# Train traveling at speed of E field question

• girts
In summary: E field, what if the train was to somehow jump the track, now in this situation the train would not be traveling at the speed of the E field, but rather the speed of the track, so again in theory if the train somehow managed to jump the track and enter into free space then it would cease to experience any power from the overhead wire and would have to find its own power to move forward?
girts
This is a thought experiment so the mentioned values are only for example purpose.

I was wondering about an electrical train. So here is the setup, we have rails and an electric train with an overhead wire. In one case the train gets its power from DC and in the other case the train is powered by AC say 50hz.
Now to make the idea simpler let's suppose that in both cases the train is traveling in a vacuum and the speed of the E field is the speed of light - c, as opposed to the speed of the E field being a fraction of c in other mediums like metal wire under Earth's atmosphere.

In the case of DC power the voltage is uniform across the length of the wire and there are no changes in voltage or current so no matter how fast the train runs it always feels a constant voltage and field strength from the wire correct?

What interests me is what happens in the case of AC, now the frequency is low only 50hz but as we know the changes in E field travel at c in a vacuum, so every time the current changes direction in the AC sinewave that change in direction travels along the wire at the speed of c.
Now what happens if our train also travels at c along the tracks? (I do realize it is impossible but just for the argument) Say the train somehow got synchronized with the moment when the current and voltage was zero on the sine crossing the middle point in the cycle, and this change travels along the wire at c but so does the train travel along at c, does that mean that from the trains perspective there is no power at all in the overhead wire along the whole length of the wire?

If I am correct in my question can this then be compared to the "slip" in the asynchronous induction motor where the rotor doesn't get any induced current if it turns at the same speed as the field rotates in the stator field coils?
Only in the induction motor case the rotor doesn't rotate anywhere near the speed of which the E field changes in the wires but instead it rotates at the speed of which one coil becomes deenergized while another one becomes energized which is normally 50/60hz.

I do realize that this is a complicated question and maybe not the best writing from my part but I thank you for any insights.

girts said:
Now what happens if our train also travels at c along the tracks? (I do realize it is impossible but just for the argument)
We can't answer this question using the known laws of physics since the premise of the question contradicts those laws. So in order to answer the question we would have to invent a new set of physical laws compatible with the question, which is directly opposed to the purpose of these forums.

The propagation speed of AC in overhead wires is roughly 0.8c, so it is possible.

Yes, your analogy of an induction motor at synchronous speed (zero slip) and the train is more-or-less correct.

Instead of a rotating induction motor, I think you are trying to describe a linear induction motor. But fortunately, linear induction motors don't have to travel at 0.8c to work.

https://en.wikipedia.org/wiki/Linear_induction_motor

Ok, @Dale I understand your concern, then let me rephrase the question in order for you and everyone else to answer it from the viewpoint of the known laws of physics. Let's take only the AC case for this argument.

A train travels here on Earth on a special test track, the E field along a wire surrounded by atmosphere of given characteristics is say 0.8c, let's suppose our train also is capable of traveling at 0.8c, I realize this is very unlikely and in any real world situation using materials known to us or in existence but this is a theoretical argument so theoretically a train or any object can achieve 0.8c.
So what happens from here on is what interests me, the train is "synchronized" essentially with the changes in the E field along the overhead line or in other words the train travels at the exact speed as the E field, so any slight minor change in speed of the train like for example 0.8c+50km/h or 0.8c-100km/h could very well set the train at such a point in the E field where there is zero field strength like in the moment of sine wave zero crossing with no current or voltage present , and so given that this moment travels along the power line at the same speed as the train does it then mean that the train doesn't experience any power from the overhead line whatsoever along the whole length of the line?

Another possibility is that the train could catch along the E field in a moment of maximum strength of field like in the peak of a sine wave, again does this then imply that the train would see the same peak voltage across the whole length of the track? I assume it should happen this way and then it means that the train is basically using DC voltage but from the sine wave generator attached to the overhead wire point of view the train is riding only the upper or lower half of the cycle so is limited by the power of just one half cycle, correct?
also thanks @anorlunda for contributing, although I think I understand that in induction motors as well as other electrical motors the physical rotors follow not the changes in the E field which are so fast they couldn't mechanically achieve that but instead they follow the changes in the b field poles and pole strength which then happen at limited speeds governed by either the input AC frequency which itself is a direct or indirect consequence of the generators physical rotation speed or by the speed at which a commutator or any other switching equipment is capable of changing the current etc.
Anyway I would very much appreciate the answer to my theoretical question based on what we know.
thanks.

girts said:
I realize this is very unlikely and in any real world situation using materials known to us or in existence but this is a theoretical argument so theoretically a train or any object can achieve 0.8c
Yes, this is fine.

girts said:
so given that this moment travels along the power line at the same speed as the train does it then mean that the train doesn't experience any power from the overhead line whatsoever along the whole length of the line?
Yes. In an ideal world this is fine because it does not take any power to travel at a constant speed. If there are some losses and hence some minimum power then the train would necessarily slow down until it "caught the wave" and started receiving enough power.

When discussing events so fast as wave propagation, you can't separate E and B fields, It is an electromagnetic field.

The wave in the wire is an EM-wave. It Doppler-shifts like an EM-wave, and it pushes the pantograph when being absorbed.

Esent_along_wire = Epush + Etrain_motor

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ok my bad, I should have called it the EM field, so from your responses I gather that indeed the train traveling at or near the speed of light along the wire would behave similarly to a rotor from an induction motor as it would "see" zero power in the wire or DC depending on the point at which it synchronizes with the EM fields sine wave. the only difference in the analogy with the rotor from the induction motor being that the rotor follows the physical magnetic pole change which is rather slow but the train from my example would rather follow or catch up with the actual propagation speed of the EM field behind the current drive in the wire.
another theoretical question is this, any electrical train traveling across tracks is basically just a resistance put across a DC load, but instead of an ordinary resistance across a fixed DC load this resistance moves, so if we draw the circuit as an electrical schematic we get something resembling the circuit of a homopolar/faraday motor/generator correct? In which there is a steady potential across a loop of wire subjected to a constant magnetic field but the loop itself is either expanding or shrinking (depending on which way the train travels) so for example in the case of the loop expanding and the constant magnetic field being in the background (Earth's magnetic field) shouldn't the outcome be that the train sees a marginal increase in voltage as it travels along the tracks?By the way jartsa what did you mean when you said that "it pushes the pantograph when being absorbed"?

girts said:
By the way jartsa what did you mean when you said that "it pushes the pantograph when being absorbed"?

Hmm, I misspoke. When the train absorbs the energy from the wire, the train absorbs the momentum of the energy, and the momentum of the train increases by that amount, without any use of train motors.

But we are now discussing the one and only case where the momentum of the energy is zero in the train frame.

So I should have said that where ever the energy that the train takes from the wire goes, that thing is being pushed by a force, if we define force as delta p / delta t, and if we are in the ground frame. In the train frame that force does not exist.Oh yes, energy can't catch the train from behind, when the train moves at the speed of light in the medium, which is the wire. So I don't know what happens, maybe the train sees zero a voltage on the wire?

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jartsa said:
Oh yes, energy can't catch the train from behind, when the train moves at the speed of light in the medium, which is the wire.

And the train can't catch the energy ahead it. The DC seems simple: There is energy stored in every segment of the wire, and the train harvests the energy of each segment that it passes. When the train accelerates from zero to 0.8 c, it observes the wire to contract, the mass-density of the wire increases, same happens to the electric energy-density of the wire.

But the AC case involves a decrease of electric energy-density during an acceleration into the direction of the energy flow.

You have to do a Lorentz transformation of the electromagnetic field. The part of the E field perpendicular to motion will be increased by a factor of gamma, and there will also be a perpendicular B field ~ -gamma*(v x E).

## 1. What is the concept of "Train traveling at speed of E field"?

The concept of "Train traveling at speed of E field" refers to the hypothetical scenario in which a train is traveling at the same speed as the electric field it is passing through. This would result in the train experiencing a constant acceleration due to the electric field, potentially reaching speeds faster than the speed of light.

## 2. Is it possible for a train to travel at the speed of E field?

No, it is not possible for a train to travel at the speed of E field. According to Einstein's theory of relativity, the speed of light is the maximum speed at which anything can travel, and this includes the speed of any object affected by an electric field.

## 3. How does the speed of E field affect the train's acceleration?

The speed of E field would greatly impact the train's acceleration. If the train is traveling slower than the speed of the electric field, it would experience a constant acceleration towards the direction of the field. If the train is traveling faster than the speed of the electric field, it would experience a deceleration in the direction opposite to the field.

## 4. What other factors would influence the train's movement in this scenario?

Aside from the speed of E field, the train's movement would also be affected by its mass and any other forces acting upon it. Additionally, the strength and direction of the electric field would play a significant role in determining the train's acceleration.

## 5. What are the potential implications of a train traveling at the speed of E field?

If it were possible for a train to travel at the speed of E field, it would have far-reaching implications in the field of physics. It would challenge our understanding of relativity and the laws of motion, and could potentially lead to the development of new technologies and modes of transportation. However, as of now, this scenario remains purely theoretical and has not been observed in reality.

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