Would this (possibly undone) electrodynamics experiment be proved right?

Electrodynamics and Magnetism

Hello everyone,

Please give me your valuable comments regarding this post which is about a possibly undone experiment in electromagnetism and I request you to come to your own conclusion regarding these. This is viewed both in terms of the effects of magnetic field and in terms of the effects of Lorentz contraction of moving charges and both of them (as for me) arrives at the same conclusion. This post deals with "classical electrodynamics" and the adjoining thread deals with the effect of Lorentz contraction.

[INDENT]As a preface – this experiment is based on these well established facts that
1) Current is the rate of flow of charge – any charge, not just the flow of electrons*.
2) This flow of charge produces a magnetic field around itself/conductor.
3) Classical physics is purely deterministic and that definite causes should have definite results.
4) Observers in the same frame of reference (and who are at the same point and stationary to each other) should agree with same or similar incidents (ie, all parameters remaining the same).
*( displacement current is not mentioned here since this article is not concerned with it.)
[/INDENT]

Before proceeding further into this article, the reasons for writing this article are explained otherwise its necessity would not be appreciated. Moreover, it greatly helps in expressing the viewpoint a lot. -thanking you for your cooperation.

The Anomaly.
Now consider this setup - AB is an infinitely long current carrying conductor carrying current I. let CD be a metal strip positioned near to the conductor.

Case 1) The conductor AB is at rest with respect to the metal strip CD (fig 1A)
Here there will be a magnetic field in and around the metal strip CD, but there won’t be any potential developed across it (since there is no magnetic force acting on the electrons in CD).

Case 2) the potential applied to AB is reversed (so drift velocity is negative), and
CD is moving with a negative drift velocity (equivalent to the conductor moving with a positive drift velocity) – i.e., here essentially CD is at rest with the conducting electrons in AB and moving with respect to non conducting charges. Here, the rod is moving in a (radially – uniform) magnetic field causing a force (dF =dBQv) to act on the various charges of the rod which eventually cause a potential to be developed across the rod CD in accordance with Fleming’s Right Hand Rule.

Now, it can be seen that in both cases the metal strip is under exactly similar conditions as shown in Fig 2- CD is stationary with respect to one kind of charges in AB and is moving with respect to the other (opposite) kind of charge.

In case1) the metallic strip CD sees a current due to the flow of electrons in the conductor AB and in case 2) the metallic strip CD sees a current due to the (net) flow of nuclear positive charge in conductor AB.

In case1) the flowing electrons in AB produce a magnetic field. And in case2) it is the net nuclear positive charge that is moving produe a magnetic field.

(Now as stated earlier, definite causes should cause definite results. Moreover, saying that there isn’t a potential developed in one and on the other there is like saying- even though the laws of physics are the same for all inertial reference frames, we can have different laws of physics (for the same phenomenon) in the same inertial reference frame).

However it is a well known fact that the potential developed in the two cases are different and if one observes closely, this anomaly of measuring different potential under identical situation can be easily explained. (same reason as stated above, but from a classical electromagnetic point of view)

[INDENT]1) The magnetic field which acts on the metallic strip CD is also acting on the probes of the potentiometer (Fig 3) which develops the same potentialacross it (i.e., the probes of the wire that are equi-distant from the wire AB are at equi -potential and hence the potentiometer reads zero potential. This creates a situation where the voltage developed can’t be measured directly.

2) The calculated potential developed in case 2) is generally of the order of Pico-volts (for a few amps) and this clubbed with the above fact (1) makes it even harder to detect.[/INDENT]

Assuming it is due to these reasons that the measured potential was different, one can straightforwardly come to the conclusion that the force (in this case and at “atomic” level) acting on the electrons in CD has to be of the form –

[INDENT]F=k q Q V²/r (force in case 2 which has to be true in case 1 also)*

Where k = a constant,
q = charge of the electrons (in CD),
Q = conducting Charge in AB,
V = drift velocity of electrons (relative velocity between the charges in motion).[/INDENT]

(* at the “macroscopic” level this still retains the equation for net force as F= Bqv which is independent of the relative velocity of the moving charges – and hence this keeps everything the same as we already have –whether it be in deriving the force between two parallel current carrying conductors or effects of a current carrying coil etc).

(It should be noted that force between charges in motion are not always related to square of their relative velocities, which is mentioned in the later part of this article**).

What was said above can be easily proved with the help of an experiment as described below.

The Experiment:-

(This experiment is based on above equation that this force on the electrons is proportional to square of the relative velocity and sign of the concerned charges. So materials with different drift velocity (or with different current carriers) should exert different force on charges placed near to them).

The same experiment that was described in the other thread is shown again, but this time this experiment is based on above equation that this force on the electrons is proportional to square of the relative velocity and sign of the concerned charges. So materials with different drift velocity (or with different current carriers) should exert different force on charges placed near to them.

(So now, would there be a potential across P-S?). I hope the answer is YES - and I do agree that it is the experiment that should decide this ultimately).

==============================================================================================================

** Consider a straight long wire AB carrying current I and a charge Q is moving perpendicular to it with a velocity V as shown in the figure 4. Here as the particle moves, it can be seen that its “r”, the distance between AB and Q that varies and hence the magnitude of the magnetic field changes and thus, it is magnetic induction that plays here and is very different from the above case.
V = dr/dt

Here clearly the equation for the force take the form

F= BQV

which is independent of the square of their relative velocities.

To conclude, (with reference to my other thread –which address the same issue in terms of the effect of Lorentz contraction of moving charges) we can see that we arrive at the same conclusion in either way. Both in terms of classical electrodynamics and in terms of the effect of Lorentz contraction, this article keeps a rational and logical approach towards the concept of magnetism.

Moreover this is not the first time an article was written about magnetism with such intentions; in fact there were many prior to this. Just a preliminary search on the net, does brings a few pages concerning similar articles co-relating magnetic field with charges and the relative motion between them. Please post your opinion regarding these and I request you to see this experiment as a classical one in answering the question “would there be a potential across P-S? - since I prefer a rational and logical answer that’s in agreement with the four facts that was quoted before.

Many thanks in advance.
Abhilash J Pillai.

Would this (possibly undone) electrodynamics experiment be proved right?

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