Electronics > Metrology

Coulomb's law and a voltage frame of reference

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Zeranin:

--- Quote from: IanB on May 11, 2016, 12:44:45 am ---
--- Quote from: Zeranin on May 10, 2016, 11:54:17 pm ---What I am asking, is where does the energy come from to accelerate a single bunch of electrons, while they are in transit, before they strike the phosphor? I have put forward the proposition that the only place this energy can come from is the EHT power supply, which means that current would need to be drawn from the supply during the transit time. Assuming you agree with this, how can such a current exist, given that during transit, the electrons do not touch and are not collected by the anode or any electrode. It’s a fair question, and as yet we have no answer. Where is Catalina to WOW us with the answer?

--- End quote ---

Firstly, the electrons left the cathode before they started on their journey. Since the electrons carry charge, they discharged the cathode a little at this point.

Next, the electrons are accelerated through the electric field towards the anode, gaining energy as they go. Since the electrons in motion form an electric current, the moving electrons are actually creating a magnetic field. In this process, some potential energy from the electric field is being converted to stored energy in the magnetic field around the electrons. As the electrons are accelerated, the electric field is weakened (by whatever minuscule amount). Given sensitive enough measurements, the potential difference between the anode and the cathode while the electrons are in transit could be observed to be decreasing. It is as if an inductor has been connected in parallel with a capacitor and some energy is transferred from the capacitor to the inductor.

It might be imagined that the voltage on the capacitor remains constant during the journey of the electrons and drops suddenly when the electrons strike the anode. But this will not be found to be the case. What will be found is that the potential difference remains the same at the moment the electrons leave the cathode, it will then drop gradually as the electrons are accelerated, and it will stop dropping once the electrons strike the anode.

(It might be asked what happens to the stored energy in the magnetic field created by the fast moving electrons? Since there is no recovery path for this energy, it will be dissipated on the collapse of the magnetic field as heat (from eddy currents) and low energy radiation.)

--- End quote ---

Hi Ian,
I’m glad you find the problem of sufficient interest to think about it, and you clearly understand that there is a ‘mystery’ here, that requires explanation.

One thing is not clear about your reply. In a CRT system, the cathode-to-anode voltage is fixed, this being the EHT supply voltage, and all my discussions have been on that basis. However, you seem to be considering the case where there is no EHT power supply as such, but only a capacitor to maintain the cathode-to-anode potential, is that correct? Assuming that you are in fact considering the case where there is no EHT power supply, I believe that your posting is largely correct, but still incomplete.

It has taken me a while to reach my own conclusion about the exact correct explanation, but FWIW I finally feel confident in my understanding, so will relate it here. I will describe the situation with a fixed-voltage EHT supply between anode and cathode.


--- Quote ---Firstly, the electrons left the cathode before they started on their journey. Since the electrons carry charge, they discharged the cathode a little at this point.
--- End quote ---

Usually the cathode is at ground potential, connected to mother Earth via the mains ground wiring, so the cathode potential won’t actually change after squirting out a bunch of electrons. In any event, we have a fixed voltage between anode and cathode, and this is the only thing that matters as far as the electric fields inside the CRT are concerned, so our analysis need not be concerned with the fact that our bunch of electrons came from the cathode.

It is true that moving charge produces a magnetic field, and also true that accelerated charge produces EM radiation, but both these effects are very small, and in my view have nothing to do with the true explanation of what is going on, and consideration of either is certainly not necessary to explain what is going on, so I will leave magnetic and EM effects out of the discussion altogether.

We agree that energy is required to accelerate our bunch of electrons while in transit, and I proposed that the only place that this energy could come from is the EHT power supply, and I maintain this is the case. During transit, current is drawn from the EHT supply, even though the anode-cathode voltage remains constant, and even though the moving electron bunch never contacts the anode or any electrode.  Furthermore, there is not a pulse of EHT current when the electrons actually strike the anode.

The question then, is how can current be drawn from the supply, when the electrons are in transit, and not touching or collected by the anode or any other electrode?

The explanation is subtle, and is concerned with the movement of charge (ie a current) through induction. As the electrons approach the anode, they attract positive charge (or repel electrons, same thing) to the anode, as per Coulomb’s Law. The only way that additional positive charge can get to the anode is from the EHT supply, so that is exactly what happens, current flows from the EHT supply to the anode. As the electrons get closer to the anode, they attract still further positive charge, with the result that there is a constant flow of current from the EHT supply to the anode, for the entire time that the electrons are moving from cathode to anode. The relationship Q=CV is in effect maintained at all times, except that Q includes a contribution from the moving bunch of electrons. As the electrons get closer to the anode, they increasingly ‘neutralize’ some of the +ve charges on the anode, and so additional +ve charge has to flow from the EHT supply to the anode, to compensate. By the time the electrons are only a tiny distance from the anode, about to strike it, the total negative charge that has flowed from the anode to the EHT supply is exactly equal to- ve charge about to strike the anode, as must be the case to maintain Q=CV, where Q is the net charge consisting of the charge on the anode, and the moving charge that is just about to strike the anode. Thus, when the moving electrons actually strike the anode and are absorbed into it, there is no pulse of anode current because Q=CV is already satisfied, and the EHT current to the anode that has been present for the entire electron journey ceases. At all times, all the equations of Physics are satisfied, and at all times during the transit and acceleration of the bunch of electrons, current is being drawn from the EHT supply, to provide the power for accelerating the electrons. Everything adds up. If it did not, then I would not sleep at night.

IanB:

--- Quote from: Zeranin on May 11, 2016, 03:34:17 am ---One thing is not clear about your reply. In a CRT system, the cathode-to-anode voltage is fixed, this being the EHT supply voltage, and all my discussions have been on that basis. However, you seem to be considering the case where there is no EHT power supply as such, but only a capacitor to maintain the cathode-to-anode potential, is that correct?
--- End quote ---

Yes, I realized after the fact that I didn't define the basis of my system model very well. I had in mind the earlier question about the ion thruster, where the electrode once charged up was isolated. By analogy, I considered the case where the anode and cathode of the CRT were charged up by the EHT supply and then the supply was disconnected, so that only the stray capacitance remained to maintain the potential difference (and in my perfect world there are no leakage currents to allow the charge to drain away).

The interesting question to me then became, what would happen to the potential difference between anode and cathode during the time the bunch of electrons were accelerated from cathode to anode? I concluded that the potential difference would gradually decrease since the only source of energy to accelerate those electrons is the energy stored up in the electric field of the capacitance between anode and cathode. The electrons acquire energy, so another part of the system must lose energy to balance it. The only source of that energy is the electric field accelerating the electrons, and nature will not be denied; ergo the field energy must be depleted and the potential difference must decrease.

It is then a small step to conceptually reconnect the EHT supply and observe that it will replace the lost charge in the stray capacitance by supplying some current.


--- Quote from: Zeranin on May 11, 2016, 03:34:17 am ---During transit, current is drawn from the EHT supply, even though the anode-cathode voltage remains constant, and even though the moving electron bunch never contacts the anode or any electrode.  Furthermore, there is not a pulse of EHT current when the electrons actually strike the anode.
--- End quote ---

This I also concluded, as evidenced by my statement here:


--- Quote from: IanB on May 11, 2016, 12:44:45 am ---It might be imagined that the voltage on the capacitor remains constant during the journey of the electrons and drops suddenly when the electrons strike the anode. But this will not be found to be the case. What will be found is that the potential difference remains the same at the moment the electrons leave the cathode, it will then drop gradually as the electrons are accelerated, and it will stop dropping once the electrons strike the anode.
--- End quote ---

The gradual drop in potential difference across the stray capacitance if isolated would correspond to the gradual supply of current from the EHT supply during transit if it were connected.

Zeranin:
We are in complete agreement, IanB.  :)  That's the great thing about science and engineering. After sufficient thought and discussion, agreement is always reached.

John Heath:
Great posts guys. I'm liking the electron slowly changing the high voltage in transit for the CRT.

The + and - 1 inch square monopole are complete. They are acting as predicted. They will not stick to each other nor a fridge. This is good.

However the complementary monopoles should have acted like an electron and positron. This did not happen? Special relativity predicts this so where is my voltage difference. I feel cheated or more likely I have misunderstood something , story of my life. However I do have an indication that the elusive voltage is there when placing a round magnet on the screen of a TV set. When north or south pole are facing the screen there is a marked black ring where there is a void of electrons hitting the phosphor . Outside and inside the round magnet is okay but not on the edge which is where the electrons should be moving. I have a picture of it.

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