J

~EAS1 - IWESIJ"; VVLU-" 11' 2. i'oiU-"13U< (j tntamat!:lnsl Nlllshaos J ~,... U A~""-M A 1:? C li 1 ~ ~ :1

fE U I i T V V STIEt=A.~ MAIQI~C)V 11'-ISTITUTI: f'{)P f'UN[)AMI:~T AL Pti.,.,SICS 1 6 1 ~ 1 A I Z I I ~ I U I S I T I ~ I I I A I

Cti Vol. 2, No. 5 January-March 1993

CONTENTS

Editorial ................................................................................... , .............. 3

When will the self-accelerating generator VENETIN COLIU become a perpetuum mobile, by S. Marinov ......................................................................................... 5

The rotating Ampere bridge, , · by S. Homann, M. Pruss, A. Wah mann, G. Vogt ............................. 25

Explanation of the effects in the closed Barlow and Faraday disks, by $. Marinov ....................................................................................... 26

A new hypothesis for the origin of Earth's magnetism, by S. Marinov ...................................................... ~ ................................ 37

Letter to the editor, ·by J.P. Wesley .................................................................................... 53

Editor's comments ......................................................................... 56

- 37 -

Ve~~che Phy~~r. 2(5)

A "!(VI HY PO THESIS FOR THE ORIGIN OF EARTH'S MAGNETISM

Stefan Marinov

Institute f or Fundarrenta l Physics

Morell enfe l dga sse 16 A-8010 Graz , Austria

I estimate the magnetic intensity generated by the convec t i on currents ap­pearing at the rotation of the negatively charged Earth about'its axis, ca l ­c ulating the e lectric charge of the Earth's surface shell by proceeding fro m the Earth 's vertical e lectri c i ntensity . As thi s magnetic intens ity i s pre t t y low(~ 3 nG ), to account for the actual magnetic intensity(; 0 .5 G) , t he only logic expl anation is that, due to the Faraday disk effect, the Earth's axis and periphery become charged with considerable amounts of opposite charges.

1. INTRODUCTION

At the present t ime we do not know whi ch is the o rigin of Earth's magnetism . Ma ­

ny hypot:--eses have been proposed , but all of them have feeble points . As there are no

experimenta l pos5ibilities to estab lish which of these hypotheses are wrong , all of

them are viable. To spare place, I shall not present here a l l these hypotheses. I

rrentioned ' them shortly in Re f . l . and the interested reader can find their more or

less detailed presentation in any b ig encyc l opedia (see the end of the paper).

Now I shall pr opose a new hypothesis for the or igin of Earth's magnet ism which

also was briefly mentioned in Ref . 1. Its essence is the following: Tak i ng i nto ac ­

count that Earth's surface is cha r ged negatively (and the ionosphere posit ive ly ) ,

one is impelled to conclude that the convection currents which haveto appear because

of its daily rotation 1~ill generate a south magnetic pole at the north geogra ph ical

pole (and a north magnetic pole at t he s outh geographical pol e ) , as the case actually

i s .

This hyrothesi s has been considered only by a few researchers, although it

seems to be the most simple one 1~hich e very child has to propose when beginning to

th ink about Ea rth's magne t ism . Why then this hypothesis has not been furthered? ­

According to rre , the guilt here, once more, is with the goddamn relativist s . Indeed,

if one should begin only to di scuss th i s hypothesis, the nonsen si ty of t he r el ativi ­

sti c concept s will imrrediatr.ly come to light, becau se , acco rding to the principle

of relativity, a ma gnet i c needle corotating with the Earth can be not deviated, as

it is a t rest with res pect to the charges fixed to the Earth . Meanwhile as every

child has seen the deviation of a magnetic needle, al l the children on t his p lanet

1·1ill begin to laugh at the idiotic theory of relativity .

l'hen, h01·1ever. the quest ion arises, why this s imple hypothsis v1as not proposed

~;e fi • rP t n~-· bi rth of the relativistic mens t er , a t the time when Gaus s and the other

- 38 -

XIX- th century investigators of Earth ' s magnetism have tried to describe mathema­tically its character. The answer is that at_that time the vertica l electric field

of the Earth (about 100 V/m) has not been measured and thus the XIX-th century scientists did not know that the Earth i s charged negatively, neither that there is an ionosphere charged positively.

2. CALCULATION OF EARTH'S MAGNETIC FIELD FROM EARTH'S VERTICAL ELECTRIC FIELD

Now I shall calculate the magnetic intensity of the Earth supposing that Earth's surface shell is charged homogeneously with such a surface density Q that the ver­tical electric intensity E is 100 V/m .

If the whole negative electric charge of the Earth is q and it is concentrated

at t he Earth's center, the electric intensity at a distance r from the center will be

. E grad¢ = - grad(q/r) = q; r2, ( 1)

where 4l is the electric potential at the distance r . If r is equal to the Earth's radius R (= 6.37x 1o6 m), we shall have

q = ER2. (2)

The same relation wi ll be val id (see, fo r example, Ref . 2, vo l. IV , p. 19) if

charge q is not concentrated at the center but is distributed homogeneously on tre Earth's surface with a surface density

Q = q/4nR2 . (3)

From (2) and (3) we obta in

Q = E/ 4n . (4)

Thi s equation written in the 51-system (see, for example, Ref. 2, vol . II, p. 34)

is

Q = £0

E. (5)

As £0

= 10-9/36n , we obta in, forE= 100 V/m,that the surface density of the electric charges will be Q = 8.84x1o-10;:; 10-9 C/m2 , and according to formu l a (3)

we obtain that the whole charge will be q = 4 . 5xl05 C.

Co nsi dering the Ear th in a Cartesian frame of reference (fig . 1) and introducing the polar -angle 6, we can consider any strip with unit breadth as a circular cur­

rent with intensity 16 = Qv6 = Q(QRsin6) = QRQ sine , (6)

1~here v6

is t he linear velocity of the strip, n (= 2n/24x60x60 7.27x10-S rad/sec)

is the angular velocity of the Earth, and Rs ine is the radius of the st rip.

I shall calculate the magnetic intensity along the ax1s of rotation, as in such

a case the integral can be easily evaluated.

- 39 - No. 5

It can be qu ickly shown (see, for example, Ref. 2, Vol. V, p. 200) that the mag­netic intensity gene rated by a circular current with radius R,at a distance z along the axis which is perpendicular to the plane of the current and crosses its center, points along the axis and has magnitude

2 B = 27TIR . (7)

c(R2 + z2)3/2

For the magnetic intensity generated by all strips with unit breadth in f ig . 1, at a distance z along the axis of rotat ion, we shall have

7T ' 2 B = f 271 I e ( Rs i ne ) R de

o c{R2sin2e + (z - Rcose)2}3/2

If taking z = R, i.e., if we wish to know the magnetic intensity at the north geographical pole,

B = 271QRQ f !Be o ( 1

we shall have

sin3e de = 27TQ RQ Jcos3(e/ 2) de

- cose)3/2 c o _ 87TQRQ _ 211RE - 3z- - 3(• (9)

The magnetic intensity at the eq ua tor can be found approximately i f we shall imagine t he Earth as a cylinder with radius R rotating with the same a·ngular velo­city n and having the same surface charge Q. In such a case , according to the for­

mula (see , for example, Ref. 2, vol. V, p. 28)

B - vxE/c, · .. (10)

we shal l have, taking into account also formula (4),

B = vE/c = nRE/c 47TQRQ/c . ( 11)

where vis the l i near veloci ty of the cylinder's surface. Formul a ( 9 ), if written in the system SI, will have the form ·

2 2 B = 3 !10

nRQ = 3 e:0

!10nRE. ( 12}

-9 -7 Putting here c0

= 10 /3671, llo = 47110 and the numeri cal values for n, Rand E, we fin d B = 3.43x1o-13 T = 3.43xlo -9 G.

I I this result i s with about 8 orders less. ----------(

~ E~rtb' s magnetic field is about 5x10-1 G, we see that

r~~ ' 3. THE HYPOTHESIS FOR THE POSITIVELY CHARGED EARTH 'S NUCLEUS Let us return to the va l ue q = 4.5x105 C for the 1vhole negative charge of the

Earth. If we should charge a condenser with capacity C = 45 F t o a potentia l U = 10 kV , the charge on any of its electrodes will be Q = CU = 4 .5x1o5 C. Such a

condenser is practical .ly realizable. Th~ if as suming that the Earth is a perfectly

conducting sphere, and we shall earth one of the condenser's e lectrodes, then by extracting electrons from the other electrode until a tensi on U = 10 kV will be

1 1

- 40 -

settled, we shall practically reduce the Earth's electric charge to zero, as the capacitance of the Earth is only (the fo nnul a is written in the S I -system)

C = 4ne: R = 7 .lx1o-4 F. (13) 0

Taking into account that the electric field of the Earth is pretty stable, it is logical to assume that its negative charge is much more bigger. How then to exp lain the small vertical electric intensity of 100 V/m?- Here I propose the hypothesis

that the Earth' s nucleus is positively charged.

If the positive charge of the Earth' s nucleus is qnucl and the negative charge of the Earth's surface is qsurf' we shall have for the vertical electric intensity (the formula is _written in the SI-system of units)

E = qsurf- qnucl = Osurf _ qnucl ( 14 ) 4ne:

0R2 e:o 4ne:

0R2 .

The nucleus can be considered as a sphere with a radius of tens of kilometers and the Earth's surface can be considered as a shel l with a thickness

of tens of kilometers. Thus Osurf is the charge in the volume of a cut pyramide with base equal to 1m2 and height equal to the thickness of the shell.

Now if accepting that the velocity of the positive charges of the nucleus is ze-ro, we shall have for the E-arth's surface density, according to formula (12), putt.ing there B = 5x1o-5 T,

Q = l__!!___= 0 .13 c;m2 surf 2 ~orlR

(15)

Now, according to formula (1~, we shall have for the positive charge at the

Earth's nucleus (which will be almost equal to the negative charge on the surface) 2 13

qnucl = 4nR (Qsurf - e:0 E) = 6.63x1Q C. (16)

All these calculations are made supposing that there is no positively charged ionosphere which rotates together with the Earth. The magnetic intensity at the north geographi cal pole generated by the rotating positively chargEd ionosphere is to be calculated in a way similar as above and will be about-·equal to the magnetic intensity (9) generated by the negative charges on the Earth's surface, but opposi ­te ly directed.

4 . THE PHYSICAL CAUSE FOR THE POSITIVE CHARGitiG OF THE EARTH'S AXIS As a matter of fact, not the Earth's nucleus is charged positively but the Earth's

axis . I introduced the hypothesis for the charged nucleus in order to make mo re

simple calculations . The ohysical explanation for the pos itive charging of the Earth's axis (and for

the negative charging of the Earth's surface) can again be proposed by eve ry chi.l d. Nevertheless I found this hypothesis in no book or paper on Earth's magnetis~ read by me , noting that, as a matter of fact, this is not a hypothesis but the mest logi ­

ca 1 conclusion .

- 41 - No. 5

it >111..' ,·r; r.<:unq lilt .. th has a certain :!_~itial magnetization, it will present nothing

~1st:! but a cer.eneted Faraday disk (as a matter of fact, a cemented Faraday sphere) .

Thus if the initial magnetization has the same orientation as the actua l Earth 's

magnet izati on , along the radii of the Earth's parallels an electric field will appear

which wi 11 push the positive cha r ges towards the axis a nd the negative charges to­

wilr·ds the pa ra l le ls . Indeed, as the actual interna l Earth ' s magnetic field points

from t he north geograph ical pole to the south geographical pol e (see the figure on

p . 50) dnd the Earth rotates from west to east, according to the ri ght -hand rule,

the Earth 's axis must become charged positive ly whil e the Earth's equator and pa ral­

le ls must become charged negatively.

lo find the t ens ion which will appear between the equa tor and the Earth 's center,

let us suppo se that the magnetic inte nsi ty , B, in the internal part of the Earth is

the san~ as the outside one {= 5.10-S T) . According t o the formula for the tension

appea ring along the ra di us of the Faraday disk (see, for example , formula (3) on p .

139 of Ref . 3), we shall have

1 2 U = "2 11R B = 74 kV. ( 17)

This tensionis pretty low and, surely, the internal Earth's magnetic in t ensity

must be much bigger than the external one. If the Earth shoul d be a suffi ciently

long charged rotating cylinder, t he relation between its interna l and external mag­

netic intensities will tend to infinity .

The Earth is not a l ong cylinder but a sphere and the relation between the inter­

na l and external magnetic intensities wi ll be not very big, but, s urely, it wi ll be

much bigger than 1.

For simplicity I shall further assume that the tension between the Earth's center

and the equato r is (17), but the reader must kee p in mind that in r eality th i s ten­

sion may be subs tant ially bigger .

Now we have two possib i l it ies : to assume that the Earth 's core is an insulato r , •

or that the Earth core is a l iquid metal (a s the geophysicists assume) and thus elec­

trically conducting .

l. At t he first assumption the 'Ea rth's axis ~till be charged positively (and t he

Earth's surface negative ly) by the polarized molecules and for the _internal "capa­

citence" of the Earth we shall have from (16) and (17)

(18)

This 'condenser" has no rretal electrodes, a s our usual condensers are made . It

presents simply a spherica l dielectric wh ich is pola rized by the electric tension

act in g a l onq the r ad ii of the Ea rth ' s parallels (first such a kind of polarization

wds observed by Wilson( 4 l).

z: At the second assumption the Earth's axis will be charged positively (and the 7 ,

- 42 -

Earth's surface negatively) by the free electric charges separated in the liquid

metal core because of the action of the induced electric tension along the radii of the Earth's parallels.

The calculation shows that the small tension (17) will separate on the Earth's

axis and surface an electric charge much lower than the necessary charge (16) for

generating the observed Earth's magnetic intensity .

Thus the explanation of the origin of the Earth 's magnetic field can be not done

by making only extremely s imple models. Neverthel ess this "simple-model" e xpl ana tion

qualitatively matches thoroughly with the observations .

Let me note that the theory of relativity can in no way accept that at the rota­

tion of the magnetized Earth there will be an electric tension induced along the

radii of the parallels, as according to this theory magnetic forces can appear only

between charges 1~hich have relati ve velocities. Meanwhile on the rotating Earth char­ged with static electric charges there are no relative velocities between the charges .

5. CONCLUSIONS

I am not a specialist in geophysics and I shall not consider the problem about

the Earth's magnetism in detail. I think only that the presented above explanation

for the primordial cause of Earth's magnetism can be the fundamental on which t he theory of Earth's magnetism can be then elaborated . Let me note that a change ' in

the pola ri ty of Earth's magnetism (the geophysicists assert this has occured in

the past) can appear if for certain reasons the Earth's surface will become charged

positively.

As mentioned at the beginning, with the present paper I wish first of all to turn

the attention of the scientifi c community to the fact that if one will begin to dis­cuss the "Rowland" origin of Earth's magnetism (Ro1~land was the first man ~1ho in

1876 measured the magnetic field of a moving charged body), then the theory of rela­tivity will immediately collapse . I repeat , accordi ng to this theory, the magnetic

field of the electrically charged Earth can be measured only by a magnetic needle

with respect to which the Earth rotates (direct Rowland experiment) . If the needl e

corotates with the Earth (comoving Rowland experiment), there can be no deviation of the needle.

Further, according to the theory of relativity, the magnetic field is to be cal­

culated according to formula (10) from the el ectric field E and its velocity v

wi th respect to the magnet ic needl e, so that whether the Earth's nucleus sho uld

be positively charged or not, relat ivi ty will al ways obtain t he same value for

t he magnetic field if the va lue of the electric field is the same.

Here the relativists will begin to cry out that inertial cases are to be calcula­ted according to the Special Theory of Relativity, while the non-inertial cases

are to be calculated by the General Theory of Relativity and will begin to spit

- 43 - No. 5

over the paper such floo ds of scholastici sm at whose reading the reader fee ls in

his stomach only an unabiding sensation t o vomit.

It is long time that I do not lead more logical discussions with the relativists,

·as I wish to have a sane stomach. I present to them only experiments to which they

have to predict the outcome: Normally the relati vi sts do not gi ve an answer but

begin to crow: "This observer will see this, , that observer will see that, accor­

ding to special rela t ivity the result will be this, according to general relativi ­

ty the result must be that''; but they diligently evade to say whether the magnetic '

needle will be deviated to the left, to the right or remain "at rest. And when some I ~

of the more stupid relativists will transgress the canon of the learned , and expe-

rienced talmudists nolto give a clear answer, - and will give a p; ediction, all

children begi n to laugh because if the deviation of the needle is to the left,

the re lativist , as a rule, predicts rotat ion to the right.

The treatment of the Earth ' s magnetic fie ld as a "Rowland " effect will make all

chil dren on the Earth laugh if the relativists will give their prediction. BUT

THEY WI LL NOT.! I assure you , the relativists will never begin t o discuss this

problem, H60 CKa3aHO HeKHMH MYAPe~aMH :

Yf ,llOJDKHbl Bbl COTBOpHTb TaJ<y!O HaYKY,

,lla6bJ Jll06oMY,llP>Je He CBO,lli1IIH KOHIJPl C KOHI(aMH.

I

REFERENCES

1. S. Marinov, De utsche Physik, 1(4) , 36 (1992) . . '

2. S. 14arinov , Classical PHysics (East-West , 1981) .

3 . S. ~1arinov, The Thorny Way of Truth , Part IV (East -Wes t, Graz, 1989) .

4. H. A. Wilson , Philosoph . Trans . Royal Soc., London, 204, 22 1 (-1905).

- 44 -

z

Smagn Ngeogr

y

Fig . 1. The rotating Earth whose surface is charged with static electricity .

- 45 -

0' co 0' .-.

<( u - u z: "' z: -<( I- "

"' 0:: u co ·~

"' <( "' - "' 0 ...., w '[ <( 0... co 0 -' "' .-. u 0' >- -o .-. u Q) z: cO w 0. 0.

0 ::3< u " w ..,., z: :>,

u w "' 0 :X: w I- >

geomagnetic field, magnetic field associated No. 5 with the Earth. It primarily is dipolar (i.e .. it has two poles, these being the north and south magnetic poles) on the Earth's surface. Away from the surface, the dipole becomes distorted.

In the 1830s, the German mathematician and astronomer Carl Friedrich Gauss studied the Earth's magnetic field and concluded that the main dipolar component had its origin in­side the Earth instead of outside. He showed that the dipolar component was a decreasing function inversely proportional to the sqvare of the Earth's radius, a conclusion that led sci­entists to speculate on the origin of the Earth's magnetic field in tenns of ferromagnetism (as in a gigantic bar magnet), various rotation theories, and various dynamo th~ries. Fer­romagnetism and rotation theories generally are discredited-ferromagnetism because the Curie point (the temperature at which ferro­magnetism is destroyed) is reached only 20 or so kilometres (about 12 miles) beneath the surface, and rotation theories because appar­ently no fundamental relation exists between mass in motion and an associated magnetic field.

Most geomagneticians concern themselves with various dynamo theories, whereby a source of energy in the core of the Earth causes a self-sustaining magnetic field. In the dynamo mechanism, fluid motion at the Earth's core involves the movement of conducting mate­rial across an existing magnetic field, thus cre­ating a current. The geomagnetic dynamo is by far the most important source, for without the field that it creates, other sources could not exist. Other sources of the geomagnetic field in­

clude crustal magnetization (which occurs when the solid materials that fonn the Earth's crust become magnetized by the Earth's main field and cause detectable anomalies); iono­spheric dynamo (the flow of charged parti­cles across magnetic field lines that is caused by the Sun's heating of the ionosphere); the ring current (the current produced by the drift of charged particles far above the Earth's surface); magnetopause current (the sheetl ike flow of particles that fonn a boundary be­tween the Earth's magnetic fields and solar wind); tail current (similar . to magnetopause current): field-aligned currents (caused by the circulation of magnetic field lines); and auro­ral electrojets (broad sheets of electric current that flow in the northern and southern auroral ovals).

- 46 -

ENCYCLOPAEDIA UNIVERSALIS (Edite~r a Paris, 1985 )

Vol. 8, p. 472

5 Theories sur "l'origine-du champ moyen Depuis quelques decenni~s, on en est venu

' -a imaginer u~e circulation de courants Une theorie complete de l'origine du champ electriques dans le noyau que Ia sismologie moyen doit expliquer aussi sa variation nous presente fluide et bon conducteur, les seculaire et, en plus, maintenant, le pheno- forces electromotrices etant dues a un (( etfet mene d'inversion considere comme une ca- - dynamo ». On admet !'existence dans ce racteristique tres im~rtante . du champ.! noyau de courants de convection, d'origine Deyuis plus d'un siecle, de nombreuses thermigue, qui peuvent etre une des sources theories ont ete baties, dont plusieurs se . d'energie necessaires. Mais il faut expliquer reduisent a Ia recherche du mecanisme de le mecanisme creant les forces electromo­production du champ dip6le. trices par suite de ces mouvements. Une

Une sphere uniformement ainiantee pro- dynamo ordinaire est heterogene avec des duisant, a l'exterieur de sa surface, un champ · c.onducteurs et des isolants; le rioyau, au equivalent a celui d'un dipole centrer telle est ' contraire, est continu; il s'agit d'une dynamo !'image qui s'est d'abord imposee pour la homogene, tres speciale. Le probleme Terre. L'accroissement de Ia temperature complet, <:J'?-i est de magneto-hydrodynami­avec Ia profondeur entrainant, a quelques que en mtl!eu dense et qui a donne lieu a d.izaines de kilometres, Ie depassement des · d'impc;>rtants travaux, s'est ~ontre jusqu'ici points de Curie connus, l'aimantation devait trop dtffictle. Seuls des problemes partiels ont etre localisee dans une couronne spherique ete .resolus, en liaison vague avec le probleme limitee par Ia surface de · Ia ' Terre et une ventable ; l'un d' eux a pu etre traite theori­surface isotherme correspondant au point de quement et experimentalement et a montre Curie maximal des mineraux magnetiq_ues au moins Ia possibilite d'un effet dynamo (670 °C). De cette hypothese; il ne reste nen, _dans un milieu conducteur continu : il s'agit sinon !'explication des anomalies locales et de deux spheres conductrices tournant dans regionales (correspondant a des surfaces ,un milieu conducteur; a partir d'un champ petites a l'echelle du globe), qui sont bien magnetique infime, accidentel, des courants dues a des aimantations de roches et qui electriques peuvent etre produits dans le restent fixes alors que les anomalies mon- milieu et il en resulte un champ magnetique diales (champ non dip6le) derivent. exterieur qui peut etre intense. Un autre

D'autres theories ont fait appel a des probleme, plus eloi~nc! encore du probleme causes electriques, par exempJe a des COU- . reel, a aUSSI ete traite, c'est ceJui d'un systeme rants de conduction crees a l'interieur du de deux dynamos couplees (mais non homo­globe a son origine et s'eteignant lentement, genes) ; le courant produit oscille irreguliere­ou a des courants de convection dus a des ment (ce qui rappelle les variations d'inten­charges electriques, entrainees par Ia rotation site du champ terrestre), puis s'inverse, soit de Ia Terre, et qui se trouveraient separees brievement (c'est l'evenement dans le pheno­en charges d'ailleurs enormes;· positives vers :nene d'inversion), S?it :plus longtemps avec I'interieur et negatives vers l'exterieur. D'au- a nouveau des osctllauons (ce qm serait tres theories encore se fondaient sur des !'equivalent de Ia periode inverse). Mais il ne phenomenes nouveaux; Ia plus recente, celle· s'agit Ia que ·d 'analogies. de Blackett (1947), qui a eu un succes enorme Le probleme s'est recemment elargi quand mais tres ephemere, invitait a considerer que on y a inclu le champ magnetique des tout astre possede un moment magnetique planetes ; les mesures directes montrent que proportionnel a son moment cinetique; les ce champ est nul ou tres faible pour !a Lune, deux moments ayant meme axe et des sens Venus et Mars, et des mesures indirectes lies, cette hypothese etait en· contradiction (rayonnement electromagnetique) montrent absolue avec le phenomene d'inversion. qu'il est appreciable pour Jupiter.

- 4 7 -

GREAT SOVIET ENCYCLOPAEDIA (t~.acmi ll an, Inc ., 1975)

No. 5

ORIGIN OF TH £ MAIN GEOMAGNETIC Fl ELD. Many different hypotheses. even the hypothesis that a fundamental law of nature exists according to which any rotating body has a magnetic moment. have been advanced to explain the origin of the main geomagnetic neld. Attempts have been made to explain the main geomagnetic field in terms of the presence of ferromagnetic materials in the earth· s crust or in its core: in !erms of the motion of electrical charges. which by participat­!ng in the earth's daily rotation generate an electrical current; In terms of the presence in the earth· s core of currents in-

·duced by the thermoelectromoti ve force at the interface of the core and mantle, and in terms of the action of the so­called hydromagnetic dynamo in the liquid metallic core of the earth. Current data on secular variations and on repeated changes in the polarity of the geomagnetic field are explained satisfactorily only by the hypothesis of a hydromagnetic dynamo. According to this hypothesis, quite complex and intensive motions that lead to the self-excitation of the magnetic field in a manner analogous to the way in which a current and magnetic field are generated in a self-exciting dynamo may take place in the electrically conducting liquid core of the earth. The action of a hydromagnetic dynamo is based on electromagnetic induction in a moving medium, which intersects the lines of force of a magnetic field during

jts movement. Research on the hydromagnetic dynamo is based on

magnetic hydrodynamics. If the rate of motion of a substance in the liquid core of the earth is considered to be given, then the basic possibility of generation of a magnetic field during motions of various typeS--steady and unsteady, regular and

- 48 -

turbulent-can be proved. The average magnetic field in the core may be represented as the sum of two components, a toroidal field B ci> and a field B v' whose lines of force lie in meridian planes (Figure 3) . The lines of force of a toroidal magnetic field Bet> close within the earth's core and do not emerge on the surface. According to the most widely used scheme of the terrestrial hydromagnetic dynamo, the field B ci>

N

s

Figure 3. Diagram of the mag­netic fields in the earth's hydro­magnetic dynamo: (NS) axis of rotation of the earth, (8,.) a field close to a . dipolar field directed _along the earth's axis 0f rotation, (Bcp) a toroidal field (of the order of hundreds of gauss) that closes within the earth's core

is hundreds of times stronger than the field B P' which pene­trates outward from the core and which has a mainly dipole character. The nonuniform rotation of the conducting fluid in the earth's core deforms the lines of force of field B P and fo rms from them the lines of force of field BcJ>. The field B , in turn, is generated by the inductive interaction of the conduct­ing fluid , which moves in an intricate manner, with the field Bet>. For the field B" to be generated from Bet>, the motions of the fluid must not be axisymmetric. Otherwise, as the kinetic theory of the hydromagnetic dynamo shows, the motions may be extremely diverse. In the process of generation the , motions of the conducting fluid also create, in addition to the field B

11, other slowly changing fields , which upon penetrating

outward from the co re , are responsible for the secula r varia­ti ons of the main geomagnetic field.

- 49 - No. 5

The general theory of the hydromagnetic dynamo, which studies both field generation and the ··motor'' of the terres­trial hydromagnetic dynamo.-that is, the origin of the motionS-is still in the initial stage of development and is largely hypothetical. Buoyancy forces caused by small den­sity nonuniformities in the core, as well as inertial for-ces, are given as the factors responsible for the motions. Buoyancy forces may be associated either with the liberation of heat in the core and thermal expansion of the liquid (thermal convec­tion) or with the heterogeneity of the core composition as a result of the separation of impurities at its boundaries. The inertial forces may be caused by the acceleration owing to precession of the earth's axis. The closeness· of the geomagnetic field to a dipole field with an axis nearly parallel to the earth's axis of rotation indicates the close relationship between the earth· s rotation and the origin of terrestrial mag­netism. The rotation creates the Coriolis force, which may play a significant role in the mechanism of the earth· s hy­dromagnetic dynamo. The dependence of the geomagnetic field's magnitude on the intensity of the motion of matter in the earth's core is complex and still inadequately studied. According to paleomagnetic studies. the magnitude of the geomagnetic field undergoes fluctuations. but on the average, in terms of order of magnitude. it remains unchanged over long periods (on the order of hundreds of millions of years).

The functioning of the earth's hydromagnetic dynamo is associated with many processes in the earth's core and man­tle; therefore. the study of the main geomagnetic field and of the earth's hydromagnetic dynamo is an essential part of the body of geophysical research on the internal structure and development of the earth. S. I. 8RAGtNSKti

- so -

Erdmagnetismus, Bez. fi.ir die mit dem Magnetfeld der Erde zu­sammenhangenden Phanomene. Weder der Mond noch die beiden N achbarplaneten Mars und Venus besitzen ein Feld vergleichbarer Intensi­tat; hingegen ist der Jupiter. wie man aus radio­astronom. Beobachtungen weil3. von einem Feld umgeben. dessen magnet. Moment 50000mal so grol3 ist wie das der Erde. Das Magnetfeld der Erde bewirkt die Bildung der t Magnetosohare. Erdmagnetisches Innen[eld: Man kann das auf der Erdoberftache gemessene Magnetfeld zerlegen in einen Anteil. dessen Ursache im Erdinnern liegt. und einen von aul3en stammenden Anteil. Der innere Anteil enthalt vor allem das Perma­nentfeld. die Sakularvariation und die Magner­felder der durch aul3ere Yariationen im Erdinnern elektromagnetisch induzienen Strome. Der aul3ere Anteil ri.ihrt von variablen elektr. Stromen in der lonosphare und der Magnetosphare her.

Rotationsachse

I

I

\: / tl \

''-"1\~,' . " . _ 1- g~magn~t. .. 11 13 - --· ---,_ Aquator

--:::;:::::=-=--t"~-------1/- gttograph

" j' 1\ .v I\ --7 I \ I I I \

Abb. 1 Dipolfeld der Erde in der dur ch die Rotations­und die Dipolachse festgelegten Ebene. Die Pfeile be­deuten die Feldstarken in Punkten d er Erdoberflache

Zur Beschreibung des Feldes an einem Ort genii­gen drei der folgenden Elemente: Horizon talin­tensitat H. Yertikalintensitat Z. Totalintensitat F erdmagnet. Deklination D, Inklination I. Die Li~ nien D =const bezeichnet man als Isogonen (spe­ziell die Linie D = Q• Agone), die Linien I= = canst ~Is Isoklinen (speziell die Linie I = o• als magnet. Aquator). die Linien H = const als Iso­dynamen. In erster Naherung gleicht das erdma­gnet. Feld dem Feld eines Dipols im Erdmittel­punkt, dessen Achse so gegen d ie Rotationsachse

MEYERS ENZYCLOP~DISCHES LEXIKON

(Lexikonverl a (J , 1973)

Vol. 8, p. 85

geneigt ist. dal3 sie die Erdoberftache in den Punkten B und A durchstol3t :

B (von boreal) 78,6° n. Br., A (von austral) 78.6• s. Br..

Auf diesen D ipol bezieht man magnetischer Koordinaten:

7Q,J 0 W. L., 109.9 ° 6. L.

das System geo-

/3* ist die geomagnet. Breite {/3* = o• kennzeich­net den geomagnet. Aquator, im Gegensatz zum magnet. Aquator. I= 0°). ). • ist d ie geomagnet. Lange. beginnend am Schnittpunkt des g~ograph. Meridians durch B mit dem geomagnet. Aquator. Fiir die magnet. Feldstarke bzw. Induktion der verschiedenen Komponenten des erdmagnet. Fel­des gilt: Fiir /3* = o• ist H = 31 300 Gamma = 31.3 11T und Z = 0 ; fi.ir /3* = 90• ist Z = 62600 Gamma = = 62. 6 11T und H = 0. Das Dipolfeld ist nur eine Annaherung an das wirkl. Erdfeld. das durch eine Reihenentwick­lung des Potentials dargestellt wird . deren Haupt­glied dem Dipolfeld entspricht. D ie weiteren Glieder enthalten die regionalen und lokalen Anomalien des erdmagnet. Feldes. Wie man aus iahrhundertelangen Beobachtungen weil3. sind Richtung und Starke des erdmagnet. Fe! des nicht unveranderlich; sie unterliegen der Sakularvariation. die sich starker in den hoheren Gliedern der Potentialentwicklung als im Diool­anteil aul3ert. Bekannt ist die Wirkung der Saku­larvariation auf die Mil3weisung am Kompal3 : Die Agone. die 1945 durch Konigsberg (Pr) lief. riickt iahrlich urn etwa 20 km nach Westen. 1975 wird sie in Berlin sein. Die Horizontalimensitat nimmt zur Zeit in Deutschland jahrlich urn 10 bis 20 Gamma ab. Ursache des erdmagnetischen Feldes: Es gibt noch ke;ne restlos befriedigende Theorie der Entste­hung des erdmagnet. Innenfeldes. Permanent­magnete kommen als Ursache nich t in Frage, da die Temperatur des Erdinneren schon ab 50 km Tiefe tiber der Curie-Temperatur ferromagnet. M ineralien liegt und die oberhalb liegende Kru­ste nicht entfernt so vie! ferromagnet. Material enthalt. wie notig ware. das Feld zu erzeugen. Das Feld mul3 daher durch elektr. Strome ent­stehen. Diese ftiel3en im au13eren Erdkern. dicht an der Grenze zum Mantel. Sie werden verursacht durch einen Prozel3 im Erdkern. der einem Strom­generator verwandt ist. dessen Magnetfeld von dem erzeugten Strom selbst gespeist wird (dyna­moelektr. Prinzip). An die Stelle des sich d rehen­den Ankers mit den Wicklungen treten turbu­lente Konvektionsstromungen im Erdkern. Die Stromungsgeschwindigkeit mul3 etwa 0.05 cmts betragen. Die Siikularvariation entsteht durch Yerlagerungen und Stromstiirkeschwankungen dieses Dynamosysrems.

- 51 - No. 5

ENC ICLOPEDI A ITALI ANA ( Istituto della encic lopedia italiana, 1934 )

CAUSE DEL MAGNETISMO TERRESTRE. - L'ipotesi che la terra sia composta in gran parte di ferro o eli composti ferromagnetici, per­manentemente magnetizzati lungo I' asse magnetico (Vi/. Gilbert), sembrerebbe fomire la piu semplice spiegazione del campo ma­gnetico terrestre: si puo calcolare (A. Schuster) che basterebbe, a tale scopo, che l'intensita di magnetizzazione avesse un valore piccolissimo (J = o,o8, unita C. G. S.); oppure che una piccola frazione del suo volwne fosse magnetizzata piu fortemente, pur sempre lungi dalla saturazione magnetica.

Ora, anche ammettendo un grado geotermico di 40 m., a ben piccola profondita in confronto al raggio terrestre si raggiunge la temperatura a cui la magnetite e il ferro perdono le !oro proprieta magnetiche; pare inoltre -che un awnento di pressione diminuisca tali temperature critiche: si e trovato necessaria pertanto ammettere (A. Nippoldt, 1925) l'esistenza di una sottile calotta sferica estema (2o- roo km. di spessore), fortemente magnetizzata, eli grande forza coercitiva, e vicina alia superficie: la variazione secolare potrebbe in tal caso ritenersi anche come dovuta a variazion·i della composi­zione della crosta, o, forse meglio, a variazioni della suscettivita per temperatura (v. L. Palazzo, Atti della Soc. it. per il progr. delle scienze, Catania 1923).

Resta da spiegare la causa di tale magnetizzazione e la relazione tra l'asse magnetico e l'asse di rotazione.

L'induzione dei campi esterni per quanto si e detto e da escludersi: ne una sfera comunque costituita e imrnersa in un campo esterno uniforme produrrebbe un campo del tipo descritto. Neppure l'ipotesi chela parte attiva della terra costituisca un elettromagnete eccitato da correnti in essa circolanti pub essere sostenuta : escluso, infatti, che tali correnti perma­n enti possano essere !a conseguenza di cause che abbiano ormai cessato di esistere, perche (A. Schuster), in un corpo come la terra, l'intensita di tali correnti diminuirebbe rapidamente, sarebbe difficile comprendere come esse potessero essere mantenute e a quale fonte fosse sottratta l'ener­gia necessaria a colmare le perdite per effetto Joule: forze termoelettriche, eccitate dalla ineguale distribuzione della temperatura, non agirebbero nel modo richiesto. ] . Larmor (1919), riguardo al problema analogo solare, avanzb l'ipotesi che possa sussistere una circolazione di materia fl.uida nel senso dei meridiani (come pub essere nel sole): in presenza . di un campo magnetico preesistente, si avrebbe allora, in tale materia, una corrente indotta nel sensa dei paralleli, tale cioe da aurnentare il campo inducente, come in una dinamo ad autoe.ccitazione; riel sol~ .un'a tale circolazione nel nucleo, e un' opposta corrente negli· alti strati, da­r ebbe ragione d el rapido indebolimento radiale del · campo: applicata alla terra, tale ipotesi condurrebbe a ritenere che i materiali profondi fossero fluidi; !a variazione secolare sarebbe facilmente spiegabile suppo­n endo che la conducibilita lungo i paralleli potesse mutare.

La s tretta relazione tra l'asse di rotazione e quello del campo

- 52 -

terrestre ha condotto ad esam!nare la possibilita (A. Schuster e lord Kelvin) che la magnetizzazione possa essere determinata dalla sola rotazione della terra (e del sole); A . Schuster e W . F. Swann (1912 e 1917), seguendo le idee di J. C. Maxwell, hanno infatti considerate che i costituenti (molecole e elettroni) degli elementi magnetici possono agire, in un corpo rotante, come microscopici giroscopi: i !oro assi tenderebbero a disporsi paralleli all'asse di rotazione del corpo di cui fanno parte e questa apparirebbe magne­tizzato in tale direzione: questa effetto dovrebbe essere uguale per tutti i volumi elementari e indipendente dalle dimensioni del corpo : opportune csperienze (S. J. Barnett, 1915) dimostrarono infatti che un corpo ferromagnetico in rotazione e accompagnato da una ma­gnetizzazione proporzionale alia velocid1 angolare e indipendente dalle dimensioni del corpo, e di senso tale da conciliarsi con l'ipo­tesi che intorno agli ultimi costituenti degli elementi magnetici ruotino particelle di elettricid1 negativa: e cioe concorda col sensa della magnetizzazione della terra e del sole. Ma, data la piccola velocita angolare della terra (r /86400 di giro al secondo), il campo cosi prevedibile e assai piu piccolo di quello terrestre (circa ro10

volte); a meno che l'alta temperatura interna non attenui i vincoli degli elementi giroscopici sopra accennati: il che sembra ammissi­bile, se i costituenti suddetti sono gli elettroni, le cui orbite. sono minime di fronte al diametro molecolare. Risulta pertanto possibile che la magnetizzazione della crosta terrestre, o il campo terrestre e la sua variazione secolare, possano essere cosi originati.

Si sono naturalmente tentate altre possibili spiegazioni, rna inutil­mente: la rotazione di una sufficiente carica negativa della superficie terrestre (o della superficie solare) o distribuita nel nucleo non potrebbe influire (A. Schuster, rgrz; 0. Venske, 1920), su un ago in rotazione con Ia terra, nel modo voluto, anzi prevarrebbe l' induzione elettrostatica che tende a dare all'ago una direzione diversa; si e ,pure immaginato che tale campo elettrostatico. (occorrerebbe ammettere ro8 V. x/cm.) po- I tesse essere compensate qualora nell'atmosfera esistesse una c;a,nca uguale • e di segno contrario a quell a del nucleo; all ora pero per generare un campo del senso di quello terrestre, occorrerebbe (W. F. Swann, 1917) che lo strata negative fosse l'estemo e l'elettricita positiva diffusa nell'intemo . della terra: e per dar conto della sua entita le cariche in giuoco dovrebbero essere molto piu grandi di quelle constatate e tali che il campo elettrico fra esse ne provocherebbe la riunione.

Difficolta non minori escludono che si possa attribuire il campo ma­gnetico terrestre a una polarizzazione elettrica delle masse (J. J. Thomson, x 894), il cui campo sarebbe bensi neutralizzato elettricamente, rna che darebbe Iuogo, per rotazione, a effetti magnetici: J. Larmor noto, ad es., che un cristallo possiede sempre una certa polarizzazione elettrica dovuta all' orientamento delle sue molecole polari: se questa polarizza­zione fosse completa, un cristallo delle dimensioni della terra produrrebbe un enorme campo elettrico compensate elettricamente, rna non . magne­ticamente: in tal modo un pianeta, i cui materiali fossero cristallizzati e orientati in qualche modo dalla gravita, o dalla rotazione, possiederebbe un certo campo magnetico; rna la stabilita dell'intemo della terra sembro al Larmor troppo grande per spieg;1re cosl le variazioni secolari.