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The EM-rotator



The EM-rotator

When you are inter­ested in physics you must read “Unbe­liev­able”!

When both masses are not con­nected through a rigid mass less rod and are charged masses, like the elec­tron (Me) and pro­ton (Mp) in the hydro­gen atom, the above prop­er­ties of the mechan­i­cal free rota­tor must also be valid in sta­ble situations.

To obtain a free EM-​rotator with sta­ble orbits, the func­tion of the mass less rod must be taken over by forces work­ing on elec­trons and nucleus in the atom. All forces must be neutralized/​equalized dur­ing the rota­tion of the elec­tron around the pro­ton at any time.

In a sta­ble sit­u­a­tion, the fol­low­ing mechan­i­cal con­di­tions for pro­ton (Mp) and elec­tron (Me) in the hydro­gen atom must be valid:

The cen­trifu­gal force Fc, work­ing equally on pro­ton and elec­tron, must be com­pen­sated by inter­nal forces; the elec­tro­sta­tic force Fe. We con­sider the EM-​free rota­tor where the cen­trifu­gal force (Fc) is com­pen­sated at all times by the elec­tro­sta­tic force (Fe). This assump­tion implic­itly assumes that the elec­tron is in a steady orbit around the proton.

The addi­tional mechan­i­cal require­ments for the steady EM-​rotator are:

and

The equi­lib­rium solu­tion for the free and sta­ble EM-​rotator is:

(1)

Where Re is the dis­tance of the elec­tron to the rota­tion point of the sys­tem (fig­ure 1), Me the mass of the elec­tron, Mp the mass of the pro­ton, Ve the rota­tion speed of the elec­tron, e the ele­men­tary charge of the elec­tron and εo the dielec­tric con­stant in vacuum.

Remark: In the pre­vi­ous chap­ters the ele­men­tary charge of the elec­tron was named “Qe”. In this chap­ter the ele­men­tary charge of the elec­tron is called “e” because in physics arti­cles that is the nor­mally used sym­bol for the charge of an electron.

This equa­tion describes the radius Re of the orbit­ing elec­tron as a func­tion of the rota­tion speed Ve in the sit­u­a­tion where the sys­tem is sta­ble (dE/dt=0) and the orbit­ing speed is con­stant (dVe/dt=0). Ana­lyz­ing this equa­tion we observe that for any speed of the elec­tron Ve there is a pos­si­ble solu­tion Re.

The sit­u­a­tion in fig­ure 1 sketches also the sit­u­a­tion where the elec­tron and pro­ton are both in a steady orbit around O. The elec­tro­sta­tic force Fe com­pen­sates now the cen­trifu­gal force Fc.

As there is for any speed of the elec­tron Ve also an orbit dis­tance Re where all forces are in equi­lib­rium, there are infi­nite solu­tions and so there are no the­o­ret­i­cal solu­tions based on this model that resem­ble the real­ity of fixed energy levels.

The pro­ton and elec­tron have, besides mass, also a charge. Because pro­ton and elec­tron do not move rel­a­tively to each other in a sta­ble orbit­ing sit­u­a­tion there are no induced mag­netic fields.

The mov­ing elec­tron and pro­ton would each present an elec­tric cur­rent when the cen­trifu­gal force is not (com­pletely) com­pen­sated by the elec­tro­sta­tic force. The mag­netic fields induced by elec­tron and nucleus, when there is no elec­tro­sta­tic force (Fe=0), would induce a max­i­mum mag­netic force Fm between pro­ton and elec­tron equal to:

This mag­netic force Fm, when rel­e­vant, would be neg­li­gi­ble com­pared to the elec­tro­sta­tic force Fe. The nuclear forces are neg­li­gi­ble at the mol­e­c­u­lar distance.

A mov­ing charge presents dynamic energy in the form of mag­netic energy. The Rutherford-​model was con­sid­ered not sta­ble because the cir­cling elec­trons around the nucleus would loose energy by emit­ting radi­a­tion; so a sta­ble EM-​rotator like the Rutherford-​model was con­sid­ered impos­si­ble. A mov­ing charge can emit radi­a­tion and loose energy, but it is not true that a mov­ing charge in all cir­cum­stances has to loose energy. We refer to the arti­cle “The Equiv­a­lence of mag­netic and Kinetic Energy” where it is proven that both energy forms are iden­ti­cal. A mov­ing mass can infi­nite cir­cle with­out loos­ing energy and so can a charge. When there is abun­dance of energy a charge may oscil­late. This oscil­la­tion energy is redun­dant energy and can there­fore induce/​emit elec­tro­mag­netic radiation.

Next chap­ter: The Energy Level of the Hydro­gen EM-​free Rota­tor Atom

When you are interested in physics you must read “Unbelievable“!

When both masses are not connected through a rigid mass less rod and are charged masses, like the electron (Me) and proton (Mp) in the hydrogen atom, the above properties of the mechanical free rotator must also be valid in stable situations.

To obtain a free EM-rotator with stable orbits, the function of the mass less rod must be taken over by forces working on electrons and nucleus in the atom. All forces must be neutralized/equalized during the rotation of the electron around the proton at any time.

In a stable situation, the following mechanical conditions for proton (Mp) and electron (Me) in the hydrogen atom must be valid:

      

   

The centrifugal force Fc, working equally on proton and electron, must be compensated by internal forces; the electrostatic force Fe. We consider the EM-free rotator where the centrifugal force (Fc) is compensated at all times by the electrostatic force (Fe). This assumption implicitly assumes that the electron is in a steady orbit around the proton.

The additional mechanical requirements for the steady EM-rotator are:

and

The equilibrium solution for the free and stable EM-rotator is:

 (1)

Where Re is the distance of the electron to the rotation point of the system (figure 1), Me the mass of the electron, Mp the mass of the proton, Ve the rotation speed of the electron, e the elementary charge of the electron and εo the dielectric constant in vacuum.

Remark: In the previous chapters the elementary charge of the electron was named “Qe”. In this chapter the elementary charge of the electron is called “e” because in physics articles that is the normally used symbol for the charge of an electron.

This equation describes the radius Re of the orbiting electron as a function of the rotation speed Ve in the situation where the system is stable (dE/dt=0) and the orbiting speed is constant (dVe/dt=0). Analyzing this equation we observe that for any speed of the electron Ve there is a possible solution Re.

The situation in figure 1 sketches also the situation where the electron and proton are both in a steady orbit around O. The electrostatic force Fe compensates now the centrifugal force Fc.

As there is for any speed of the electron Ve also an orbit distance Re where all forces are in equilibrium, there are infinite solutions and so there are no theoretical solutions based on this model that resemble the reality of fixed energy levels.

The proton and electron have, besides mass, also a charge. Because proton and electron do not move relatively to each other in a stable orbiting situation there are no induced magnetic fields.

The moving electron and proton would each present an electric current when the centrifugal force is not (completely) compensated by the electrostatic force. The magnetic fields induced by electron and nucleus, when there is no electrostatic force (Fe=0), would induce a maximum magnetic force Fm between proton and electron equal to:

This magnetic force Fm, when relevant, would be negligible compared to the electrostatic force Fe. The nuclear forces  are negligible at the molecular distance.

A moving charge presents dynamic energy in the form of magnetic energy. The Rutherford-model was considered not stable because the circling electrons around the nucleus would loose energy by emitting radiation; so a stable EM-rotator like the Rutherford-model was considered impossible. A moving charge can emit radiation and loose energy, but it is not true that a moving charge in all circumstances has to loose energy. We refer to the article “The Equivalence of magnetic and Kinetic Energy” where it is proven that both energy forms are identical. A moving mass can infinite circle without loosing energy and so can a charge. When there is abundance of energy a charge may oscillate. This oscillation energy is redundant energy and can therefore induce/emit electromagnetic radiation.

Next chapter: The Energy Level of the Hydrogen EM-free Rotator Atom

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