1. Preamble

Electric Charge emits uniform electric field in all directions around it. So long as the charged
particle is stationary there is no difficulty in understanding its emission. However, when it
was discovered that a particle has spin and magnetic properties attached to it, things required
review about the whole structure of the particle. Discovery of spin and magnetic moment
suggests that the particle must be a dynamical system of magnetic fields and its electric charge
like properties should be the result of the movements of magnetic fields. Keeping this in view,
a dynamical system comprising of a pair magnetic rings spinning around their tangential axis
has been evolved. The system emits uniform electric field and appears to be correct replacement
of electric charge. More so because such a system has inherent spin and magnetic moment.

The proposed theory is conceptually satisfactory and does not need any abstract mathematical 
picture. The theory tells us that there is no electric charge as we understand it now. The
basic structure of the particle comprise of spinning magnetic rings and electric charge like
properties of the particle, are due to this spin

Further the dynamical structure of the particle makes it an electromagnetic system
which has close resemblance to electromagnetic waves.
 

     Lorentz force law state that force acting on a moving charged particle in an electromagnetic
     field is

                                                                                         (1)

    Such force has two components. One is force due to electric field which is 

                                                                                            (2)

   Second part of force is due to action of magnetic field in which the charge Q moves. This is

                                                                                         (3)

   we propose following postulate with the help which we can derive above Eq.(3)

   Magnetic field in motion at a point generates electric field which is equal to cross
   product of the magnetic field intensity and its velocity.

   In other words , electric field generated due to the moving magnetic field is

                                                                                         (4)

 Suppose there is charge Q moving with the velocity v in magnetic field B . Relative velocity of B
 with respect to Q will then be -v.Then according to postulate Eq.(4), electric field generated
by motion of magnetic field will be

                                              

                                                        

   Thus magnetic component of the force

                                              

  This is same as the force law Eq.(3)

   With the help of the postulate stated above, we can construct a dynamical system of
   spinning magnetic rings that would give out electric field very much like that emitted
   by electric charge.

                  
 
 

Fig-1 shows construction of a typical particle. There we see that there are two magnetic
field rings OM and ON each having field intensity B. Size of the ring is of the order of
^{m diameter.The field of the right hand side ring OM is in clockwise direction whilst the}
field of ring ON is counter clockwise. Both the rings are rotating around their common
tangential axis X-X¢in the direction as indicated in the figure. Radius of each ring is r.Since
the rings are spinning around the axis X-X¢, velocity of the ring is highest at the tips M and N.
Let this tip velocity be equal to u.C₁and C₂are the centres of the two rings ON and OM
respectively and P₁ and P₂ are two points arbitrarily chosen on the rings such that radial lines
C₁P₁and C₂P₂ make same angle q with the horizontal. P₁N¢and P₂M¢are perpendiculars
from points P₁ and P₂to the horizontal.
At point P₁ , the magnetic field vector B₁is tangent to the circle of the ring and its direction is
as indicated in the figure. Thus

                                     

^{Let be the velocity of the ring at point P}₁^{. The velocity is perpendicular to the page}
coming outwards in the direction of z axis and its value will be proportional to its distance
from the axis.
 

So
                                    
 

                                           
      Therefore, velocity vector

                                         



 From Eq (4) we get electric field E₁ generated at the point P₁ due to the motion of magnetic
  field

                                          

                                                 

                                                   

                                                   

Because

                                                   

So we have electric field E₁ along the direction of the radius C₁P₁ as shown in the Fig-1.
Same way we can calculate electric field intensity E₂ at the point P_2. Here ,

                                                  
                                         
                            
 

Thus we see that E₁and E₂are pointing in the same direction. Since the distance
between the two parallel vectors is of microscopic dimension, we take the
resultant field as
                                                    
       Therefore                            

The result is that for any value of angle q , the electric field E emitted is same and its
direction is along the radius. So the spinning system of Fig-1, when viewed from any
angle from outside lookslike a positively charged particle emitting uniform electric
field radially in all spherical directions.

If we reverse the directions of magnetic field of rings OM and ON, the spinning system will act
as negatively charged particle.

The spinning system of Fig-1 also possesses energy. It should be noted that magnetic field of the
rings has rest energy, which is proportional to the square of field intensity B ´ Volume. The total
energy of the system will be the rest energy of magnetic field plus kinetic energy of its spin. This
energy constitutes the mass of the system.

Besides it may be noted that such a dynamic system, inspite of the rotations of its rings, does
not radiate energy in form of electromagnetic waves because there is no change in electric field
emitted. Uniformity of electric field is maintained by the fact that electric field emitted by one
ring in any particular direction is compensated by that of the other ring in that same direction
such that the constancy of the field is maintained in all directions. Since the system does not
radiate or give away its energy, it is a stable system that keeps its energy to itself.

Thus we can see that the spinning system of Fig-1 is a unique rotating system that satisfies all
conditions expected of a particle. Over and above that such dynamic system has inherent
properties like spin, magnetic moment and magnetic polarization.

We may state that a sub-atomic particle is a dynamic system comprising of a pair or pairs of
magnetic rings rotating around the common tangential axis. It acts as a stable particle having
(1) Electric Charge (2) Mass (3) Spin (4) Axis of polarization and (5) Magnetic Moment.
 
 

         Suppose there is a particle comprising of a pair of spinning magnetic rings such as shown in
         ^{Fig-1. Let the frequency of spin be equal torevolutions per second.}

         So long as the spin frequency is constant, the particle is stable and does not radiate energy.
         However, when the particle is disturbed by external forces so that its spin frequency is reduced
         ^{from to say , then an electromagnetic wave is emitted by the particle. The}
         frequency of the wave or the photon so emitted will be equal to the difference or the beat
         ^{frequency. In this case it will be. The energy carried by the photon will bewhich}
         should be same as the energy lost by the particle. So we may state that if the energy of a
          particle is initially equal to E then after the loss of a photon it will be

          Now suppose if the spin frequency is reduced to zero, the particle will loose all its energy
         ^{and vanish. Then .This gives}
                                           

                                        ^or 

          Thus we see that the total energy of the particle is equal to its Spin Frequency ´ Planck’s
          Constant. It may be noted that Eq (14) is derived on the basis of beat frequency photon
          generated due to the change in the spin frequency.

          Here we see a close link between Particle and Electromagnetic wave. Both have
          common components namely electric and magnetic fields and both have same equation
          ^{for energy i.e.. In one case the frequency is the frequency of spin and in the other}
           it is  the frequency of the wave.

         A particle may also gain energy when struck by electromagnetic wave or accelerated by
         external forces. In that case spin frequency will increase. In other words spin frequency
         is the overall measure of particle’s energy.

         However the energy of a particle is
                                           
                                                            Combining Eq(14) and (15) we get

      4. Equivalent Electric Charge
 
 

                                        
            To calculate equivalent charge of the whole system, we assume charges q₁ and q₂at the
                center of each ring as shown in Fig-2. The equation for electric field at a distance r
                (radius of the ring) due to a charge q₁is

               Here e_o is the permittivity of the medium, q₁ is charge at the center of ring ON and
               r is radius of the ring.

               For charge q₂ of ring OM we get

                The net effective electrical intensity due to both rings will be
 

                     ^{Here is the equivalent charge of the whole system, which will be}

                    Again

                    Therefore

                   In terms of diameter of the ring R=2r the equation becomes

             5. Equivalent Mass

         Mass associated with energy is given by

                                                            

         ^{Since the energy E of the particle iswe get equivalent mass of the particle as}

                                                             

       Total Energy of the particle comprises of the rest energy of the magnetic field of the rings
       plus the kinetic energy of the spin. The rest energy of the magnetic field is too small to be
       considered. Main contribution is that of the kinetic energy.

       Fig-3 shows two spinning rings with their thickness d which is the diameter of its circular
       cross-section. Here we can see that velocity of two tips M and N is highest. So when the tip
       velocity u is very near to the velocity of light c, the kinetic energy of the tips becomes so high
                           
 

       that the energy of other parts of the ring becomes insignificant. In other words mass of the
       particle is mainly concentrated in the two tips M and N.

       ^{If E is the total energy andis the rest energy of the two tips then relativistic equation}
       for the total energy of the tips become

                                                   
 
 

         ^{The ratiobeing very high, the value of uis almost equal to c.}
         So for all practical purposes we can take

                                           

         The Eq (20) for equivalent charge then becomes

             Since the tip velocity equals to the velocity of light c, and R is the diameter of the ring
             ^{which is the radius of rotation and is the number of revolutions per second.}

                                           

                                                        

            This indicates that the diameter of the rings shrinks as the spin frequency increases.
            This is because of the limitations of the tip velocity which cannot exceed the value of c.

            In Sec-4 we saw that

                                                       

                                                    Combining Eq (26) and (27) we get

                                                       

            Thus we see that the diameter of the ring decreases as its mass increases. This means
            that the size of electron must be nearly 2000 times bigger than proton.
 
 

             We have seen that when a particle gains energy, its size reduces. So when a particle is
             accelerated by external forces, its total energy increases. As a result, its spin frequency
             increases and the diameter of its magnetic rings decreases.

             For example when an electron is accelerated so that its total energy is increased say one
             hundred times then its size gets reduced to one hundredth.

             This applies to both linear acceleration as well as circular motion. As the particle gains
             speed, its size decreases.
 

             It is generally observed that charge of particles is always constant. It is either +e or –e.
             This is irrespective of the mass of the particle. For example, we find that electron and
             proton has same charge although the former is 2000 times lighter than the latter. This is
            ^{so because total magnetic fluxof the ring remains constant and that the ratio of the}
             diameter of the ring to the diameter of its cross-section remains constant. Let us take
            ^{diameter of cross-section as d as shown in Fig-3. Then we assume that ratio}
             is always constant when the ring either expands or shrinks.

             Then total magnetic flux in the ring cross-section will be

                                                          

             Charge of the particle

                                                          
 
 

             From Eq (24) and (29), we get
 
                                                         

           ^{The right hand side of the equation is constant because ratio is constant.}

                                              Thus 

           ^{Thus we see that so long as the flux of the ring is constant, the charge of the particle}
            remains same irrespective of change in its mass.

             Angular momentum of the spin will be

                                                             

             Here m is the relativistic mass, which is concentrated near the tips M and N of rings
             (see Fig-3), u is the tip velocity which is equal to the speed of light c and R is the radius
             of rotation, which is equal to the diameter of the ring.

                                               

                                                              

                                                             
 

               Let us take example of Electron. Mass of electron as known to us, is

                                                            
              Therefore, its spin frequency

                                                            

              The diameter of the magnetic ring of the electron will be

                                                           

             ^{The electron charge Coulomb. From this we can work out flux
             densitywith the help of Eq (24)}
 

                                             

                                             

                                                                    

               It may be noted that magnetic intensity of ring is quite high compared to the intensities
               of magnetic fields that we find in ordinary magnets.
 
 

                ^{For proton mass. The corresponding spin frequency will be}

                                                                  

               The diameter of the proton ring will be

                                                                     
 

              We can find the flux density of proton ring
                                                                   

               In all probability, proton is a multi-pair particle i.e. the particle with more than one pair
               of spinning rings. In that case, the values worked out as above may need correction.
 
 

                      Neutron must be a multi-pair particle. Simplest form we can imagine comprises of two
                      pairs. One pair generates positive electric field and the other negative electric field of the
                      same magnitude. The two fields cancel one another and the particle behaves like an
                      electrically neutral one.

                      Neutron may have more than two pairs of rings. Some pairs generate positive field and
                      others generate negative field. Sum total of all the fields is zero.
 

             14. Mass less Particles

                      Multi-Pair particles are those having more than one pair of spinning rings. Neutron is just
                      one example of such multi-pair particle. Most of the heavy particles are likely to be
                      multi-pair  particles. Such particles may have any number of pairs of rings, not just two.

                      For example a neutron may have as many as three pairs. Let us suppose each pair has its
                      ^{own charge and mass. Sayare the charges of each individual pair and
                      are corresponding mass values. Then}

                       because neutron is electrically neutral. Its mass will be

                       During collision the pairs separate, resulting into several fragments. In the above example,
                       there will be three fragments.

                       It is interesting to note that a multi-pair particle of positive charge can have a negatively
                       charged component also. That is how we find positive and negative fragments of a particle
                       which was originally just a positive one.

              16. Magnetic Moment of a Particle

            Unit of magnetic moment is

                                                                 

            This equation has been derived on the basis of loop current ´area of the loop. We now
             know that magnetic moment is the torque produced due to magnetic dipole field of the rings
             of the particle interacting with external magnetic field in which the particle is placed. It is like
             the torque experienced by a magnetic needle placed in a magnetic field. So we may translate
             above Eq (43) in terms of the magnetic flux of the rings and their diameters.

            ^{We substitute values for}

                                                                   

              From Eq (28) we get

                                                                    

                                 

              Magnetic flux of the ring is
                                                                

                                        

                      The quantity in the bracket [ ] is a constant because R/d is constant as stated in
                      the Sec-9 earlier. So we see what is obvious. Magnetic moment being the torque
                      experienced by a particle when placed in an external magnetic field is proportional to
                     ^{the total fluxof the rings ´total width}

                 17. Magnetic Moment of Multi-pair Particle

                     For a multi-pair particle, magnetic moment of the particle will be sum of moments of
                     Individual pairs. Let us take an example of a neutral particle described in Sec- (14). Here

                     ^{Total electric charge is. The magnetic moment will be}

                                                                     
 

           The expression in the bracket above need not necessarily be zero because ratios of
           charge to Mass of individual pairs may not be same. This explains why a neutron, which
           is electrically Neutral has non-zero magnetic moment. Same argument applies to other
           multi-pair particles wherein their equivalent electric charge and their magnetic moment are not
           in same proportion

               18. Electric Charge

                     We now know that there is nothing like electric charge carried by a particle. It is the charge
                     like properties of spinning magnetic rings.

                    An important fact that we have been observing all the time, is that electric charge can never
                    be separated from matter. The magnetic ring theory tells us the reason why it is so.

                   We have been dealing with electric charge since centuries. So we cannot eliminate the notion
                    of the charge. We have to continue with it as equivalent charge just the way we have been
                    continuing with the direction of electric current from positive to negative although we know
                    that in reality the flow is in the reverse direction.
 

              19. Point Charge

                    One of the riddles posed by electric charge is about infinite magnitude of force that acts
                    between two point charges when brought close to one another. Now when we look to the
                    structure of particle (fig-1), we see that there is nothing like point charge. The particle emits
                    electric field from peripheries of its magnetic rings. The force between two particles never
                    blows to infinity however, small is the distance between them.
 

             20. Interaction at close distance

                   One interesting aspect of magnetic ring theory is that the electric field radiated by the particle
                   is not uniform when viewed from close distance – distance comparable to the size of the
                   particle. Vector sum of E₁and E₂(see Fig-1) is not equal to (E₁ + E₂ ) at that small distance.

                   Therefore, the inverse square law does not apply when separation between two
                   particles is comparable to there size. In that case the force between the particles becomes
                   a complicated interaction between the fields of two particles.

            21. Conclusion

                  The Magnetic Ring Theory as described here may not be complete by itself. It may need
                  modifications as it develops. However basic idea of replacement of electric charge by
                  dynamic system solves many problems that hitherto remained paradoxical. The theory answers
                  in simple mathematical terms almost all question about subatomic particles. It is conceptually
                  satisfactory. It explains :

1) Significance of mysterious spin and its spin frequency.

2) Close link between particle and electromagnetic waves.

3) Magnetic moment and magnetic polarization of the particle.

4) Size and shape of sub-atomic particles. We now know that heavier particles
    are smaller in size.

5) Constancy of electric charge.

6) Mass is all energy which is mostly kinetic energy.

7) Annihilation of Electron/Positron pair and its conversion to Electromagnetic Waves.

                                                                            15-Jan-2001

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Ó 2000