ and 2ar(ing onl( ith the concentration o' the solution= the

molecular conducti2it( being a))roximatel( 3,6 times as great in the 2er( dilute solution as in

the concentrated solution,

I ish to call (our attention to the stri4ing similarit( beteen the ratio o' conducti2it(

ex)erimentall( determined in elec>

.

trol(tes o' small and large concentration and the ratio o' conducti2it( o' the ro o' s)heres

here the s)heres are 'ar a)art or close together, I do not )retend at this moment that a

)lausible modi'ication o' the theor( o' conduction thru electrol(tes and gases can be bused on

such a coincidence= and in 'act+ assum)tions ould ha2e to be made, or exam)le+ a lineal

arrangement o' the ions in the direction o' the static 'ield im)ressed on the electrol(te or on

the gas must be assumed,

But the 'act that such ratio in the case o' the s)heres is deduced from geometrical

considerations alone+ cou)led ith the 'act that in electrol(tes the same ratio 'ollos 'rom

)urel( geometrical considerations+ is su''icient to arrant 'urther thought, I do not hesitate to

bring this interesting coincidence to (our 4noledge+ "ith the ho)e that other )h(sicists ma(carr( on in2estigations

in the same direction, I ha2e said that the molecular conducti2it( o' electrol(tes arose 'rom

geometrical considerations onl(+ and I thin4 it ad2isable to call (our attention to the 'ounda>

tion o' such a statement, %hile it is true that the conducti2it( o' di''erent electrol(tes 2aries

considerabl(+ it has been 'ound that the molecular conducti2it( is the same 'or all electrol(tes,

The similar beha2ior+ o' the same number o' molecules+ inde)endentl( o' the eight o' the

molecule+ there'ore reduces the )henomenon to a )urel( geometric basis,SHMMA" Considering that electrostatic energ( is actuall( in the s)ace surrounding a charged bod(+ the Htter iscalled a .terminal sur'ace,. It is shon that ca)acit( is )redominantl( a 'unction o' the maximum lineal dimension

o' the terminal sur'ace, The 2olumetric and lineal energ( densities in the 'ield are de'ined and studied in a number

o' cases, It is )ro2en that the ca)acit( beteen to terminal sur'aces is greatl( a''ected b( changing the lineal

dimensions o' the smaller terminal sur'ace+ but not so 'or changes o' the larger, Certain current errors in

connection ith .mutual ca)acit(. are considered,The )ractical a))lications to a radio antenna and to aero)lane counter)oises arc gi2en,%hen a charge tra2erses a s)here+ entering )arallel to a diameter+ the s)here beha2es as a conductor o' uni'orm


37/37

lineal ca)acit(,

A))lications o' the theoretical considerations are also gi2en in connection ith the conducti2it( o' concentrated

and dilute electrol(tes,

condensed intro tesla coils

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