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

[abhilash]

This article is an abridged version of the original article posted in google groups. For further proofs or clarifications please download the file titled electrodynamics and magnetism.pdf from the link that is given at the last part of this article. Even though this article is regarding classical electrodynamics, it definitely has its tentacles grasping on certain aspects of relativity and hence posting it here.

 

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).

*(not talking about displacement current here since this article is not concerned with it.)

 

Before coming to the experiment, the reasons for this experiment are explained otherwise its necessity would not be appreciated. Moreover, it greatly helps in expressing the viewpoint a lot so that you can answer correctly to the point. -thanking you for your cooperation.

 

The Anomaly:-

 

Consider the 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 the conductor is 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, there will be a magnetic field and there will be magnetic force acting on the conducting electrons of the metallic strip CD. This causes a potential to be developed across CD. (Depending up on the situation, the potentiometer may or may not read this potential - but a potential is developed across CD which is caused by the action of Lorentz Force F = e(BXV)on the electrons in CD)

 

(Please see this in a classical way, where there is just one frame of reference which is at rest with respect to CD)

 

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.

In case2) it is the net nuclear positive charge that is moving. Shouldn’t they produce a magnetic field?

 

Now as stated earlier, definite causes should cause definite results. However it is a well known fact that the potential developed in the two cases are different.

 

Now if one observes closely, this anomaly of measuring different potential under identical situation can be easily explained.

 

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 potential across 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.

 

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 –

 

F=k q Q V^2/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).

 

(* at the “macroscopic” level this still retains the equation for net force F= Bqv which is independent of the relative velocity of the moving charges and is described in the orginal version of this article and it's link is given at the final part of this article).

 

(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 latter 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).

 

Consider a straight long tube CD which on conduction electro-deposition of copper takes place at the cathode (-). The cathode is in contact with a long piece of wire AB (as shown in fig 3) which is connected to the negative terminal of the battery and the anode is connected to the positive terminal. PQRS is a piece of wire or a metal plate shaped as shown and is placed near this (AB – CD) arrangement.

 

On the tube, the carriers of current are the positive ions where as in the wire; it is the electrons that conduct electricity. On conduction (as per the equation-given above), the conducting electrons in AB repel electrons in PQRS away from it whereas the moving cat ions on the tube attract electrons towards it. This causes a potential to be developed in PQRS and can be measured directly. (Here the length of QP/RS has to be much smaller than the length of AB and CD preferably QP=1cm and QR= 200cm).

In the above experiment, in place of AB and CD, n-type and P-type semiconductors can be used which should develop much more voltage across PS (of the order of nano-volts) since the drift velocity of electrons in semiconductors is much greater.

So the question is –

would there be a potential developed across P-S?

 

 

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

 

** 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.

For a detailed description about this article please download the file titled Electrodynamics and Magnetism.pdf from the site

Electrodynamicsandmagnetism | Google Groups

 

Please post your opinion regarding these and i request you to see this experiment as a classical one since I prefer a rational and logical answer thats in agreement with the four facts that was quoted at the beginning of this article.

 

Thank You and welcome.

Abhilash J Pillai.

[Qfwfq]

So the question is –

would there be a potential developed across P-S?

No.

[abhilash]

Thank You for your reply.

 

Now do you see any difference between case 1 and case2?

[Qfwfq]

Now do you see any difference between case 1 and case2?

Charge density of opposite sign, going the opposite way: [imath]j=(-\rho)(-v)=\rho v[/imath] The current density is the same.

[abhilash]

Yes, that is right, thank you for your reply.

 

Moreover in case 1 there is no potential developed in the strip CD whereas

 

in case 2) there is a potential developed which is caused by the action of Lorentz force on the electrons in CD and this can be measured physically.

 

However, in both the cases, there is one kind of charge moving with respect to CD and all conditions are same except for the sign of the moving charges and that should not matter.

 

we all know that classical physics is purely deterministic and that definite causes should have definite results. So how can there be two different results for the same cause?

 

For this reason, shouldn’t it be impossible for a different potential to be developed across CD in case 1 than in case 2. That the reason why the potentiometer reads zero potential is due to reasons explained with reference to fig 2B.

 

Thanking you.

Abhilash J