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Preface

Let us suppose that there is a device which helps us to fuse any object having an extremely small size with an air molecule such that after fusion, the position of the air molecule remains static wrt the Earth irrespective of any environmental disturbances, drag forces or any other factors which may disturb the configuration of the air molecule

Main Question

A one-dimensional plate having a charge of -$Q$ spread evenly throughout its length is placed on the Earth's surface. Another plate with identical dimensions but with a charge +$Q$ spread evenly throughout its length is held statically at a height of $R$ from the Earth's surface. An air molecule which is precisely at the median(from a distance perspective) between the 2 charged plates is chosen and a massless hook is fused to it. From the hook, we attach a nanowire(considering it massless as well but having a tensile ability) and manually extend it vertically downwards and at the point where the nanowire is just about to make contact with the charged plate placed on the surface, we attach an electron to its end. The electric field intensity is E and the acceleration due to gravity is g. Mass of the electron is m . What must be the horizontal velocity to be supplied to the electron at its lowermost point(from the ground frame) for it to complete a vertical circular motion and in its path, it should brush through both the plates. We can corelate this situation to the circular motion of an electron between capacitor plates.

Several Important considerations

  1. For the time-being, we must ignore drag forces and any other contact forces that may have an impact in reality on the scenario.
  2. The charged plates must be considered stationary from the frame of the Earth.
  3. The plates are sufficiently long enough so that at all points during it's circular motion, the electron remains in the Electric Field region.
  4. The two plates are placed parallelly.
  5. Variation in gravity is negligible as we move away from the surface.
  6. Consider the electron only as a classical particle and all quantum interactions are to be ignored

With all these considerations in mind, first of all- If such conditions are actually reciprocated, will the electron undergo circular motion in the first place? If yes, what will be the horizontal velocity value. Also we can exclude the effect of gravity because it is an electron and won't be much impacted by gravity but if we consider the impact of the gravitational force on the electron's motion, then how much deviation will occur compared to as previously stated. Also, are there any other forces or key factors that may have an impact but I have missed out on counting them?

This is a self-devised question and therefore could have a great amount of errors in it. Please feel free to point them out in the comments.

Thank You!!

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    $\begingroup$ There is a basic misunderstanding here. You are ignoring that molecules and electrons are quantum mechanical entities and you are treating them like classical particles. It is only when they are not interacting that quantum particles have trajectories. ( an electron turning in a magnetic field for example) When you talk of "attaching" and using "hooks" the problem needs quantum mechanical interactions , $\endgroup$
    – anna v
    Commented Feb 10, 2022 at 20:09
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    $\begingroup$ for difference between trajectories and quantum states see my answer here physics.stackexchange.com/questions/693591/… $\endgroup$
    – anna v
    Commented Feb 10, 2022 at 20:22
  • $\begingroup$ @annav Thank u for your reply. Honestly, I knew that the quantum nature of electrons will surely have an impact on the motion. That was one of the important considerations that I should have mentioned but forgot to do so I have made the required edits . I could have chosen any negatively charged particle to serve the same purpose but an electron if considered only classically has 2 advantages $\endgroup$
    – Krish Ratta
    Commented Feb 11, 2022 at 3:43
  • $\begingroup$ - 1.It's extremely small mass provides a new prospect to the calculation. 2.For the time being, I only want to get a grasp of what is happening in general and once I understand that, I can consider actual factors like wave nature and quantum interactions and their effect on the scenario. $\endgroup$
    – Krish Ratta
    Commented Feb 11, 2022 at 3:44
  • $\begingroup$ I am saying that this is a science fiction scenario, you cannot attach a wire on an electron without quantum mechanics. $\endgroup$
    – anna v
    Commented Feb 11, 2022 at 4:32

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