THE MAGNETIC INTERACTION

(Modified)

Mahmoud E. Yousif

^C/_O Physics Department - The University of Nairobi

P.O.Box 30197 Nairobi-Kenya

PACS No: 41.20.-q, 21.10.Hw, 21.30.-x, 94.20.Qq, 94.10.Rk, 34.20.Cf, 32.10.Dk, 34.50.Fa, 32.30.-r

ABSTRACT

A magnetic interaction hypothesis (MIH) is suggested which leads to a re-interpretation of the interaction mechanism for the magnetic force. This MIH is used to explain energization of charged particles on micro scale. Further considerations including the nuclear force, inter-atomic stability, and the reproduction of spectral lines, are reported.

1:0 INTRODUCTION

Energization mechanism for charged particles has been a subject of much interest in the plasma physics [1]. The Sun emits these particles during various phenomena (such as, the solar flares, and the solar wind), [2,3] all of which interact with the geomagnetic field giving rise to several phenomena such as, the ring current, the Van Allan radiation belt, and the aurora in which the particles are highly accelerated, [4,5,6]. Many theories have tried to explain such accelerations. Among them are: acceleration by hydromagnetics shock waves, acceleration through atmospheric dynamo process, and the electric field acceleration[3]. But they have not been able to duplicate or explain the energization mechanism causing these phenomena[7]. Disclosing of this mechanism could help unlocking many of present unsolved mysteries, such as, the nuclear force formula [8], nuclear fusion mechanism [9], aurora mechanisms [10] and several other phenomena [11]. It is known that the forces keeping electrons around nucleus, are both the electrostatic and the electromagnetism [12], but no mechanism had been suggested for it. This paper however tries to tackle these problems by (I) re-interpreting the nature and mechanism of the magnetic force, and (ii) suggesting a magnetic interaction hypothesis (MIH), through which any generalised magnetic field interacts with a circular magnetic field (CMF) and (iii) re-defining the spinning magnetic field (SMF) interaction in terms of the nuclear force that binds the nucleons. Using both the CMF and SMF the atom formation, inter-atomic energization processes and the reproduction of the spectral lines are considered. MIH was published in 2003 [13], the present modification re-address among others, the inter-atomic forces.

2:0 THE MAGNETIC FORCE

2:1 THE CIRCULAR MAGNETIC FIELD (CMF)

Through experience [14], the attractive and repulsive forces between two conductors C₁ and C₂ carrying electric currents I₁ and I₂ separated by distance d metre, adopted for the definition of electric current [14], is given electrically by

But since the above conductors (C₁ and C₂) carrying electric currents (I₁ and I₂) therefore, the circular magnetic field (CMF) produced by each at a distance r_C from the conductor is given by

Where, k= 2x10^-7 Newton per square ampere [12].

As supposed by Faraday [15] magnetic lines of force tends to shorten in length or repelling one another sideways, such that the force obtained by Eq.(1) could be conceived as due to both conductor’s CMF shorten or repelling each other, as shown in Fig.1 and Fig.2, such that the repulsive and attractive force is give magnetically by

Where, both B_c1 and B_C2 are CMF (in Tesla) produced by conductors C₁ and C₂ respectively, while r₁ and r₂ are the CMF's radii in metre, l₁ is the length of the conductor in metre.

Fig.1. Production of circular magnetic field (CMF) [12], the figure also shows the direction of CMF, the interaction line and direction of the produced force.

The Catapult force or the motor effect [12] is given by:

Where, B₁ is the magnetic field, l₂ is the length of the conductor cutting the field in metre; I₁ is the current in the conductor in Ampere and the magnetic force F_e.m_, given by electric-magnetic parameters is in Newton.

Fig .2. Cross-section views of conductors carrying electric current. Produced circular magnetic field (CMF) [12] interacted magnetically producing the magnetic force. Direction of both CMF’s determined the direction of the force [12], in (a) it is attractive, while repulsive in (b).

The repulsive and attractive nature of magnetic lines of force causing Catapult force above, is express magnetically by

Where, B₁ is a general magnetic field, B_C2 is the CMF produced by the conductor, r₂ is the radius of the CMF, l₁ is the length of the conductor producing the CMF that interact with B₁, the magnetic force F_m is in Newton. Table.1. Shows the parameters relating magnetic force given by Eqs.(1), { 3}, (4) and {5}.

*I₁=I₂* A	l₁ m	D M	R M	*B₁=B_C1=B_C2* T	*r₁=r₂=l₃* m	*F_e=F_m=F_e.m.=F_m* N
1	1	2.0	1.0	2x10^-7	0.707106781	1.0 x10^-7
1	1	1.6	0.8	2.5x10^-7	0.632455532	1.25x10^-7
1	1	1.2	0.6	3.333333333x10^-7	0.547722557	1.666666667x10^-7
1	1	1.0	0.5	4x10^-7	0.5	2x10^-7
1	1	0.6	0.3	6.666666667x10^-7	0.387298334	3.333333333x10^-7
1	1	0.4	0.2	1x10^-7	0.316227766	5x10^-7
1	1	0.2	0.1	2x10^-7	0.223606797	1x10^-6

Table.1. Samples of parameters that gives an equivalent magnetic force in Eqs.(1), {3}, (4) and {5}, when used in its proper equation.

From both Maxwell's and Einstein's theories about magnetic field produced by charge in motion [16], it can be deduced that the magnitude of the CMF (or B_2e and B_2p for electron and proton respectively) produced by a charged particle in motion[17, 18, 19] is given by

Where, c is the speed of light, q is the particle's charge in coulombs, v is the charged particles velocity in ms^-1, r_m is the magnetic radius at which the CMF is measured (representing r_me and r_mp or electron's and proton's magnetic radius respectively). The circular magnetic field B₂ is given in Tesla.

Fig.3. ECMF and PCMF [16,17,18] (B_2e and B_2p respectively) of equal energies interacted with magnetic field (B1), at specific points. Resulted magnetic force (Fm) caused electron and proton to gyrate oppositely at specific radius.

The Lorentz force ascribed to the existence of electrostatic field, used in explaining the characteristics of the magnetic force [20], while the magnetic force as associated with moving source charges is related to interaction of current bearing wire [21] shown by Eq.(1), the force is given by

Where, q is the angle between the trajectory and the fields. This force, is given with electric-magnetic parameters can be conceived to be caused by the magnetic interaction, where, as shown in Fig.3 the CMF (B₂) given by Eq.(6) interact magnetically with the general magnetic field B₁ such that

Where, q is the angle between the two fields. While Fig.3 shows the magnetic interaction patterns between both the electron's CMF and the proton's CMF with the general magnetic field B₁, Fig.4, shows variation of F_m with r_m.

2:2 THE SPINNING MAGNETIC FIELD (SMF) and NUCLEAR FORCE

2:2:1 THE SPINNING MAGNETIC FIELD

The magnetic field produced above the poles of the spinning nucleon [22] is due to total magnetic field (B_T), and is here identified as the spinning magnetic field (SMF). For proton, the magnitude of the total magnetic field (B_Tp) produced above each pole as shown in Fig.5.a, is derived from Newton’s second law, Coulomb’s electrostatic law and Biot-Savart law for magnetic field outside a loop [14], given by:

Where, B_1p is proton's SMF (B_1U for nucleus hydrogen atom), f_ps is the proton's spinning frequency, r_O is the radial distance from proton surface to a point at which B_TP is produced (r_o=0.468 fm), r_r is distance from proton's surface along the magnetic field, m_O is the permeability of the free space, e_Ois the permitivity of free space.

Fig.5. The proton’s dipole spinning, magnetic field (PSMF) production [21], above the surface in (a) it also shows two PSMF interacted magnetically.In (b) attractive produced magnetic force increased exponentially till r = 0.936fm (r_r = 0.468fm) (fm = 10-15 m), then the force decreased, where it becomes repulsive, due to PSMF characteristics, using Eqs. {12}, all of which showing nuclear force (Fn) characteristics.

2:2:2 THE SPINNING MAGNETIC FORCE or (SMFc) THE NUCLEAR FORCE

When opposite proton's spinning magnetic field (PSMF) comes under the field influence of each other as shown in Fig.5:a, an attractive spinning magnetic force (SMF_CA) or (F_NA) is established as in Fig.5:b, and derived from Eq.{8}, this force is given by:

Which we here interpret as the nuclear force, In according to characteristics given [8]. The SMFc or nuclear force F_N varies as shown in Fig.5.b, whereby at relatively large distances the attraction of both SMF dominates up to r_r = 0.468fm (r =0.936fm), (fm = 10^-15) as given by Eq.{10}. Thereafter, for r_r smaller than 0.468 fm, magnitude of the SMF starts to decrease and so does F_NA given by the right hand part of Eq.{11}.

For smaller values than r_r = 0.468 fm, the preceding parts of the poles with similar SMFs interact with each other thus producing an F_NR opposing the two protons from fusing together, given by the left part of Eq.{11}. This repulsive force (F_NR) is the resultant of both two forces, as shown in Fig.5b, given by:

Based on this hypothesis, whenever an electron comes under the influence of a nucleus electric field at an electrostatic distance r_e the electron is accelerated by the electrostatic force such that its velocity v_c and CMF increases. Thus at a specific radius regulated by m_e in Eq.{25}, the electron will interact magnetically with the nucleus spin magnetic field (NSMF) forming an atom, or increasing the nucleus constituent. NSMF in its simplest form comprising the proton spinning magnetic field PSMF to form a hydrogen atom when interacted with electron's CMF.

At specific electrostatic atomic radius r_ee the electrostatic force F_e is balanced with the produced magnetic force F_m, and both forces are balanced with the centripetal force (F_C)}, leading to the stability of the atom as shown in Fig.7, for hydrogen atom and given generally by Eq.{15} bellow, while the degree of this stability is determined by m_e in Eq.{25}. The balance of forces is such that

Where, B_1U is the nucleus SMF, B_2e is orbital electron’ CMF, m_e is electron's mass, r_ee is the electron's electrostatic atomic radius, r_me is the electron's magnetic radius, v_o is electron's natural orbital velocity around the nucleus, e_O is the permittivity of the free space.

Fig.6. Stable hydrogen atom, where Electron CMF (B_2e) interacted with Proton SMF (B_1p), then at specific magnetic radius (r_me) and electrostatic radius (r_ee), both magnetic force (Fm) and electrostatic force (Fe) are balanced with the centripetal force (F_C ).

Since Eq. {8} represents Eq. (7), therefore the above equation becomes

From Eq.{16}, the following is derived:

From the balance of electrostatic and magnetic forces given by Eq.{17} above, the electrostatic orbital atomic radius r_ee at which an electron stabilised is given by

Relating Eq.{17} with angular momentum introduced by Bohr, in his atomic hypothesis [25], the electrostatic orbital radius r_ee is also given by

While the orbital velocity v_O could be derived from Eq.{32}, or from Bohr atomic hypothesis [25]

Where, h is Planck's constant.

4:2 ELECTRONS’ PARAMETERS AT ORBITAL RADIUS

We assumed that the stability of an atom at certain orbital radius is due to the balance of both F_e and F_m with F_C, as shown in Fig.7, with parameters given in Table.2. Hence the electrostatic atomic radius r_ee (all of the following parameters are derived from Eq.{17}, as given in Table.2.) at orbital level take the form

While the magnetic radius r_me (equal to Bohr radius r_B) takes the form

Where, r_B is Bohr radius, and the SMF radius r_r is given by:

And the NSMF (B_1U) or B_1p for hydrogen atom is given by:

For hydrogen atom, parameters obtained due to the balance of both F_e and F_m with F_C are given in Table.2. From Eq.{22}, the electrostatic atomic radius also could be given by

*Parameters*		*Magnitudes*
*Electrostatic and Magnetic Forces*	*F_e = F_m*	8.257749961 x10^-8 N
*Inter-Atomic Forces*	*2F_c = F_e+F_m*	8.257749961 x10^-8 N
*Electrostatic Atomic Radius*	*r_ee*	0.528566407 x10^-10m
*Magnetic Radius*	*r_me = r_B*	0.5291793603 x10^-10m
*Stable Orbital Velocity*	*V_O*	2190219.655 m.s^-1
*SMF radius*	*r_r*	2.546269208 x10^-12m
*NSMF*	B₁_U	235322.5112 T
*Electron's SMF*	*B_2e*	0.417706473 T
*Magnetic Moment*	*µ_e*	9.284770122 x10^-24J/T

Table.2. Electron's parameters at natural in for hydrogen atom. This Table should be read in connection with Fig.7, and Eqs.{16, 18, 19, 20, 21, 22, 23, 24, 25, 26, and 31}.

4:3 THE MAGNETIC MOMENT

The flipping effect (i.e. the magnetic moment) produced in magnetic resonance experiments [9] are seen as, the response of an energetic charged particle's CMF to any specific magnetic field. For an electron in an atom, this magnetic moment (m_e = E_O/B_U) is obtained by substituting electron’s orbital energy and nucleus SMF given by Eq.{24} in the following sequence

Where, B_1U is nucleus spinning magnetic field (NSMF), m_B is Bohr magneton, m_e is atomic electron magnetic moment related to atom stability.

Eq.{26} can be used to determine the stability orbit for both the electron's CMF and NSMF as shown in Fig.7, and numerically as in Table.2, for atomic hydrogen.

5:0 INTER-ATOMIC ENERGIZATION and the REPRODUCTION of SPECTRAL LINE

From the magnetic interaction hypothesis based on Eqs.{8}, {13} and {14}, any electron gyrating at its natural orbit in an atom under the influence of the spinning magnetic force, continually undergoes an energization process so that it acquires an amount of orbital energy

With reference to Fig.8, whenever such an electron is subjected to an excitation potential, both its kinetic energy and the CMF (B_2e) increases and hence the magnetic force increases as well. This force increases the orbital radius so that the radial energy change is obtained as

Where, v_D is the excitation velocity, r_n is the excited orbital radius. The quanta of energy acquired by the electron at that radius will be radiated as an electromagnetic radiation, the sequence of which is shown in Table,3., with the wavelength given by

From Eqs.{18} and {27}, the general excitation energy at any radial distance within the atomic excitation range becomes

Where, v_n = v_D + v_O , i.e. the excited radial velocity.

*E_D* Ve	*V_n* m.s	*B_2n* T	*F_n* x10^-7 N	*r_n* x10^-11 m	*F_r* x10^-8 N	*E_n* Ve	l Å
5.0	3516424.623	0.6706328886	1.325791924	8.496039785	5.000169275	13.257470411	0935.8503044
3.399525	3283759.893	0.626260367	1.238070714	7.933898117	4.122957183	10.20833388	1215.380283
1.0	2783316.547	0.530818604	1.049389364	6.724776059	2.236143679	4.692853031	2643.809136

Table.3. Samples of sequences through which an excited electron in hydrogen atom transverse, before radiating specific wavelength using Eq.{28}, as shown in Fig.8.

Thus the radiated wavelength l due to such a specific energy quantum (an example of which is shown in Table.4, to be compared with Table.3.) is given by

Hence,

No	E_D Ve	V_n m.s	l Å
1	5.0	3516424.623	0935.8503044
2	3.399525	3283759.893	1215.380284
3	1.0	2783316.547	2643.809137

Table.4 Reproduction of spectral lines by excited electrons, using Eq.{31} and Eq.{32}, reducing steps used in Table.3.

Fig.8. Spectral line sequential reproduction for hydrogen atom. Each quanta of series energy is due to multiplication of both the magnetic level accelerating force (Fn) by the spinning distance (ds). After radiating the quanta of energy, electron is accelerated back to the natural orbit by Fee.

6:0 DISCUSSION

1- Although magnetic fields are produced due to relative motion of charged particles, the direct cause of the magnetic force is here considered to result from the interaction of magnetic fields. This interaction explains the mechanism behind the attractive and the repulsive forces between any two wires carrying electric currents as shown in Fig.2. It also explains the orbital excitation energy characteristics for charged particles and why the direction gyration of an electron is opposite to that of a proton, as shown in Fig.3.

2- The exponential nature of Fig.5 is due to the production of spinning magnetic fields, and above proton's surface (r = 0.468fm) as proved for neutron’s SMF [26], compared with Fig.4.

3- The exact measured magnitude of the nuclear force for the proton is determined by the magnitude of produced B_Tp given by Eq.{9}. In this case it is related to the magnetic moment value. Since the value of the proton's angular frequency (w_p) has been determined as 0.5 rad. sec. (i.e. from Eqs.{26},{27},{28},{29},{30}, and {31}), therefore its spinning frequency (f_ps) is of the magnitude of 0.079577471 s^-1, from which B_Tp is derived.

4- The CMF interaction with the magnetic field (B₁) is represented in Fig.3. The same mechanism occurred inside an atom where the balance of both the F_e and F_m with F_C at specific r_ee and r_me brings stability to the atom, as shown in Fig.7.

5- The nature of the magnetic interaction is that, the weaker CMF (B₂) interacts with the stronger magnetic field (B₁) at two specific points. These two points arise due to the variation in the strength of B_1p as shown in Fig.7, for hydrogen atom.

6- From Eqs.{18}, {20} and {24}, the value of r_ee include proton's radius r_p, and electron's radius r_e. Both are thought to be equal, and derived from Eq.{9}.

7- The Bohr radius (r_B), giving in the right hand side of Eq.{22}, is resulted from the balance of both the Coulomb's electrostatic and centripetal forces, (with value of 0.5291793603x10^-10 m) [27, 28], it gives the same value given by the magnetic radius (r_me), therefore both are equal and given by Eq.{22} and shown in Table.2.

8- The known value for electron's orbital angular momentum (L_o)[29] is 1.054x10^-34 kg.m²s^-1. While the value obtained from Table.2, parameters are 1.054572669x10^-34 kg.m²s^-1using r_ee.

9- Electron's magnetic moment m_e = 9.284770119x10^-24 j/T obtained from multiplication of Bohr magneton (m_B) [30] by 1.001159652193 as verified by experiments [22, 31], is obtained with the same value using any of Eq.{26}, thus Bohr magneton (m_B) gives correct magnetic moment value when using correct parameters (v_O and r_me).

10- The electrostatic radius, r_ee which determined v_o, F_e, r_me, r_r, and B_1U is derived by Eq.{19} using (m_e and h), or Eq.{21}, or Eq.{25}, all of which give the value of 0.528566407x10^-10m, and given in Table.2.

11- The v_o is derived either from Planck's relation Eq.{20} or the radiated spectral line, given by Eq.{32}.

12- The known proton's radius (r_p) [22], is 1x10^-15 m, while from Eq.{9}, r_p=1.1060236231x10^-15m.

13- The excitation energy (E_D) is relative to the ionisation energy[27, 28], for hydrogen atom the ionisation energy, used in Eqs. {27},{28},{29} {30} and{31} is 13.5981 eV[26].

14- For any atom if both the radiated wavelength l and the excitation velocity v_D is known then the electron's natural orbital velocity v_o (at natural orbital radius) can be obtained using Eqs.{20} or {32}.

15- With reference to two points above, atomic spectral lines can be reproduced as shown in Fig.8. While Table.3, shows the reproduction sequential mechanism, and Table.4, summarised all of Table.3, using only Eq.{31}, both tables gives the same results.

16- Energy changes for charged particles therefore take the following two forms:

(a) The normal work done due to the displacement of the magnetic force from the normal orbital radius (r_me) to the excitation orbital radius (r_n) inside an atom, the energy of which is radiated, as shown in Fig.8.

(b)Starting from the single particle micro-level, energy as given by Eq.{14} and shown in Fig.6, electrons and protons can proceed to higher radial energy, due to the produced external magnetic field (ExMF). The several steps of energization may lead to acceleration mechanisms, such as those found in the magnetopause boundary in the transition region [3, 32], both aurora oval [6], and stable aurora red arc system (SAR-arc) [33], radiation belts [3], and the ring current's [6] comprising charged particles.

17- From Fig.5:b. The degree of stability for two nucleons depends on the equilibrium distance, where attraction and repulsion forces are balanced, similar to forces between two atoms [34]. Relative unbalance of the nuclear force magnitude causes the vibration (or oscillation) motion of both nucleons (around 0.7 Fm, as shown in Fig.5.b.). Similar to the molecule's vibration motion of the spring form, associated with energy [35, 36]. Larger nucleus B_TU magnitudes, give higher oscillations and lower nucleus nuclear stability, with the associated energy and consequently leading to decay processes.

18- From point (15), the smallest excitation potential of 1.982807168x10^-3eV can reproduce Pfund series of 74599.21569Å in hydrogen atom. This therefore reveals the precision of all natural phenomena mechanisms.

19- The 1922, silver atoms beam experiment carried out by Otto Stern and Walther Gerlach, where the beam split into two sub-beams on the detecting plate by the action of the electromagnetic field [29].

The experiment is re-interpreted as:

(a) While in motion, the silver atom NSMF foreheads consist of both NSMF.

(b) In uniform field, each forward NSMF detected the field as relatively equal magnitude of B.

Thus F = (B₁) (B_2N) r² c, gives net F = 0.

-NSMF is attracted upward by -F = (+B₁) (-B_2U) r² c.

+NSMF is repelled downward by +F = (+B₁) (+B_2U) r² c.

Therefore the silver atoms formed split on the detected glass.

20- The measured nuclear force between two protons which is (45)² times greater than the electric force [8], is re-interpreted as kinetic energy phase of great accelerated nucleons.

21- The MIH open the door for several new ideas in many fields.

22- Physical constant used, are:

q = 1.60217733x10^-19 C.

m = 9.1093897x10^-31 kg.

h = 6.6260755x10^-34 J.s [12].

e_O= 8.854223x10^-12 C².N^-1.m^-2 [37].

Acknowledgement

My gratitude to my sister Sophya and her husband Abubakar Mohamad and children for their hospitality. The Chairman of Physics Department, University of Nairobi, Prof. B.O. Kola for providing the scientific umbrella, and Dr John Buers Awuor and Dr Lino Gwaki in the Physics Department without whom this work could not have taken the present form. Late Leader Yousif Kuwa Makki, SPLA/M commander in the Nuba Mountains, for his moral supports, The late Dr. Tajudeen Abdul-Raheem, the stuff of Nuba Relief Rehabilitation and Development Organization (NRRDO), particularly Mr Ali Abdulrahman , Amar Amon and Jacob Idriss. Brothers and sisters, Mustafa, Mahamad, Halima, Hukmalla, Arafa, Asha, Ahmad and Esmaeil. Finally, Dr Ali Khogali, Prof.John O. Owino, Dr C. Oludha, Dr P. Baki, Shiekh-Eldien Mousa, Katoo T. Nzivo, Chiromo Library Stuff, Kenya National Library and University of Makerery Library (Uganda).

7:0 Glossaries

B₁: Magnetic field

B_1U: Nucleus spinning magnetic field (NSMF)

B₂: The CMF

B_2e: Electron's CMF.

B_2e: Orbital electron’ CMF

B_2p: Proton's CMF.

B_T: Total Magnetic Field.

B_Tp: Proton's total magnetic field.

CMF: Circular magnetic field.

d_K (d_X = d_Y + d_Z): Energization distance travels by magnetic force.

ExMF: External Magnetic Field.

F_C: Centripetal force.

F_e: Electrostatic force.

F_m: Magnetic force.

f_ps: Proton's Spinning frequency.

h: Planck's constant.

K: Kinetic energy of charged particles.

L_o: Electron's orbital angular momentum.

m_e: Electron's mass.

MIH: Magnetic Interaction Hypothesis.

NSMF: Nucleus spinning magnetic field.

PSMF: Proton's Spinning Magnetic Field.

r_B: Bohr radius.

r_ee: Electron's electrostatic atomic radius.

r_m: Magnetic radius of gyration.

r_me: Electron's magnetic radius (equivalent of Bohr radius).

r_n: Excitation orbital radius.

r_r: SMF radius.

SMF: Spinning magnetic field.

SMF_CA: Attractive spinning magnetic force.

v_c: Charged particles velocity.

v_o: Electron's natural orbital velocity around the nucleus.

v_n = v_D + v_O: The excited radial velocity.

e_O: Permittivity of the free space.

q : Angle between two fields at interaction moment.

l: Wavelength.

m_B: Bohr magneton.

m_e: Atomic electron magnetic moment related to atom stability.

w_p: Proton's angular frequency.

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