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Thread: A thought experiment with Electrostatic forces.

  1. #1 A thought experiment with Electrostatic forces. 
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    Hi everybody!

    I try to figure out what happens in regards to the following situation: Let us assume that we have put an electron exactly in the middle between two metallic parallel plates having both negative and equal amount charge. What will be the reaction of the electron? Normally it is supposed to not move, right?

    Another question is: On the above situation, does the electron absorbs Energy from the electrostatic field of the plates or not?
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    I made the mistake and I put this thread on Relativity. My apologies.

    Ioannis
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    My money would be on it going one way or the other due to quantum uncertainty. It will be in a unstable equilibrium.
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    Hi Jilan!
    Yes due to quantum uncertainty, the electron will appear a minimum vibration, resulting in an unstable equilibrium. That is the most probable. On the hand, the electron could be said approximately that is positioned in the mean of this unstable equilibrium. Supposing that it will stay almost at the center of the distance between the two potentials, then my question is: Does the particle absorb Energy from the electrostatic field? And if yes what is the total Energy of the particle?
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    Quote Originally Posted by Ioannis View Post
    Another question is: On the above situation, does the electron absorbs Energy from the electrostatic field of the plates or not?
    No. Why would it? It would take energy to accelerate an electron but requires no energy for it not to move.
    You can do everything right, strictly according to procedure, on the ocean and it'll still kill you, but if you're a good navigator at least you'll know where you were when you died.
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    Hi Strange, how is it going?

    You are right but partially. Let us say that we remove one of both potentials, then due to the repulsive force the electron will accelerate. Now let us do the same for the other potential: We remove the previous potential and then due to the other, appears again a repulsive force, resulting to electron's acceleration but to the opposite direction. Correct? Correct. Since both potential are equal as also the distances from each potential are equal, the forces will be equal but opposite. In each of both cases a force acts upon the electron or an amount of Energy is transferred through the field, resulting to acceleration (increasing of its momentum). Now from the moment it remains nearly stationary (when both potential are present), the forces continue to apply upon the electron even if it does not move. Consequently, the electron must absorb energy even if it stays still.
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    Quote Originally Posted by Ioannis View Post
    Consequently, the electron must absorb energy even if it stays still.
    No - if the net force is zero, then no work is being done by the field on the electron, and hence no energy is expended. This is the same as in classical mechanics.
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    Ioannis, I misread your question. If both plates are negatively charged the electron would escape out sideways. You might put it instead in the centre of a negatively charged hollow sphere. It would wiggle about in the centre, alternatively absorbing and emitting energy from the field, the net effect over time being zero. Borrowing and releasing energy in good quantum style.
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    OK! Let us take the proposal of Jilan that will make my question more clear. The electron at the center of a negative hollow sphere will appear to wiggle about in the center. Then Markus says there will be NO Energy absorbed by the electron since the net force is zero. Very well! But the forces are always presents developing a symmetrical pressure upon the electron, right? Since there is evidence about an acting pressure upon the electron then why does it not absorb or release energy? This question may also apply in hydrostatics where small volume of a stone sphere immersed in water in a depth of 100 meters under sea's surface will experience always a pressure (a force). It seems that it will not absorb energy, on the contrary it will release energy.

    So the question is would the electron release energy instead absorbing on the above situation?
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    OK Ioannis, prepare yourself! Energy is not absorbed from a field unless there is a net force acting over a distance. The particle or stone has to move under the pressure of the force to gain energy to gain energy from the field. We experience a force under gravity for example but don't gain energy from it unless we are accelerated by it. Energy = force x distance.
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  11. #11  
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    Quote Originally Posted by Ioannis View Post
    So the question is would the electron release energy instead absorbing on the above situation?
    No.
    You can do everything right, strictly according to procedure, on the ocean and it'll still kill you, but if you're a good navigator at least you'll know where you were when you died.
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    Correct Jilan and thanks Strange for the short but fully meaning answer (as usual but I really appreciate your direct way)!

    Please let me re-define my argument because I used the wrong words to describe of what I had in my mind. Let us say that we have a spherical balloon filled with air but with relative hard shell having a known volume at sea level. We immerse it inside and deeply in sea water. As it is understood when the volume is completely immersed inside the water then this volume receive an equal pressure on its surface from all directions. As we go down to deeper waters the pressure will increase that will force the balloon to decrease its effective volume. Now on the other hand if the balloon is set several kilometers above sea level then due to reduced air pressure, it will expand as we know, right?

    Instead of deep waters, we use an equal spherical distribution with increasing negative charge with time. At the center of this distribution we put an atom first (because with the electron we will start the endless discussion about zero volumes).

    Question: Since an atom has a volume as defined by the orbiting electrons, the increasing potential of the spherical distribution will normally force electrons to orbit at higher Energies by reducing the total volume of the atom, right? If the previous are correct, then the atom must normally radiate energy with the aim to reduce its volume or not? Keep in mind that in case the atom will radiate energy, it still remains nearly stationary (due to the equal spherical charge distribution around it).
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    For an electrostatics problem, this thread is morphing pretty quickly. I can envisage that the atom in the centre could become compressed as the field is turned up. In which case having an atom in the middle would increase by a very tiny amount the energy required to turn the field up. When the field is turned down the energy is given back to the national grid. There would be no need for the atom to irradiate photons and no quantum jumps between energy levels.
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    Quote Originally Posted by Ioannis View Post
    then why does it not absorb or release energy?
    Already been answered - because there is no net force acting on it.

    So the question is would the electron release energy instead absorbing on the above situation?
    No - the energy level of the electron will not change at all.

    Keep in mind that in case the atom will radiate energy
    This is a different scenario now, because unlike an electron, an atom is a composite system. This system will not behave the same way as an isolated electron.
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    Markus as I mentioned I used the word words to present my argument. Would the atom be compressed according to my comment #12 as also would it radiate Energy?
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    Quote Originally Posted by Jilan View Post
    For an electrostatics problem, this thread is morphing pretty quickly. I can envisage that the atom in the centre could become compressed as the field is turned up. In which case having an atom in the middle would increase by a very tiny amount the energy required to turn the field up. When the field is turned down the energy is given back to the national grid. There would be no need for the atom to irradiate photons and no quantum jumps between energy levels.
    Jilan, I have to add that there is theoretically no limit of shell's charge increment. As for turning shell's field down, of course will the atom return to its initial status.
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    Sorry if I wasn't clear enough. It won't irradiate energy.
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    Quote Originally Posted by Ioannis View Post
    Markus as I mentioned I used the word words to present my argument. Would the atom be compressed according to my comment #12 as also would it radiate Energy?
    I am not quite sure what you mean by "compressed", but it certainly would not radiate any energy.
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    Between two equally negatively idealized charged parallel plates of infinite size. The electron would stay in the middle. Like in a stable lagrangian point with added quantum effects.

    Inside a negatively charged sphere it would feel nothing since all forces cancel. I guess that at the sub-atomic level of the charged inner surface things get a bit more complex. The electrons in the shell are moving.
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  20. #20  
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    Quote Originally Posted by Jilan View Post
    You might put it instead in the centre of a negatively charged hollow sphere. It would wiggle about in the centre, alternatively absorbing and emitting energy from the field
    The electric field is zero inside a hollow charged sphere (Gauss's law).
    pikpobedy likes this.
    A tensor equation that is valid in any coordinate system is valid in every coordinate system.
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