This article should show that static crossed electric and magnetic fields force electrons to move in one direction. This can be used to produce an electric current. While moving, they convert heat into electric energy, which would contradict the 2nd law of thermodynamics. The first part of the article shows the principle of the idea. The second part describes some possible applications.
Given is a situation of a static electric field E in -y direction and a static magnetic field B in z direction (in a vacuum), see Fig. 1. Every electron in these crossed fields is forced to move in cycloids in the x direction. The initial speed and direction only influence the type of cycloid, but not the overall direction - this is always the x direction. This effect is described in every good physics book.
Fig. 1: In a crossed electric and magnetic field every electron (regardless of its initial speed and direction) moves in the same direction
Fig. 1 shows an example: At position (1) an electron is accelerated in y-direction because of the electric field E. The electrons have a certain speed and because of the Lorentz-force of the magnetic field it will divert right towards the x direction (2). At (3) the electron has the highest speed and will further divert right and so move towards point (4). Since it goes up an electric potential, it slows down and at (4) it stops. And at this position the same happens again, it will be accelerated again, will divert, comes to position (5) and so on ...
Fig. 2 shows another situation, again in vacuum: In part I and III there are no fields, however in the middle part II there are again the crossed electric and magnetic fields.
Fig.2: All electrons are pumped from part I into part III
So more and more electrons go from part I into part III, but none of them can return from III to I. So after a finite time, all electrons from part I are moved to III.
Most importantly, the movement of electrons is not driven by the energy taken from the fields. The fields are only used to divert the electrons in the x-direction. This is the main difference to the normal situation WITHOUT a magnetic field: The electrons are accelerated by the electric field, so they gain energy from this field. WITH a magnetic field the electrons gain NO ENERGY of the fields, because the speed will not be increased.
In Fig. 3 part I and III are connected with a switch. Since in part III there are no electric fields there is the same electron distribution. If the switch is opened, electrons will move into part I.
Fig. 3: If the switch is opened, electrons flow into part I.
If the switch remains opened, electrons will flow clockwise through this arrangement. If the switch is closed electrons are collected again in part III.
Suppose the switch automatically opens if a certain potential difference at the two sides of the switch is reached, then the switch opens and closes periodically. So electrons periodically flow at the switch into part I and this causes a pulsed magnetic field which can be used to produce an electric current (like in a transformer).
If this method would work, electric energy could be produced. But from which source should the energy come? If Fig 3 you can see that in part III there are more electrons than in part I. So if an electron is in part II and is forced to move towards part III it has to move against an electric potential and so it converts some of its kinetic energy into potential energy. When it arrives in part III it has a lower kinetic energy and therefore a lower temperature than an average electron in III. The electron with the lower temperature absorbs kinetic energy at the next pushes with the walls. So every electron which reaches part III will COOL DOWN this part but INCREASE the electric potential. This potential can be used for an electric current. So heat is converted into electric energy.
If an electron in part I has not enough kinetic energy to climb up the potential at the part III, it cannot go in this part. This method therefore works at best with high temperatures.
This idea does not contradict the 1st law of thermodynamics, since the whole energy will be conserved, only the distribution will be changed. However it contradicts the 2nd law of thermodynamics, since heat energy (and not only heat difference) will be converted into electric energy.
As shown in Fig.3, at both sides of the switch there will be produced an electric potential. This can be used directly to generate an electric current, moreover if more of these arrangements are put together, the potential could be multiplied, see Fig. 4.
Fig. 4: More arrangement can be put together to increase the potential
This arrangement can be simplified, because the parts I and III can be removed. Inside the metal plates there is no electric field from outside, so the electrons do not move in cycloids. So they behave like inside parts I and III, see Fig. 5. Though there is an influence charge at the plates because of the external electric field, the function is the same.
Fig. 5: A simplified structure
Instead of vacuum, it is also possible to take very small layers of semiconductors. The reason is that it inside the material it remains a part of the external electric field, the space charge area (in contrary to metals). In the layer, collisions occur and after that the direction of an electron is random. However the electron is immediately forced to go in cycloids in the same direction as before the collision. If the relaxation time is high enough, it can be shown that the average direction of electrons are not influenced by collisions, see Fig. 6.
Fig.6: Though there are collisions, the electrons move in average in the same direction.
Another interesting application is by using electrolytes, like accumulators. In this case there are positive and negative ions in the electrolytes, which can be forced to move in one direction. Unfortunately, the positive and negative ions are moving in the same direction, so this cannot be directly used. However, because of the electric field, the ions are separated and this can be used, see Fig. 7. In the upper zone there are mainly negative ions, which are forced to move to the right. In the lower zone, there are mainly positive ions. The magnetic field in this zone is reversed, so these ions move to the left.
Fig. 7. In electrolytes positive and negative ions are diverted in different directions, when the magnetic field in the upper and lower zone is reversed
Normally such a stream of ions, the positive in one direction and the negative in the reverse, is produced by an electric current. In this case it is produced by static fields and the energy comes from the heat energy of the ions. This method can be used to charge up accumulators by simply converting heat into electric energy.
Gerhard Kainz
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