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Journal ofELECTRICAL ENGINEERING, VOL 59. NO 7/s, 2008, 74-77

Brno University of Technology, Faculty of Mechanical Engineering, Technicka 2, 616 69 Brno, Czech Republic; osmera@fme.vutbr.cz

ISSN 1335-3632 2008 FEI STU

MAGNETICDIPOLEMOMENTOFELECTRON

Pavel Omera Imrich Rukovansk*

We would like to find some plausible structure of the electron as a vortex-fractal-ring structure and its parameters. But it is incontradiction with general accepted knowledge, where the electron has not a structure. This paper is an attempt to calculate the spinand the magnetic dipole moment of the electron (magnetic moment). The vortex-fractal theory could possibly explain what thespin, the magnetic dipole moment, etc actually are.

Keywords: spin of the electron, magnetic dipole moment of the electron, vortex-fractal-ring structures

1 INTRODUCTION

Most of our knowledge of the electronic structure ofatoms has been obtained by the study of the light givenout by atoms when they are exited. The light that isemitted by atoms of given substance can be refracted ordiffracted into a distinctive pattern of lines of certainfrequencies and create the line spectrum of the atom. Thecareful study of line spectra began about 1880. Theregularity is evident in the spectrum of the hydrogenatom. The interpretation of the spectrum of hydrogen wasnot achieved until 1913. In that year the Danish physicistNiels Bohr successfully applied the quantum theory to thisproblem and created a model of hydrogen. Bohr alsodiscovered a method of calculation of the energy of thestationary states of the hydrogen atom, with use of Planckconstant h. Later in 1923 it was recognized that Bohrs

formulation of the theory of the electronic structure ofatoms to be improved and extended. The Bohr theory didnot give correct values for the energy levels of heliumatom or the hydrogen molecule-ion, H2

+, or of any otheratom with more than one electron or any molecule. Duringthe two-year period 1924 to 1926 the Bohr description ofelectron orbits in atoms was replaced by the greatlyimproved description of wave mechanics, which is still inuse and seems to be satisfactory, [1].

The discovery by de Broglie in 1924 that an electronmoving with velocity v has a wavelength =h/mev, [1].The theory of quantum mechanics was developed in 1925

by the German physicist Werner Heisenberg.An equivalent theory, called wave mechanics, wasindependently developed early in 1926 by Austrianphysicist Ervin Schroedinger. Important contribution tothe theory were also made by the English physicist PaulAdrien Maurice Dirac. The most probable distance of theelectron from the nucleus is thus just the Bohr radius ro;the electron is, however, not restricted to this distance.The electron is not to be thought of as going around thenucleus, but rather as going in and out, in varyingdirections, so as to make the electron distributionspherically symmetrical, [1].

This paper is an attempt to attain a new and profoundmodel of the natures structure using vortex, fractal andring structures. Scientists try to explain some phenomenain Nature that have not been explained so far. The aim ofthis paper is the vortex-fractal modeling of vortex-ring

fractal structure of atoms, molecules, and a creation ofelements in the Mendeleev periodic table with vortex-ringparticles which is not in contradiction to the known lawsof nature, [6].

The discovery of the electron was a landmark inphysics and led to great technological advances. Theelectron emission is the process when negative charges inthe form of electron, escape for example from the hotfilament. Streams of electrons moving at high speed arecalled cathode rays or electron rays. The rays aredeflected by a magnetic field too. If the N pole of amagnet is brought up to the neck of the tube, the raysmove upwards, using Fleming left-hand rule. The ratio ofthe charge q of an electron e to its mass me is called itsspecific charge and can be found from experiments inwhich cathode rays are deflected by electric and magneticfields. It was first done by J. J. Thomson in 1897 using adeflection-type tube. His work is regarded as proving theexistence of the electron as a negatively charged particleof very small mass and not, as some scientists thought aform of electromagnetic radiation like light.

Electron is defined as a fundamental particle of matter,with negative electric charge, which populates the outerregion of atoms.

The electrical force decreases inversely with the

square of distance between charges. This relationship iscalled Coulomb law. There are two kinds of matter,which we can call positive and negative. Like kinds repeleach other, while unlike kinds attract unlike gravity,where only attraction occurs, [1-2]. When charges aremoving the electrical forces depend also on the motion ofcharges in a complicated way, [2-4].

Fractals seem to be very powerful in describing naturalobjects on all scales. Fractal dimensions and fractalmeasures are crucial parameters for such description.Many natural objects have self-similarity or partial-self-similarity of the whole object and its part, [5].

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Journal ofELECTRICAL ENGINEERING, VOL 59. NO 7/s, 2008 75

2 ELECTRON WITH VORTEX-FRACTAL-RINGSTRUCTURE

The structure of the electron in Fig. 1 presents theelectron as pure ring fractal structure. Electrons 0e (or e)

in the electron ray

0

r are hold together by photon vortexstructure 0f (a pair of vortices), [6]. Generally, in thefractal structure of the electron, the number n defines thelevel of substructure ne. The name osmeron we derivedfrom the name Osmera of Egyptian deity with 4 pairs ofgods as primary creative forces (from a chaos beginning).Osmerons are too small that is why have unmeasurablesize and mass. Osmerons on osmeron trajectory creates anosmeron ray.

Fig. 1. The vortex-fractal structure of the electron raywith two electrons

For a calculation [5] of the fractal-ring electron structurewe will use the structure that is shown in Fig.1 and Fig.2.In the ring electron structure (see Fig.2) the subelectronse0 rotate with a velocity ve and subsubelectrons e1 with avelocity v0. The radius of the electron isRe and a radius ofaxes of subelectrons e0 is re. A rough estimation ofnumber of subrings is Nand number of subsubring is N2.

They are determined in the electron structure by the massmpof the proton structure [5].

a AF F (1)

The fundamental physical law for an acceleration force Fafor mass m with velocity v and distance ris

2

a

vF m

r (2)

The mass m0e of the subelectron e0 for the fractalstructure of the electron is

0e

e

mmN

(3)

where N is number of subelectrons. To cover creation ofthe proton structure and the electron structure from thesame very small rings (N2 subsubelectrons e1) [5]

42 2 3 7p

e

mN

m (4)

where mp is the mass of the proton and me is the mass ofthe electron. From the fractal structure of the electron inFig.2.

22 22 2

e ea ao

e

m vN NF F

N r (5)

The average value of forces Fa0 for N/2 subelectrons 2/was calculated in according to Fig. 3.

Fig. 3. Average value of the acceleration force

The fundamental physical law for attraction force FA(Ampere law) between two wires with a current I, a lengthl, a distance d, and a permeability o of vacuum

2

2o

A

lF I

d

(6)

Electric charges q1 in the subring e1 create the currentI. Let us calculate properties of the electron with a vortex-fractal theory [5]. This requires that subelectrons are

accelerated towards the centre of the electron ring. Theamount of the acceleration force Fa has to be in balance

Fig. 2. The fractal-ring structure of the electron

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76 P. Omera I. Rukovansk: MAGNETICDIPOLEMOMENTOFELECTRONwith two coulomb forces F0. A whole force of attractionFA can be calculated by Ampere law

1q NdQIdt T

(7)

2 oe or v T (8)

1 2

eq

N (9)

2

2

22

o

oe

o o

e e

eN

eveNIT NT N r

ev ev

r rN

N

(10)

2 erdN

(11)

Equation (10) and (11) we use in (6)2 2

2 2

22 2

22 4

e

o oa A o

ee

r

e v N F F F rr

N

(12)

From (5) and (12)

2 2 2

2 2

222

22 2 4

e

e e o o

ee e

r

m v e vN Nr N r r

N

(13)

2 2

2 24o o

e

e e

e vr

m v

(14)

and the radius re of the electron (in Fig. 2) isIf velocities of rings and subrings are

o ev v c (15)

then2

152

0.89 104

oe

e

er

m

m. (16)

We can now calculate the size of the electron with thefractal geometry in Fig. 4. Full calculation is in reference[5]. But it is only for the free and quite electron. The size

of the electron in the hydrogen atom is not constant.

Energy E0 of a quite electron0e, which has velocity

v=0 and quite mass me0, can be calculated from kineticenergy of their subelectrons -1e with velocity v-1 (ve),subsubelectrons -2e with velocity v-2 (v0), sub-subsubelectrons -3e with velocity v-3, sub subsub-subelectrons -4e with velocity v-4 [6]

If velocities of substructures are

0ev v , 3

2o

cv v

, 4v c (17)

their inner kinetic energy of the quite electron is

2 2 2 30 032 3

1 1

2 2e e

o o

m m E v N v N

N N

2 4 204 04

1

2e

e

mv N m c

N

. (18)

This result is in coincidence with the well-knownEinstein equation

20o e E m c . (19)

3 THE SPIN OF THE ELECTRON

It was discovered in 1925 that the electron hasproperties corresponding to its spin S. It can be describedas rotating about an axis of a ring structure of the electron(see Fig.1). The spin of the electron is defined as angularmomentum

( )e e eS m r v

(20)For the spin on axis z

e z e e

mS N r v

N (21)

In [6] the formulae (14) is modified to2

2 20

1

8e e e

er

m v (22)

2o

cv (23)

where

m

e

v

v

(24)2

02m

ev

h (25)

2 2 2

2 2 200

1

88e ee m m

e er

mm v v

(26)

2 2 220 04 2

0

4

8 2e e

h he

m e m e

(27)

the spin on axis z

m z e e e e e

vS m v r m r

22 02

0

1 1 12 2 2 22e se

he hm mh m e

(28)

1

2sm (29)

The result (28) is in coincidence with the generallyequation for the spin, where ms is spin quantum number.

Magnetic momentum Mzisdefined as

zM IS (30)

whereIis an current around a surface S2

e

e

r

T v

(31)where Tis period for calculation of currentI

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Journal ofELECTRICAL ENGINEERING, VOL 59. NO 7/s, 2008 77

2 12 2

e

e e

e

eN

evQ NIT r r

v

(32)

2eS r (33)

2e ez e

e e

ev mM IS r

r m

1

2z Be e

e eS

m m (34)

where B is Bohr magneton [1]. We received well knownresult but with a fractal-ring model.

4 CONCLUSIONS

Our science creates terrific demands on theimagination [2]. To understand the electromagnetic fieldrequires a high degree of imagination. The degree ofimagination that is required is much more extreme thanthat required for some of the ancient ideas. The modernideas are much harder to imagine. We usually usemathematical equations and rules, but we used a lot ofpictures to describe very complex vortex-fractal models.There is not easy to formulate mathematical models. Wecannot allow ourselves to seriously imagine things, which

are obviously in contradiction to the known laws ofnature. We created vortex-fractal-ring model of theelectron, of the proton and hydrogen and then calculatedsizes, forces, energies and covalent bonds [6].

Acknowledgement

This work has been supported by the Czech GrantAgency; Grant No. MSM21630529.

REFERENCES

[1] PAULING, L.: General Chemistry, Dover publication, Inc, NewYork, 1988[2] FEYNMAN, R.P. LEIGHTON, R.B. SANDS, M.: The Feynman

Lectures on Physics, volume I, II, III Addison-Wesley publishingcompany, 1977[3] FEYNMAN,R.P.: QED The Strange Theory o f Light and Matter,Princeton University Press, 1988[4]FEYNMAN, R.P.: The Character of Physical Law, Penguin Books, 1992[5] OMERA, P.: Vortex-fractal-ring Structure of Electron, Proceedingsof the 6th International Conference on Soft Computing ICSC2008,January 25, Kunovice, Czech Republic, (2008), 151 158[6] OMERA, P.: Vortex-fractal-ring Structure of Molecule,Proceedings of the 4th Meeting Chemistry and Life 2008, September 9-11, Brno, Czech Republic, (2008), Chemick listy (ISSN 1803-2389),1102-1108

Received 21 September 2008

}

Fig. 4. Geometry of the electron and the subelectron