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Nederlands E le c tro n ik a - en Radiogenootschap

Postbus 39, Leidschendam. Gironummer 94746 t . n . v . Penningmeester NERC, Leidschendam.

HET GENOOTSCHAP

Het Genootschap s t e l t zich ten doel in Nederland en de Overzeese R ijksdelen de w etenschappelijke ontwikkeling en de toepassing van de e le k tro n ic a en de radio in de ruim ste zin te bevorderen.

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P r o f .D r .I r . J . Davidse, v o o r z i tt e r I r . F. de Jag er, v ic e - v o o r z itte r I r . C. van Schooneveld, s e c r e t a r i s I r . L.R. Bourgonjon, penningmeester I r . E. Goldblom

Prof. Dr. H.Groendijk I r . G.L. Reijns

Prof. I r . C. Rodenburg J.W.A. van der Scheer Ing.

Lidmaatschap

Voor lidmaatschap wende men zich to t de s e c r e t a r i s .

Het lidmaatschap s ta a t -behoudens b a llo ta g e - open voor academisch gegradueerden en hen, wier kennis of ervaring naar het oordeel van hét bestuur een vruchtbaar lidm aat­

schap m ogelijk maakt.

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anderen worden verleend.

HET TIJDSCHRIFT

Het t i j d s c h r i f t v e r s c h ijn t zesmaal per j a a r . Opgenomen worden a r t ik e l e n op het gebied van de e le k tro n ic a en van

de telecommunicatie.

Auteurs die p u b lic a tie van hun w etenschappelijk werk in het t i j d s c h r i f t wensen, wordt verzocht in een vroeg stadium kontakt op te nemen met de v o o r z i tt e r van de re d a c tie commissie.

De tek sten moeten, getypt op door de r e d a c tie v e r­

s tr e k te te k stb la d e n , geheel p e rsk la a r voor de o f f s e t ­ druk worden ingezonden.

Toestemming to t overnemen van a r t ik e l e n of delen daarvan kan u i t s l u i t e n d worden gegeven door de redac­

tiecom m issie. Alle rechten worden voorbehouden.

De abonnementsprijs van het t i j d s c h r i f t bedraagt f 4 0 ,— . Aan leden wordt het t i j d s c h r i f t kosteloos toe- ges tu u rd .

Tarieven en verdere in lic h tin g e n over a d v e rte n tie s worden op aanvrage v e r s tr e k t door de v o o r z i tt e r van de redactiecom m issie.

Redactiecommissie

I r . M .S te ffe la a r, v o o r z i tt e r I r . L.D.J. Eggermont

I r . A. da Silva C u riel.

DE EXAMENS

De examens door het Genootschap in g e ste ld en afgenomen

zijn:

a. op lager technisch n iv e a u : "E lektronica monteur NERG"

b. op middelbaar technisch niveau: Middelbaar E le k tro ­ nica Technicus NERG"

c. voor het oude examen "E lektronica Technicus NERG"

kan volgens de b e e in d ig in g sre g e lin g nog s le c h ts t o t en met 1975 worden ingeschreven.

Brochures waarin de exameneisen en het examenre­

glement z ijn opgenomen kunnen s c h r i f t e l i j k worden aan­

gevraagd b ij de A dm inistratie van de Examencommissie.

Voor deelname en in lic h tin g e n wende men zich to t de A d m in istratie van de Examencommissie NERG, Gehe-

m uidenstraat 279, den Haag, gironummer 6322 te Voorburg.

Examencommissie

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JAM ES CLERK MAXWELL

P r o f e s s o r R. V. Jones

U niversity of A berdeen, Scotland

A sketch of M axw ell's life, with p a r tic u la r re fe r e n c e to his developm ent of the e le c tro m a g n e tic th e o ry .

In c e le b ra tin g the C en ten ary of J a m e s C le rk M axw ell's T r e a tis e on E le c tric ity and M agnetism , we re c a ll one of the g r e a te s t of all p h y s ic is ts . He was 42 y e a r s old when the T r e a tis e was p u b lish e d ,’ and he had only

an o th e r six y e a r s to live; but he had a lre a d y m ade m a jo r contributions to the th e o ry of colour vision, to o u r understanding of S a tu rn 's R ings, to the th e o ry of optical in s tr u m e n ts , to the kinetic th e o ry of g a s e s , and to the th e o ry of m ech an ical s tr u c t u r e s , and he had initiated the th eo ry of c y b e rn e tic s. Any one of th e se contributions would have e n su re d him a place in the h is to ry of p h y sic s, but it is above all for his th eo ry of

• the e le c tro m a g n e tic field that he is fam ous, for as E in stein (1931) said

'If we leave aside the im p o rta n t special r e s u lts which Maxwell contributed in the c o u rse of his life to p a r tic u la r dom ains of p h y sic s, and confine o u r attention to the m odification that he produced in our conception of the n atu re of P h y sic a l R eality, we m ay say that, b efo re M axwell, P h y sic a l R eality, in so fa r as it was to r e p r e s e n t the p r o c e s s e s of n a tu re , was thought of as consisting of p a r tic le s , whose v a ria tio n s co n sist only in m o v e m e n ts governed by p a rtia l d ifferen tia l equations. Since M axw ell's tim e , P h y sical R eality has been thought of as

r e p re s e n te d by continuous fie ld s, and not capable of any m ech an ical in te rp re ta tio n . This change in the conception of R eality is the m o st profound and the m ost fruitful that P h y sic s has e x p erien ced since the tim e of Newton'.

Let me th e re fo re tell you som ething about the m an who thus changed the d ire c tio n of physical thought, and about the way in which he cam e to develop the

e le c tro m a g n e tic theory.

J a m e s C le rk Maxwell was b o rn in Edinburgh on 13th June 1831. His fa th e r was John C le rk M axwell, a Scottish gentlem an with a country e s ta te in

K irk c u d b rig h tsh ire in so u th -w e st Scotland. His*

m o th e r, who before h e r m a r r ia g e had been M iss F r a n c e s Cay, was E nglish, and cam e from

N orth u m b e rlan d . We know som ething of M axw ell's boyhood, which was spent at the fam ily hom e,

G le n la ir, for th e re a re m any pencilled sk etc h es m ade by one of his co u sin s. He was constantly w o rrying his fa th e r to explain the working of any piece of

m e c h a n ism , and he was fond, both in childhood and in m a tu rity , of playing jo k e s. His m o th e r died when he was eight y e a r s old; and his fa th e r, faced with the p roblem of his education, brought in a tu to r. The la t t e r proved to be a bully, and J a m e s m ade at le a s t one escap e fro m him by sailing out in a wash tub in the duck pond, an incident faithfully sketched by his cousin. T h e re a f te r his fa th e r in 1841 sent him to Edinburgh A cadem y, and even b efo re he left the

A cadem y to go to Edinburgh U niversity at the age of six teen , J a m e s had read a p a p e r to the Royal Society of Edinburgh.

A fter Edinburgh he went in 1850 to C a m b rid g e , w here his c o n te m p o ra rie s noticed that w henever the subject adm itted it, he had r e c o u r s e to d ia g r a m s , even though his fellow stu d en ts, and indeed his

l e c t u r e r s , m ight m o re e a sily solve the p ro b le m by a tr a in of a lg e b ra ic a n a ly s is . This tendency to think in t e r m s of d ia g ra m s and p ic tu re s , which has p e rh a p s alw ays been one of the s tr o n g e r c h a r a c te r is tic s of

B ritis h s c ie n tis ts , was e s s e n tia l to M axw ell's

approach to m any of his p ro b le m s . And as soon as his u n d e rg ra d u a te work at C am b rid g e had finished, Maxwell put his g e o m e tric a l insight to w ork on

F a r a d a y 's L ines of F o r c e . Even so, he knew that to think in p ic tu re s could have its lim ita tio n s , as he stated in his f ir s t p a p e r on the L ines of F o rc e (1855).

'The f ir s t p r o c e s s th e re fo re in the effectual study of the sc ie n c e , m u st be one of sim p lificatio n and

Tijdschrift van het Nederlands Elektronica- en Radiogenootschap deel 39 - nr. 1 1974

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J a m e s C le rk M axw ell, aged 3, escap in g fro m his tu to r.

Drawn by his co u sin J e m im a W ed d erb u rn .

D raw ing by J a m e s C le rk M axw ell.

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reduction of the r e s u lts of p rev io u s investigation to a form in which the mind can g ra s p th e m . The

r e s u lts of this sim plification m ay take the fo rm of a p urely m a th e m a tic a l fo rm u la o r of a physical

h y p o th esis. In the f ir s t case we e n tire ly lo se sight of the phenom ena to be explained; and though we m ay tr a c e out the consequences of given la w s, we can

n ev er obtain m o re extended view s of the connexions of the su b ject. If, on the o th e r hand, we adopt a physical h y p o th esis, we see the phenom ena only through a m ed iu m , and a r e liable to that blindness

>

to facts and r a s h n e s s in assu m p tio n which a p a rtia l explanation e n c o u ra g e s. We m u st th e re fo re

d isc o v e r som e m ethod of investigation which allows the mind at e v e ry step to lay hold of a c le a r

physical conception, without being com m itted to any th e o ry founded on the p h ysical scie n ce fro m which that conception is b o rro w e d , so that it is n e ith e r draw n aside fro m the subject in p u rsu it of

analytical s u b tle tie s , nor c a r r ie d beyond the tru th by a favourite h y p o th e sis'.

What M axwell set out to do in this 1855 p a p e r was to take F a r a d a y 's p ic to ria l ideas of L in es of F o r c e , and to give them analytical e x p re s s io n . He said in the p a p e r that the p o ssib ility of such e x p re s s io n a ro s e

in his mind a fte r reading K elvin's work of 1847 on 'M echanical R e p re se n ta tio n of E le c tro m a g n e tic and G alvanic F o r c e s by m ean s of the d isp la c e m e n ts of the p a r tic le s in an e la s tic solid in a sta te of s tr a i n '. And about the sa m e tim e he re c e iv e d an o th e r stim ulus

fro m read in g F a r a d a y 's 'Thoughts on Ray V ib ratio n s' (F a ra d a y , 1846). In fact, when in 1864 Maxwell

fo rm u lated the e le c tro m a g n e tic th e o ry , he stated that F a r a d a y 's thoughts w ere the sa m e in su b stan ce as those which w ere now developing into the

e le c tro m a g n e tic th eo ry of light. It m ay th e re fo re be of in te re s t at this point to r e c a ll how F a ra d a y cam e to publish the thoughts that w ere to prove such an

in sp ira tio n to M axwell.

F a r a d a y , having com e from a hum ble hom e and having p e rsu a d e d H um phry Davy to take him as a la b o ra to ry a s s is ta n t in the Royal Institution, had

succeeded Davy as D ire c to r of E x p e rim e n ts , and was com ing to w ard s the end of his fam ous e x p e rim e n ta l r e s e a r c h e s . One of his duties was to a r r a n g e each F rid a y evening during the w in ter a public D isc o u rse to be d eliv e re d e ith e r by h im se lf o r by som e o th e r em inent m an of sc ie n c e . It w as, and still is ,

tra d itio n a l in th e se D is c o u rs e s for the l e c t u r e r to a p p e a r in full evening d r e s s , to p e rfo rm as m any s p e c ta c u la r and inform ative d e m o n stra tio n s as p o ssib le , and to take exactly one h o u r. On 10th A p ril 1846 the D isc o u rse was to have been given by Sir C h a rle s W heatstone (known to p h y sic ists for the B ridge - which he did not invent - and not for the mouth h a rm o n ic a which, a cco rd in g to the Oxford

Com panion to M usic - he did. He also invented what is p e r v e r s e ly known to c ry p to g ra p h e rs as the P la y fa ir cypher) but W heatstone, who was a nervous l e c t u r e r , had taken fright at his com ing o rd e a l. In the m inutes b efo re the le c tu re , th e r e fo r e , instead of com posing

h im se lf he escaped fro m the building, and F a ra d a y was thus forced to satisfy the audience as b e st he could.

It happened that W heatstone had been due to talk about his e le c tro -m a g n e tic ch ro n o sco p e, by which he had

shown that the speed of e le c tric ity along w ire s

a p p eared to be v e ry high indeed, at le a s t as g re a t as the velocity of light through sp a c e . F a r a d a y , who had b rie fe d h im se lf on W h eatsto n e's d e m o n s tra tio n s , was th e re fo re able to s u m m a riz e what W heatstone would have said, and he then went on to give his own

speculations about the possib ility that since light and e le c tric ity ap p e a re d to tra v e l at c o m p a ra b le sp e e d s, it was plausible that light was som e kind of wave propagation along his postulated lines of fo rc e .

F a ra d a y (1846) said '1 do not think that I should have allowed th ese notions to esc a p e from m e, had I not been led u n a w a re s, and without p rev io u s

c o n sid e ra tio n , by the c irc u m s ta n c e s of the evening on which I had to a p p e a r suddenly and occupy the place of a n o th e r'. But the tr a in of thought thus s ta r te d by F a ra d a y was picked up by M axwell, in whose mind it m u st have s im m e r e d through the changes that w ere sh o rtly to o c c u r in his life. M axwell c e rta in ly

believed that his mind op erated in this way fo r, as he w rote to a friend (M axwell, 1857a) T believe that th e re is a d e p a rtm e n t of the mind w here things a r e ferm ented and decocted, so that when they a r e run off they com e c l e a r ' .

The f ir s t of the changes in M axw ell's

c ir c u m s ta n c e s was a m ove from C am b rid g e to A berdeen, w here he was appointed to the C h a ir of

N atural Philosophy in M a risc h a l College in 1856 at the age of 24. The a ttra c tio n of this Scottish C h a ir was that it would b rin g him n e a r e r to his fa th e r, with whom he had a v e ry w a rm re la tio n sh ip . U nfortunately, his

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«4M

James Clerk Maxwell as a young man , holding a spinning-top

From a photograph in the possession of the Master and Fellows of Trinity College, Cambridge.

J a m e s C le rk M axwell as a young m an, holding one of

his c o lo u r to p s.

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fa th e r died a few weeks a fte r M axw ell's election, and so the m a jo r a ttra c tio n was lo st. Maxwell

conscientiously set h im se lf to teach his stu d en ts, who w ere at a m uch m o re e le m e n ta ry level than that to which he had been accu sto m ed in C a m b rid g e . F o r

som e tim e , he found the A berdonians u n re sp o n siv e . Indeed, a fte r a few m onths he was w riting (1857b) to a friend 'No jokes of any kind a r e understood h e r e . I have not m ade one for two m onths, and if I feel one com ing I shall bite my tongue'.

His f ir s t p a p e r a fte r com ing to A berdeen was on a d ynam ical top, developed fro m a s im p le r top on which he used to spin coloured s e c to rs for his e x p e rim e n ts on co lo u r vision. M axwell took one m odel of the top with him when he paid a v isit to C am bridge to take his M. A. in 1857; and he am u se d his C am bridge friends with it in his room one evening a fte r d in n er. It had c o n sid e ra b le in e r tia , and was still spinning when they left. The following m orning Maxwell happened to look out of his window and see that two of his guests w e re re tu rn in g . He p rom ptly set the top spinning again and went back to bed, leaving his astonished frie n d s to w onder at the exam ple of n e a r -p e r p e tu a l m otion.

M axw ell's f ir s t m a jo r investigation at A berdeen was to explain the m otions of S a tu rn 's Rings, and he went on to in vestigate the th r e e - c o lo u r th eo ry of

vision. In som e of th e se investigations of visions he was joined by K atherine D ew ar, the daughter of the P rin c ip a l of M a ris c h a l C ollege, and they becam e

engaged to be m a r r i e d e a rly in 1858. In the following y e a r , the m eeting of the B ritis h A sso ciatio n was held

in A b erd een , and it was at that m eeting that Maxwell announced his c e le b ra te d law governing the

d istrib u tio n of m o le c u la r v elo cities in a gas, and also m ade the b rillia n t p re d ic tio n that the v isc o sity of a gas should be independent of p r e s s u r e . Maxwell h im se lf l a t e r verified this p red ictio n by e x p e rim e n t, and it so delighted Rayleigh that the la t t e r said of it (1890) that physics contained 'no m o re beautiful or telling d isc o v e ry than that gaseous v isc o sity is the sarm at all d e n s itie s '.

We have v e ry few r e lic s of M axw ell's te n u re of the C h a ir at A b erd een , but th e re is one that will in te re s t all radio e n g in e e rs (Jo n es, 1973). It is a c e rtific a te signed by M axwell, re c o rd in g the e x e m p la ry conduct of one of his stu d en ts, G eorge Reith, in the y e a r 1859.

G eorge Reith l a t e r b e c a m e M o d e ra to r of the C hurch of

Scotland, and the fa th e r of John Reith, the f ir s t Managing D ire c to r of the B ritis h B ro a d c a stin g

C o rp o ra tio n . John Reith who, like his fa th e r, was an intensely relig io u s m an saw it as his destiny to put to w ork for the public good the rad io waves whose

existence had been p re d ic te d by his f a th e r 's te a c h e r . So m uch so, that during the whole of his te n u re of office at the BBC, John Reith kept this c e rtific a te fra m e d on the wall of his office, as a constant

in sp ira tio n . As Reith has re c o rd e d (1949), with his rep u tatio n for piety it was the belief am ong his junior staff that this was a c e rtific a te that he h im se lf had won for re g u la r attendance at Sunday School.

1859 w as, unhappily, the la st full y e a r that Maxwell was to see at A berdeen. Up to that tim e A berdeen had had two independent u n iv e rs itie s , Kings and M a ris c h a l, and in 1860 they w ere fused into the p re s e n t U niversity of A berdeen. A fter the fusion the U niversity would th e re fo re have had two p r o f e s s o r s in e v e ry su b ject, and so in each subject it decided to r e t i r e one of the two p r o f e s s o r s . The g e n e ra l rule was that the se n io r p r o f e s s o r was to be re tire d ; and although at f ir s t sight this would ap p e a r to conflict with the policy of 'f ir s t in, la s t out', it has to be r e m e m b e re d that the re tir in g

p r o f e s s o r was to be given a pension, and that since he was likely to be o ld e r, the U niversity would have to provide a pension for a s h o r te r tim e . C uriously, an exception was m ade in n a tu ra l philosophy, w here the ju n io r p r o f e s s o r was r e tir e d , which m eant that

Maxwell had to go; and A berdeen lo st e a sily the m ost distinguished m an it e v e r had. The em inent h isto ria n of sc ie n c e , Sir Edmund W h ittak er, told m e that he

understood that this was at le a s t p a rtly en g in eered by M axw ell's wife who, as daughter of the P rin c ip a l, had le s s than the usual r e s p e c t for p r o f e s s o r s . She m uch

p r e f e r r e d the p ro sp e c t of being the wife of a Scottish la ird , which was M axw ell's right by b irth . She

th e re fo re hoped that he would r e t i r e , at the age of 29, to his country e sta te in so u th -w e st Scotland. M axwell, how ever, was evidently anxious to go on p ro fe s sin g

n a tu ra l philosophy, and he succeeded to th e

C h air in K ing's C ollege, London. It n e v e rth e le ss s e e m s that M rs . Maxwell u ltim ately had h e r way, for he r e tir e d fro m K ing's College to live on his e sta te in

1865.

In the intervening y e a r s , he succeeded in verifying ex p e rim e n ta lly his p red ictio n about the independence of the v isc o sity of a gas with p r e s s u r e , thus providing the

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M ax w ell's d y n am ical top, developed fro m a s im p le r top on which he used to spin coloured s e c to r s for his

e x p e rim e n ts on co lo u r vision.

I hr Zoetrope or vvhrrl of lift*, forerunner of the cinematograph.

I hr 'parr cartoon strips shown were drawn by Maxwell himself.

Z o e tro p e , with c a rto o n s tr ip s draw n by M axw ell.

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m o st convincing co n firm atio n of the validity of the kinetic th e o ry of g a s e s . A lso, based on his

r e s e a r c h e s on colour vision at A berdeen and on ideas that he had p rev io u sly developed at C a m b rid g e , he took the f irs t colour photograph, which he showed at the Royal Institution in 1861; this was the b irth of colour photography, with all the p le a s u re that it has since given throughout the w orld.

1861 was also the y e a r of M axw ell's p a p e r to the P hilosophical M agazine 'On P h y sic a l L ines of F o r c e '.

In this p a p e r he trie d to m ake a m en tal m odel of the p r o c e s s e s that m ight be going on in e le c tro m a g n e tic induction. This m odel co n sisted of a honeycom b of v o rtic e s in the m edium all ro ta tin g in the sa m e

d ire c tio n s , the gaps betw een th em , c o rre sp o n d in g to the wax in a tru e honeycom b, being filled by p a r tic le s of e le c tric ity all ro tatin g in a s e n se c o n tra ry to that of the v o rtic e s . This m odel, along with the concept of a m edium in a sta te of e la s tic ten sio n , led him in 1862 to the conclusion that even a d ie le c tric would

e x p erien ce the phenom ena a s so c ia te d with an e le c tric c u r re n t while the tension was being built up. Since this is probably the f ir s t m ention of the fam ous

d isp la c e m e n t c u r r e n t, let me read you what he said (M axwell, 1861):

'In a d ie le c tric under induction, we m ay conceive that the e le c tric ity in each m olecule is so displaced that one side is re n d e re d positively, and the o th e r

negatively e le c tr ic a l, but that the e le c tric ity re m a in s e n tire ly connected with the m o lecu le, and does not p a ss fro m one m olecule to a n o th er.

The fact of this action on the whole d ie le c tric m a s s is to produce a g e n e ra l d isp la c e m e n t of the

e le c tric ity in a c e rta in d ire c tio n . This

d isp la c e m e n t does not am ount to a c u r r e n t, because when it has attained a c e rta in value it r e m a in s

constant, but it is the co m m e n c e m e n t of a c u r r e n t, and its v a ria tio n s constitute c u r r e n ts in the positive o r negative d ire c tio n , acco rd in g as the

d isp la c e m e n t is in c re a sin g o r d im in ish in g '.

On the next page, he goes on:

'In Ihe following investigation I have co n sid e red the re la tio n betw een the d isp la c e m e n t and the force

producing i t ...I have deduced fro m this r e s u lt the re la tio n betw een the s ta tic a l and dynam ical m e a s u r e s of e le c tric ity , and have shown, by a c o m p a riso n of the e le c tr o ­

m agnetic e x p e rim e n ts of MM. K ohlrausch and W eber

with the velocity of light as found by M. F iz e a u , that the e la s tic ity of the m agnetic m edium in a ir is the

sa m e as that of the lu m in ifero u s m ed iu m , if these two co ex isten t, co ex ten siv e, and equally e la stic

m edia a re not r a t h e r one m e d iu m ...

The velocity of t r a n s v e r s e undulations in our

hypothetical m edium , calculated fro m the e l e c t r o ­ m agnetic e x p e rim e n ts of M M .K ohlrausch and W eber, a g re e so exactly with the velocity of light calculated fro m the optical e x p e rim e n ts of M. F iz e a u , that we can s c a r c e ly avoid the in fe ren ce that light

c o n s is ts in the t r a n s v e r s e undulations of the sa m e m edium which is the cause of e le c tric and m agnetic p h e n o m e n a '.

So, h e re in these p a p e rs of 1861 and 1862, we have the f ir s t conception of the d isp la c e m e n t c u r r e n t, and the f ir s t c le a r s ta te m e n t that light is an e l e c t r o ­

m agnetic phenom enon.

One is tem pted to think that M axwell had a m agnificent clue from the m e a s u re m e n t by W eber and K ohlrausch (1856) of the ra tio of the e le c tric a l units, which was known to have the d im en sio n s of a velocity, and whose n u m e ric a l value cam e out so close to that of light. One re a s o n for W e b e r's re s u lt not having d ire c tly influenced Maxwell was that - as the la t t e r a fte rw a rd s r e m a rk e d - W eber had used units which did not produce the fa m ilia r n u m e ric a l value of

3 x 1 0 ^ . As he explained in a l e t t e r of 10th

D ec e m b e r 1861 to Kelvin ( L a r m o r , 1936) '1 m ade out the equations in the country before I had any suspicion of the n e a rn e s s betw een the two values of the velocity of propagation of m agnetic effects and that of lig h t'.

This co m m en t, incidentally, shows us that the b i r t h ­ place of the e le c tro m a g n e tic th e o ry was M axw ell's country house which now, a la s , stands in ru in s.

The p a p e rs of 1861 and 1862, suggestive though they w e re , did not sa tisfy M axwell h im se lf, dependent as they w ere on an im aginative but questionable m odel of e le c tro m a g n e tic induction. He th e re fo re re tu rn e d to the p ro b le m and two y e a r s l a t e r produced, in the

Royal Society T ra n s a c tio n s , a p a p e r on 'A D ynam ical T h eo ry of the E le c tro m a g n e tic F ie ld ', in which his thinking ascen d s a stage in fo rm a lity . In the

p re a m b le to this p a p e r (M axwell, 1864) it b e c o m e s c le a r that M axwell was extrap o latin g the p r o p e rtie s of a vacuum fro m those which he had com e to a ttrib u te to a tangible d ie le c tric , for he sa y s that when we have em ptied a space of all g r o s s m a tte r 'T h e r e is alw ays,

7

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M a ris c h a l College A b e rd e e n , w here M axwell was

P r o f e s s o r fro m 1856 to I860. His le c tu re ro o m was on the f ir s t floor behind the to w e r on the le ft, and it was pro b ab ly h e r e th a t he announced his d is trib u tio n law to the 1859 m e e tin g to the B r itis h A sso c ia tio n .

The ru in s of M a x w e ll's country h ouse, G le n la ir,

w h ere he f ir s t w orked out the velocity of e le c tro m a g n e tic

w a v e s .

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how ever, enough of m a tte r left to re c e iv e and tr a n s m it the undulations of light and h e a t’. And since heat can be tra n s m itte d through a vacuum by undulations, the en erg y in the m ean tim e

’m u st have been half in the fo rm of m otion of the m edium and half in the fo rm of e la s tic re s ilie n c e . F r o m th ese co n sid e ra tio n s P r o f e s s o r W. T hom son has arg u e d , that the m edium m u st have a density

capable of c o m p a riso n with that of g ro s s m a tte r , and has even assig n ed an in fe rio r lim it to that density.

We m ay th e re fo re r e c e iv e , as a datum d erived from a b ra n c h of scie n ce independent of that with which we have to d eal, the ex isten ce of a prevading m edium of sm a ll but r e a l density, capable of being se t in

m otion, and of tra n s m ittin g m otion fro m one p a rt to a n o th e r with g re a t, but not infinite, v e lo c ity ...

A m edium having such a constitution m ay be capable of o th e r kinds of m otion and d isp la c e m e n t than those which produce the phenom ena of light and heat, and

som e of th e se m ay be of such a kind that they m ay be evidenced to our s e n se s by the phenom ena they

p ro d u c e 1.

This is effectively the point at which Maxwell m a k e s the p re d ic tio n of e le c tro m a g n e tic waves with c h a r a c t e r i s t ic s o th e r than those of light and heat, and which m ay th e re fo re be said to be the f ir s t pointer to the possible ex isten ce of radio w aves. So, it is

p e rh a p s 1864 r a t h e r than 1873 which ought to be re g a rd e d as the date of b irth of the concept of radio w aves; but b efo re we look fo rw ard to 1873, let us tr a c e M axw ell's steps in the intervening y e a r s .

As we have m entioned, he left K ing's College in 1865, so as to live p e rm a n e n tly at his country house in K irk c u d b rig h ts h ire , G le n la ir. But his rep u tatio n was now so g re a t that his fellow p h y sic ists m ade

re p e a te d dem ands on his e ffo rts. They p e rsu a d e d him to becom e P r e s id e n t of the M ath e m atics and P h y s ic s Section of the B r itis h A sso ciatio n in 1870, and his P r e s id e n tia l A d d re ss (M axwell, 1870) was a su p e rb exam ple of scientific exposition. It included the fam ous p a ssa g e :

'T h e r e a r e m en who, when any re la tio n o r law,

how ever com plex, is put before them in a sym bolical fo rm , can g ra s p its full m eaning as a re la tio n

am ong a b s tr a c t quantities. Such m en s o m e tim e s t r e a t with indifference the f u rth e r s ta te m e n t that quantities actually ex ist in n atu re which fulfil this

re la tio n . The m en tal im age of the c o n c re te re a lity s e e m s r a t h e r to d istu rb than to a s s i s t th e ir

co n tem p latio n s. But the g re a t m a jo rity of mankind a r e u tte rly unable, without long tra in in g , to re ta in in th e ir m inds the unem bodied sym bols of the pure

m a th e m a tic ia n , so that, if sc ie n c e is e v e r to becom e p o p u lar, and yet re m a in sc ie n tific , it m u st be by a profound study and a copious application of those p rin c ip le s of the m a th e m a tic a l c la ssific a tio n of

quantities which, as we have se e n , lie at the root of e v e ry tru ly scie n tific illu stra tio n .

T h e re a r e , as I have sa id , som e m inds which can go on contem plating with sa tisfa c tio n pure quantities p re se n te d to the eye by sy m b o ls, and to the mind in a fo rm which none but m a th e m a tic ia n s can conceive.

T h e re a re o th e rs who feel m o re enjoym ent in following g e o m e tric a l f o rm s , which they draw on p a p e r, o r build up in the em pty space b efo re them . O th e rs , again, a re not content u n less they can

p ro je c t th e ir whole physical e n e rg ie s into the scene which they conjure up. They l e a r n at what a ra te the planets ru sh through sp ace, and they e x p erien ce

a delightful feeling of e x h ila ra tio n . They calculate the fo rc e s with which the heavenly bodies pull at one a n o th e r, and they feel th e ir own m u s c le s s tra in in g with the effort. To such m en m o m en tu m , en erg y , m a s s a r e not m e re a b s tr a c t e x p re ss io n s of the

r e s u lts of scientific inquiry. They a r e w ords of pow er, which s t i r th e ir souls like the m e m o rie s of childhood.

F o r the sake of p e rso n s of th ese different types, scientific tru th should be p re se n te d in different

fo rm s , and should be re g a rd e d as equally sc ie n tific , w hether it a p p e a rs in the ro b u st fo rm and the vivid colouring of a physical illu stra tio n , o r in the tenuity and p alen ess of a sy m b o lical e x p r e s s io n '.

At this tim e Maxwell was in the c o u rse of

tra n s fo rm in g e le c tro m a g n e tic th eo ry fro m 'the ro b u st form and the vivid colouring of a physical illu stra tio n ' of the f ir s t sta g e s of his thought into the sym bolical e x p re ss io n that has e v e r since been known as the Maxwell equations, and which w ere to a p p e a r in the T r e a tis e that he was then p re p a rin g . But before the T r e a tis e was com pleted, an im p o rta n t change had o c c u rre d in M axw ell's life. If it was im p o rta n t to M axwell h im se lf, it was vital to the developm ent of C am bridge p h y sic s, for what happened was that Maxwell was p r e s s e d to be the f ir s t C avendish

9

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Ç @ fa 1+*~ £ « . J L $m4A. -»*» c n -h .

C e rtific a te g ra n te d by M axwell to M r. G eorge R eith, l a t e r M o d e ra to r of the C hurch of Scotland and fa th e r of L o rd R eith, the f i r s t D ir e c to r G e n e ra l of the

B r itis h B ro a d c a s tin g C o rp o ra tio n .

M a x w e ll's f ir s t m o d el of the e le c tro m a g n e tic field, showing the m e d iu m c o n sistin g of v o r tic e s (hexagons) all ro ta tin g in the s a m e d ire c tio n , and s e p a ra te d by p a r t ic l e s of e le c tr ic ity ro ta tin g in the opposite

d ire c tio n (from P h il. Mag. 1861).

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P r o f e s s o r of P h y sic s and Head of the new C avendish L a b o ra to ry in C a m b rid g e . As we all know, he set both the C h a ir and the L a b o ra to ry on a c o u rse which has probably n e v e r been equalled in any o th er

u n iv e rsity o r in any o th e r su b je c t, for he was

su cceeded in tu rn by Rayleigh, J . J. T hom son, and R u th erfo rd .

One of his f ir s t duties was to give an inaugural le c tu re and this occasioned one of his c h a r a c te r is tic jo k es. F o r som e r e a s o n , p e rh a p s en g in eered by Maxwell h im se lf, the le c tu re was inadequately

a d v e rtiz e d , and he th e re fo re gave it to an audience co n sistin g of a handful of stu d e n ts. A few days la te r it was announced that Maxwell would begin his

le c tu r e s , and by way of com plim ent to the new

p r o f e s s o r the s e n io r m e m b e rs of the u n iv e rsity cam e in fo rc e . M axw ell’s delighted students th e re fo re saw the delicious p ro s p e c t of such distinguished m en as A dam s, C ayley, and Stokes sitting in the front row, with Maxwell g ra v e ly expounding to them , though with a p e rc e p tib le twinkle in his eye, the re la tio n between the fa h re n h e it and c e n tig ra d e s c a le s . The inaugural le c tu re (Maxwell, 1871) itse lf was a m agnificent

exposition of the place of e x p e rim e n ta l physics in a

u n iv e rsity , and of the m ethods of teaching and research.

'When we shall be able to em ploy in scientific education, not only the tra in e d attention of the student, and his fa m ilia rity with sy m b o ls, but the keen n ess of his eye, the quickness of his e a r , the d elicacy of his touch and the a d ro itn e s s of his

fin g e rs , we shall not only extend our influence o v er a c la s s of m en who a re not fond of cold a b s tra c tio n s , but by opening at once all the gatew ays of knowledge, we shall e n s u re the a sso c ia tio n of the d o c trin e s of scien ce with those e le m e n ta ry sen sa tio n s which fo rm the o b sc u re background of all o u r conscious thoughts, and which lend a vividness and re lie f to ideas which, when p re se n te d as m e r e a b s tr a c t t e r m s , a re apt to fade e n tire ly fro m the m e m o ry '.

Although he is, ju stly m o re fam ous as a th e o r is t, M axwell was also a v e ry good e x p e r im e n te r , and he delighted in using both his eyes and his hands. Sir A rth u r S c h u ste r (1911) re c o rd e d how M axwell had one day succeeded in the difficult ta sk of cutting and

grinding a plate out of a doubly re fra c tin g c r y s ta l to show conical r e fra c tio n . Delighted with his

ac h ie v e m e n t, M axwell m et T odhunter, one of the m o st fam ous of m a th e m a tic a l tu to rs at C am b rid g e.

'Would you like to see conical re fra c tio n ? ' asked M axwell, only to re c e iv e from T odhunter the

astonishing rep ly 'No. I have been teaching it all my life and I do not want to have all m y ideas upset by seeing it'. It was against such a background that M axwell succeeded in designing the Cavendish

L a b o ra to ry for e x p e rim e n ta l physics and in setting it on its s p e c ta c u la r c o u rs e .

We now com e to 1873, the y e a r in which the

T r e a tis e was published. It is, of c o u rs e , one of the g re a t books of p h y sic s, and indeed of all s c ie n c e . As we have seen , its m o st r e m a rk a b le conclusions had a lre a d y been given in M axw ell's p a p e rs of 1861 to

1864, but now the th e o ry behind them was m uch m o re fo rm a liz e d . The tentative scaffolding of the e a r l i e r p a p e rs w as, as it w e re , strip p e d away, and the edifice of e le c tro m a g n e tic th e o ry was now c le a rly re v e a le d . Of the new r e s u lts published in the T r e a t i s e , the m ost im p o rtan t is M axw ell's calculation of the p r e s s u r e in a b eam of e le c tro m a g n e tic ra d ia tio n . It o c c u rs in p a ra g ra p h 792, which concludes:

'H ence in a m edium in which waves a r e propagated th e re is a p r e s s u r e in the d ire c tio n n o rm a l to the w aves, and n u m e ric a lly equal to the en erg y in unit of v o lu m e '.

E v e r since Newton, e x p e r im e n te r s had trie d to detect the p r e s s u r e e x e rte d by a b eam of light, but without conclusive r e s u lts . M axw ell's calculation in the T r e a tis e at la s t showed them the o r d e r of

m agnitude of the p r e s s u r e that was to be expected, and that it was so sm a ll that it would r e q u ire c o n sid e ra b le im p ro v em en t in e x p e rim e n ta l techniques before it

could be o b se rv e d . Indeed, it was not until 27 y e a r s l a t e r that Lebedew in R u ssia and Nichols and Hull in A m e ric a w ere able to o b se rv e rad iatio n p r e s s u r e with

c e rta in ty , and show by m e a s u re m e n t that the

m agnitude was that expected by M axwell. Radiation p r e s s u r e h a s, of c o u rs e , since becom e recognized as an im p o rta n t phenom enon, for exam ple as an e s s e n tia l com ponent in the s tr u c tu r e of s t a r s . It was also of g re a t significance to E in ste in , who by m ean s of a thought e x p e rim e n t involving the p a ssa g e of radiation fro m one side to the o th e r of a closed box was able to develop a sim ple a rg u m e n t with which to convince his fellow s c ie n tis ts of the validity of his fam ous equation

„ 2

E = m e .

E in ste in , incidentally, s ta rte d his fam ous 1905

p a p e r on re la tiv ity by pointing out how he had been

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J a m e s C le rk M axw ell in l a t e r life.

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s tru c k by the a s y m m e tr y b ased on the Maxwell

equations of the phenom enon of inducing a c u r re n t in a c irc u it with a m agnet, depending on w hether one r e g a r d s the m agnet as m oving and the c irc u it fixed, o r vice v e r s a .

M axwell did re la tiv e ly little o rig in a l work a fte r the p u b lic a tio n of the T r e a tis e , b e c a u se his e n e rg ie s w ere la rg e ly a b so rb e d in e sta b lish in g the Cavendish

L a b o ra to ry and in editing the unpublished p a p e rs of H enry C avendish, who was a m e m b e r of the fam ily of the Duke of D ev o n sh ire, whose g e n e ro sity had m ade the c o n stru c tio n of the L a b o ra to ry p o ssib le .

When M axwell died in 1879 his e le c tro m a g n e tic th eo ry had by no m e a n s gained g e n e ra l acce p ta n c e , as som e of his o b itu ary notices acknowledge. But in that y e a r the P r u s s i a n A cadem y of Science offered a p riz e for the e x p e rim e n ta l confirm atio n of the re la tio n betw een e le c tro m a g n e tic action and the p o la riz a tio n of a d ie le c tr ic that was the c e n tra l point of M axwell's th e o ry . The p riz e conditions w ere re a d by the young H einrich H ertz who, how ever, did not e n te r for the p riz e b e c a u se he saw no way of m eeting the challenge.

But a y e a r a f te r he had been m ade p r o f e s s o r at K a rls ru h e in 1885 at the age of 28, he happened to notice that a s p a rk jum ped a c r o s s a gap in a c irc u it of copper w ire when a n earby induction copper w ire was being used. This gave him the clue that it might be p o ssib le to jum p d ire c tly to the e x p e rim e n ta l

con firm atio n of the m ain consequence of M axw ell's th e o ry , which was that th e re should exist e le c tr o ­

m agnetic waves of quite different o r d e r s of wavelength fro m those of light itse lf. S u rp risin g ly quickly, he g ra sp e d the idea of taking a s tra ig h t piece of w ire, cutting it in the m iddle, and connecting the two cut

ends to a s p a rk gap a c r o s s an induction coil, and using this as a r a d ia to r . He trie d a s im ila r ly cut w ire with its cut ends connected to a m uch s m a lle r s p a rk gap as a d e te c to r, and he succeeded in getting s p a rk s a c r o s s this gap when the induction coil was activating the

tra n s m ittin g antenna. Within a few m onths he

b rillia n tly e sta b lish e d the e x isten ce of e le c tro m a g n e tic waves of radio w avelengths, and in showing that th e ir p r o p e rtie s w ere what M axwell would have expected.

He a lso , in c id e n ta lly , d isc o v e re d the p h o to electric effect in the sa m e investigation, fro m the influence of incident light on the behaviour of the secondary s p a rk gap. The m ain consequences of M axw ell's theory

w e re thus b rillia n tly e sta b lish e d as one of the m o st

im aginative ste p s e v e r taken by m an.

M axw ell's im agination had been v e ry soundly based As he said in the p re fa c e to the T r e a tis e :

'B efo re I began the study of e le c tric ity I re so lv e d to re a d no m a th e m a tic s on the subject till I had f ir s t re a d through F a r a d a y 's e x p e rim e n ta l r e s e a r c h e s on e le c tr ic ity ...It is of g re a t

advantage to the student of any subject to re a d the o rig in al m e m o irs on that su b ject, for scien ce is

alw ays m o st com pletely a s s im ila te d when it is in the nascent s ta te , and in the c a se of F a r a d a y 's

r e s e a r c h e s this is c o m p a ra tiv e ly easy,* as they a r e published in a s e p a ra te fo rm , and m ay be read

consecutively. If by anything I have h e re w ritte n I m ay a s s i s t any student in u n d erstanding F a r a d a y 's m odes of thought and e x p re ss io n , I shall r e g a rd it as the acco m p lish m en t of one of my p rin c ip a l a im s - to com m unicate to o th e rs the sa m e delight which I have found m y self in read in g F a r a d a y 's r e s e a r c h e s '.

And in his inaugural le c tu re at C a m b rid g e , Maxwell said :

'The m en whose nam es a r e found in the h isto ry of science a r e not m e r e hypothetical co n stitu en ts of a crow d, to be re a so n e d upon only in m a s s e s .. We recognize them as m en like o u r s e lv e s , and th e ir actions and thoughts, being m o re fre e fro m the

influence of p a ssio n , and re c o rd e d m o re a c c u ra te ly than those of o th e r m en, a re all the b e tte r m a te r ia ls for the study of the c a lm e r p a rts of hum an n a tu r e '.

Of the type of m an that Maxwell had in m ind, th e re is no b e tte r exam ple than him self; and for this re a s o n m en of science m ight offer him to the world as an

exam ple of all that they m ight hope to be. He had no e n e m ie s, and he in sp ire d no je a lo u s ie s . Shining

through his v a st intellect was his intense hum anity.

We do indeed reco g n ize in him a m an, no m e r e hypothetical constituent of a crow d, who not only

re a c h e d the pinnacle of c la s s ic a l ph y sics but who also in his everyday life set an exam ple of s e re n ity and m o d esty , and twinkling hum our and u n s e lfish n e ss .

It has been a p rivilege for m e to com e and join you in c o m m e m o ra tin g the work of a g re a t p h y sic ist who, like o th e rs in the sa m e tra d itio n - G alileo, Newton, Huyghens, Young, F r e s n e l , F a ra d a y , L o re n tz and E in stein - belongs not ju st to one country but to the whole w orld. We in W e ste rn E urope m ay r e m e m b e r with pride and gratitu d e that it was in our c u ltu re , to which th e se m en contributed so m uch, that they w ere

13

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th e m s e lv e s n o urished. May o u r c lo s e r u n d erstan d in g of re c e n t y e a r s add stre n g th to the h e rita g e that they have left us.

R E FE R E N C E S

E in ste in , A. (1931). Maxwell C o m m e m o ra tiv e Volum e. C am bridge U niversity P r e s s .

F a r a d a y , M. (1846). E x p e rim e n ta l R e s e a rc h e s in E le c tr ic ity , III, pp. 447-452. Q u a ritc h , London,

1855.

Jo n e s, R .V . (1973). Notes and R ec o rd s of the Royal Society of London, Vol. 28, pp. 57-81.

L a r m o r , J . (1936). P r o c . C am b. P h il. Soc. , Vol. 32, pp. 695-750.

M axw ell, J . C . (1855). The Scientific P a p e r s of

J a m e s C le rk M axwell, Vol. 1, p. 155. Edited by Niven, W .D . , C am bridge U niversity P r e s s , 1890.

R eprinted by D over P u b licatio n s. A fte rw a rd s r e f e r r e d to as SPJC M .

M axwell, J . C . (1857a). C am pbell, L. and

G a rn e tt, W. The Life of J a m e s C le rk M axwell, p .2 6 8 . M acm illan, London, 1882.

M axw ell, J . C . (1857b). C am pbell and G a rn e tt, p . 297.

M axw ell, J . C . (1861). SPJCM I, p p . 451-513. The quotation com es fro m p .4 9 1 .

M axwell, J . C . (1864). SPJCM I, p p . 526-597.

M axw ell, J . C . (1870). SPJCM II, p p . 215-229.

M axw ell, J . C . (1871). SPJCM II, pp. 241-255.

M axw ell, J . C . (187 3). A T r e a tis e on E le c tric ity and M ag n etism . C am bridge U niversity P r e s s .

R ayleigh, L ord (1890). N atu re, Vol. 28, pp. 26-27.

R eith, J . C . W . (1949). ’Into the W in d '. H odder and Stoughton, London.

S c h u ste r, A. (1911). The P r o g r e s s of P h y s ic s , pp. 25-26. C am bridge U niversity P r e s s .

T hom son, W. (1847). C am b rid g e and Dublin M athe m atical J o u rn a l, Vol. 2, pp. 230-235.

W eb er, W . E . and K o h lrau sch , R. (1856). Pogg. Ana Vol. 89, pp. 10- 25.

Voordracht gehouden op 13 december 1973 in de T.H. Delft Afdeling der Elektrotechniek, tijdens werkvergadering nr. 234.

(17)

RECENTE OPVATTINGEN OVER DE VERGELIJKEN VAN MAXWELL.

Prof. Dr. Ir. J.P. Schouten, Em., Technische Hogeschool Delft.

Vijftig jaar na het verschijnen van het boek, getiteld

"A Treatise on Electricity and Magnetism" by James Clerk Maxwell in 1873 hield professor H.A. Lorentz in Cambridge "The Rede Lecture for 1923". Zijn rede droeg de titel: "Clerk MaxwellTs Electromagnetic Theory", en was gewijd aan de geweldige vooruitgang en de nieuwe in­

zichten die deze theorie met zich meebracht.

Het is uiteraard niet de bedoeling om hierbij, nu vijf­

tig jaren later, lang stil te staan daar de physicus van vandaag en de wetenschappelijk geinteresseerde electrotechnicus met wat men noemt "de theorie van Maxwell" vertrouwd is of dit dient te zijn.

Aan het eind van zijn rede vroeg Lorentz zich af of de

"vergelijkingen van Maxwell" op den duur te handhaven zouden zijn. Daarbij wordt niet gedacht aan kleine wij­

zigingen in verband met de relativiteits-theorie. Een groter en reëel gevaar zou dreigen van de zijde van de quantum-theorie.

De grandioze ontwikkeling der quantum-theorie sedert­

dien heeft wel het belang van de vergelijkingen van Maxwell aangetoond als basis voor de quantum-electro- dynamica. Nochtans is met het ontstaan van de moderne atoom-fysica de belangstelling van de natuurkundigen voor de klassieke theorie van het electro-magnetisme verflauwd, dan wel verdwenen. Aldus uitte zich Richard Courant in het voorwoord van het boek "The theorie of Electromagnetic Waves" dat door Morris Kline in 1951 werd uitgegeven. De hierin vervatte artikelen werden oorspronkelijk gepresenteerd op een symposium in 1950 in de Verenigde Staten van Amerika. Courant merkt op, dat het gehele "klassieke gebied" aan de wiskundigen werd overgelaten. In het begin werden brillante bij­

dragen geleverd door H. Poincaré, Lord Rayleigh, Arnold Sommerfeld, Herman Weyl, G.N. Watson en anderen.

Zij gaven de wiskundige behandeling van belangrijke problemen van electromagnetische golfvoortplanting. Ge­

leidelijk aan verflauwde de belangstelling voor een gebied dat steeds minder vruchtbaar werd. In de daarop volgende periode toen de natuurkundigen noch de wis­

kundigen zich meer voor het klassieke elektromagnetisme interesseerden kwamen de ingenieurs met vele nieuwe

problemen, vooral op hoogfrequent gebied. Verdiepte kennis was nodig op vele terreinen zoals de theorie van de golfpijpen en trilholten, van problemen betref­

fende diffractie, reflectie en voortplanting in niet- homogene media van electromagnetische golven en van de opwekking hiervan.

De behoeften van de industrie, gekoppeld aan militaire behoeften brachten toen vooraanstaande geleerden terug

naar dit gebied.

Het is genoegzaam bekend hoe J. Schwinger en medewerkers met geheel nieuwe methoden verreikende resultaten be­

reikten, waardoor ook wiskundigen weer in‘ het géweer kwamen. Het hierboven vermelde, door Kline uitgegeven boek weerspiegelt de situatie omstreeks 1950.

De aanloop hiertoe speelde zich af in de jaren dertig.

Spreker zat in die jaren op een studeerstoel bij de Oc- trooiraad en verslond de literatuur- en octrooi-aanvra- gen van Carson, Scheltermof en anderen op dit gebied.

Ook de voorboden van de "radar" dienden zich toen aan.

Bij al deze ontwikkelingen spelen de vergelijkingen van Maxwell een belangrijke zo niet fundamentele rol.

De vergelijkingen beschrijven de electromagnetische ver­

schijnselen bij deze toepassingen in hoofdzaak op macro­

scopische schaal. De materiële eigenschappen worden vrij­

wel uitsluitend beschreven door geleidbaarheid, diëlec- trische constante en permeabiliteit dan wel bij aniso- trope media door hiermede corresponderende tensoren.

Het is niet de bedoeling om in deze voordracht op deze ontwikkeling nader-in te gaan. Veeleer moge de be­

langstelling worden gericht op meer fundamentele ont­

wikkelingen, die er op uit waren en nog zijn om de bete­

kenis van de vergelijkingen te verdiepen en ze eventueel uit te breiden. De eerste hint van het bestaan van

kleinste electrische ladingen kwam van Faraday als re­

sultaat van zijn analyse van de verschijnselen der elec- trolyse. Faraday was echter bijzonder voorzichtig in zijn uitspraken en beschouwde de atoomtheorie van de materie als niet meer dan een prettige hypothese of

therminologie. Eerst in 1881 was men zover, dat het be­

staan van een elementaire elektrische lading als vast­

staand werd aangenomen en met de naam "electron" werd aangeduid.

Geschiedkundige beschrijving van het ontstaan van de elektronentheorie zijn te vinden in het zeer leesbare boekje van L. Rosenfeld: "Theory of Electrons", (4) dat

in 1951 verscheen en in 1965 als Dover publikatie uit­

kwam. Uiteraard wijst dit boek op het werk van onze be­

roemde landgenoot H.A. Lorentz terug.

Immers heeft Lorentz als eerste door de ontdekking van het Zeeman-effekt (1896) en daarna door Thomson’s ca-

thode-straal experimenten in 1897 een electronen-theorie ontwikkeld. Een beroemde uiteenzetting daarvan vindt men in het boek "The Theory of Electrons and its applications to the Phenomena of Light and Radiant Heat (1909)".

Tijdschrift van het Nederlands Elektronica- en Radiogenootschap deel 39 - nr. 1 1974 15

(18)

I

Hoewel door het ontstaan van de quantumtheorie en/of van de golfmechanica en de enorme ontwikkeling daarvan de belangstelling voor de vergelijkingen van Maxwell als

zodanig, sterk is afgenomen, zijn toch onderzoekers in de laatste decennia zich gaan bezig houden met het pro­

bleem, dat Lorentz als eerste zich steldej te weten: hoe worden de vergelijkingen van Maxwell voor ponderabele materie afgeleid uit vergelijkingen voor bewegingen van met massa behepte bewegende ladingen, die in geweldige

aantallen de materie vormen? Het uitgangspunt vormt daarbij het stelsel vergelijkingen van Maxwell, zoals deze in de vrije ruimte zouden gelden.

In 1967 en 1968 verschenen in Physica zeven arti­

kelen allen getiteld " The Relativistic Energy Momentum Tensor in Polarized Media" (5) van de hand van Professor S.R.de Groot en van L.G.Suttorp. .

Laatstgenoemde promoveerde in 1968 op een proef­

schrift waarbij het gaat over de covariante afleiding van de macroscopische electrodynamica uit de electronen-

theorie. (6)

Prof. de Groot schreef tevens een boek (7) waarin een afleiding wordt gegeven van de vergelijkingen van Maxwell uitgaande van de electronentheorie onder toe­

passing van statistische methoden. De opzet is om de Max­

well vergelijkingen zowel in de klassieke als in rela­

tivistische "covariante" vorm af te leiden uitgaande van de grondvergelijkingen van Lorentz voor de vrije ruimte waarin ladingen (elektronen en atoomkernen) zich bewegen.

Het schijnt wel, dat door het grote werk van beide geleerden een afsluiting is verkregen van het probleem een correcte formulering te geven van de macrocopische vergelijkingen van Maxwell in covariante vorm. Dit geldt

tevens voor de relativistische impuls-energie-tensor in gepolariseerde media.

Toepassingen op een aantal situaties, zoals bij de behandeling van plasma’s, vloeistoffen, metalen, isola­

toren, gassen en elctrolyten komen er in voor. Het is wel een indrukwekkende hoeveelheid arbeid, die hier is verricht en men krijgt de indruk, dat hiermede veel pro­

blemen zijn opgelost.

Er zijn echter ook ontwikkelingen aan de gang, die naar het mij voorkomt de electrotechnische ingenieur meer zullen aanspreken, en die op oude problemen terug­

gaan. Zo beschreef Einstein in 1905 in " Zur Elektro­

dynamik bewegter Körper" (8) tegenstrijdigheden, die de electrodynamica van Maxwell aankleven en die "den Phäno­

menen nicht anzuhaften scheinen". In het bijzonder werd de aandacht gevestigd op de relative beweging van een geleider en een (permanente) magneet. Bij de gebruike­

lijke (klassieke) opvatting dienen de twee gevallen dat één van beide lichamen in beweging is, van elkaar die­

nen onderscheiden te worden.

Is de geleider in rust en beweegt de magneet dan ontstaat in de omgeving van de magneet een elektrisch

veld, dat in de geleider een stroom opwekt.

Beweegt echter de geleider en blijft de magneet in rust dan zal, bij dezelfde relatieve beweging van beide licha­

men in de omgeving van de magneet geen electrisch veld ontstaan, doch komt in de geleider een electro-motorische kracht tot stand die tot dezelfde electrische stromen aanleiding geven als in het eerste geval. Deze overwe­

gingen stonden, zoals alom bekend, aan het begin van het ontstaan van de speciale relativiteits-theorie. Hierbij worden coördinaat-systemen beschouwd die ten opzichte van elkaar een eenparige snelheid vertonen. Daardoor kon nog de volgende puzzel ontstaan die betrekking heeft op unipolaire inductie.

Deze kan worden opgewekt door een cylindrische per­

manente magneet met cirkelvormige dwarsdoorsnede om zijn as te laten draaien. Leggen we een geleidende draad zoals

1

in de figuur is aangegeven, dan ontstaat daarin een elek­

trische stroom. Draaien we de zaak om, dat wil zeggen staat de magneet stil en laten we de draad in tegenge­

stelde richting als eerst de magneet deed draaien dan ontstaat in de draad dezelfde stroom. Beschouwingen hier­

omtrent zijn te vinden in het proefschrift van Dr. W.

van den Berg, dat in 1920 tot stand kwam. De promotor was Prof. Lorentz. (9) (blz.45 - 48) Volgens klassieke beginselen redenerend stuiten we op een tegenstrijdig­

heid. Volgens de beginselen van de electronentheorie zullen bij draaiende magneet de elektronen in het mag­

netische materiaal krachten ondervinden van het magne­

tische veld, waardoor ze bewegingen krijgen, die de oor­

zaak zijn van de stroom in B. Draait echter de draad bij stilstaande magneet dan ondervinden de electronen in de draad een kracht in het veld van de magneet en komen daardoor in beweging. In een assenstelsel dat met B mee­

draait zetelt de elektro-motorische kracht in A en in een assenstelsel dat met A verbonden is zetelt de elek­

tro-motorische kracht in B. De tegenstrijdigheid wordt

(19)

opgelost met behulp van een gravitatie-veld, dat in een van de assenstelsels wordt ingevoerd en door toe­

passing van transformatie-formules die in de algemene relativiteits-theorie optreden. De moeilijk te verwer­

ken conclusie luidt, dat de vraag naar de zetel van de elektro-motorische kracht bij het besproken verschijn­

sel van unipolaire inductie pas zin heeft, indien men daarbij aangeeft, welk coördinaten stelsel men als nor­

maal beschouwt.

Onder "normaal" wordt dan verstaan, dat het stelsel geen gravitatie-veld vertoont.

Er zijn de laatste tijd ook ontwikkelingen gaande, die wellicht minder diep grijpen dan het werk van de Groot en Suttorp,doch die voor de electrotechnicus zeer

aantrekkelijke aspecten vertonen. Het gaat de ingenieur vaak om zodanig inzicht in de verschijnselen dat met redelijke nauwkeurigheid ontwerp-berekeningen kunnen worden gemaakt. In electrische machines bewegen een sa­

menstel van delen uit magnetisch materiaal en electrisch geleidende staven, die stroom voeren. Er zijn eenvoudi­

ge situaties van bewegende materie zoals die van homo- polaire inductie, waarop we reeds wezen doch ook nog an- I dere, waarop we nog zullen ingaan en die verrassend

eenvoudig kunnen worden behandeld indien men ertoe over­

gaat principieel magnetische ladingen in te voeren, vol­

komen analoog met elektrische ladingen.

Op de rechtvaardiging hiervan komen we nog terug.

We zullen aandacht besteden aan het verschijnsel van homopolaire inductie waarover we reeds spraken.

Een ander interessant geval wordt gevormd door een verend gesloten ring waardoor een staafmagneet is ge-

stroken. Trekt men de staaf in zijn langsrichting uit de ring dan ontstaat een inductie-stoot. Beweegt men de staaf in dwarsrichting buiten de ring door de verende sluiting dan treedt geen inductie-stoot op.

Een derde voorbeeld waarbij magnetische ladingen in het geding kunnen worden gebracht is dat van een

geleidende staaf in de gleuf van het anker van een elek­

trische machine waarbij de elektrische veldsterkte kan worden berekend door te rekenen met de magnetische in­

ductie, die zou optreden als geen gleuven aanwezig wa­

ren. Men kan wel stellen, dat bewegende magnetische la­

dingen een elektrisch veld opwekken op dezelfde wijze als bewegende elektrische ladingen een magnetisch veld opwekken.

Deze bewering klinkt wel zeer ongewoon, hoofdzakelijk omdat immers vrije magnetische ladingen, in tegenstel­

ling tot vrije elektrische ladingen niet bestaan, al­

thans niet zijn aangetoond. Nochthans stellen we vast, dat het magnetische veld in gemagnetiseerde materie divergenties heeft en deze divergenties wensen wij aan te duiden met de term: magnetische ladingen.

Deze zijn dus slechts aan te treffen binnen de ma­

terie . Gaan we er van uit, dat de magnetische inductie B, het magnetische veld _H en de magnetisatie M met el­

kaar in verband staan dan geldt B = y (H + M)

o —

Daar in de theorie van Maxwell geldt div B = o moet der­

halve ook div H = - div M gelden.

Hieruit volgt uiteraard dat div H slechts binnen de materie van nul kan verschillen, daar immers M, de "mag­

netisatie" een materie vektor voorstelt.

Het in het geding brengen van magnetische ladingen, zelfs in de vorm van een monopool werd door geleerden op het terrein van de quantum-electrodynamica voorge­

steld. Te dien aanzien kan worden verwezen naar een artikel van Julian Schuringer in "Science"(1969)(10).

In dit artikel wordt naar oudere publicaties verwe-

, »

zen o.a. naar beschouwingen van Dirac in 1931.

Echter hebben ook, meer electrotechnisch geinteres- seerde geleerden en schrijvers in de vergelijkingen van Maxwell termen opgenomen waarin magnetische ladingsdicht- heden voorkomen. Ten eerste kan worden gewezen op het

werk van de drie auteurs Fans, Chu en Adler verschenen in 1966 (11). De auteurs wijzen erop (blz.175) dat drie van de vier mogelijke magnetiseringsverschijnselen: fer- romagnetisme, ferrimagnetisme en paramagnetisme vrijwel uitsluitend afhangen van de magnetische momenten van de elektronen. Er zijn twee modellen mogelijk voor de mag- neetsterkte van een elektron. Eén model is gebaseerd op circulerende elektrische stromen, het andere op magneti­

sche ladingen. Deze twee modellen kunnen niet door enige uitwendige veldmeting van elkaar worden onderscheiden omdat zij hetzelfde dipool veld produceren.

Met vele argumenten, die echt wel indruk maken, trachten de auteurs de lezer te laten inzien dat geen tegenstrijdigheden ontstaan indien men de consequenties van de invoering van magnetische ladingen in de verge­

lijkingen van Maxwell onderzoekt.

Ten aanzien van de homopolaire inductie, die we nog willen bezien in het licht van magnetische ladingen, moge nog worden gewezen op een publikatie van Geo B.

Pegram uit het jaar 1917 (12). Hierin worden proeven en metingen beschreven waarbij in een cirkel-cylindrische

spoel een geleider wordt geplaatst loodrecht op de as van de spoel. Laat men de geleider om de as van de spoel

draaien dan treedt daarin een stroom, althans een elek­

trisch veld, op.

Staat de geleider stil en laat men de spoel draaien dan treedt geen stroom of spanning in de geleider op.

Hieruit blijkt wel, dat homopolaire inductie gebonden is aan de beweging van gemagnetiseerde materie.

Uitvoerige beschouwingen in het werk van Fans e.a.

(11) ( 9 blz. 37b e.v.) leiden tot de volgende verge­

lijkingen:

curl H - £ “ o 3t "f 31 = Jr + + curl (P x v)~

curl E + y — Oo t d t O- ~ (y M) - curl (y O- —v)

div e E = o — f - div P-

17

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