Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: Jack Qwek on 10/07/2016 17:01:16
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I know that if we switch on a torch on a train, the speed of light cannot be added to that of the train. What about speed of electricity on a wire? Can it be added to the train's speed?
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No, on the contrary, the velocity in a cable is generally slower than the speed of light.
Velocity factor (the ratio of propagation speed in a medium to the speed of light in a vacuum) is given by V=1/√k, where k is the dielectric constant or relative permittivity of the insulation. Dielectric constant is the ratio of the permittivity of the insulator to the permittivity of free space (which is also the ratio of the capacitance of the insulator to the capacitance of free space). For open wire lines the VF might typically be 95%, reducing to about 66% in a polythene insulated coax.
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No, it cannot Period!
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What about speed of electricity on a wire? Can it be added to the train's speed?
Yes, if the wire is on the train then relative to the ground the electricity is speed in wire + speed of train.
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What about speed of electricity on a wire? Can it be added to the train's speed?
Yes, if the wire is on the train then relative to the ground the electricity is speed in wire + speed of train.
I disagree but because you have been thanked 96 times I am most likely wrong.
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What about speed of electricity on a wire? Can it be added to the train's speed?
Yes, if the wire is on the train then relative to the ground the electricity is speed in wire + speed of train.
Let's say that at the end of a wheel there is a wire that measure electricity speed, this spinning wheel is quite big, diameter 500 meters, rpm is 100000, so the speed of this wheel will be 5236000 m/s, which is more than 1% the speed of light. So in theory, they can measure if electricity can go faster than light?
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What about speed of electricity on a wire? Can it be added to the train's speed?
Yes, if the wire is on the train then relative to the ground the electricity is speed in wire + speed of train.
Not if relativistic speeds are involved. No information can travel faster than c.
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What about speed of electricity on a wire? Can it be added to the train's speed?
Yes, if the wire is on the train then relative to the ground the electricity is speed in wire + speed of train.
Not if relativistic speeds are involved. No information can travel faster than c.
Source Quora
https://www.quora.com/Assume-a-train-travelling-in-the-speed-of-light-and-I-was-running-inside-the-train-along-the-train-is-it-am-travelling-faster-than-light
This is the standard velocity-addition problem in relativity, which we have to use in this case. Remember, the relative speed between any two coordinate systems can never equal or exceed c, the speed of light. So, stated in more exact terms, suppose we have three reference frames: A platform R1, a train moving by the platform R2, and yourself R3 inside the train. We set the train speed by the platform R2 – R1 = .99 c and your speed in the train at R3 – R2 = .99 c. in the same direction as the train. Then what is your speed relative to the platform R3 – R1?
The velocity-addition formula gives R3 – R1
≈ 0.99995c
≈0.99995c.
Now we can take the case of where the train's speed is .99 c east and your speed in the train car is .99 c to the south. What is your speed and direction relative to the platform? The velocity-adddition formula gives a speed of
0.9998c
0.9998 c in the direction of only
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What about speed of electricity on a wire? Can it be added to the train's speed?
Yes, if the wire is on the train then relative to the ground the electricity is speed in wire + speed of train.
Not if relativistic speeds are involved. No information can travel faster than c.
I agree. I must confess I was thinking of an ordinary, everyday train.
At relativistic speeds I assume a velocity addition rule, but I haven't sat down to work out what would happen. I suspect PmbPhy would know.
Edit: interesting, I notice Alan had replied above, but his response wasn't there when I was typing this reply. Odd things happening at the moment
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Let's say that at the end of a wheel there is a wire that measure electricity speed, this spinning wheel is quite big, diameter 500 meters, rpm is 100000, so the speed of this wheel will be 5236000 m/s, which is more than 1% the speed of light. So in theory, they can measure if electricity can go faster than light?
A rotating system is not an inertial frame so it is possible for one observer to measure light in another location to be faster than c, although if the observer were on the rim of the disc they would only measure it to be c. This is similar to the effect of a gravitational field.
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Although the flow of electricity in a wire is often referred to as the movement of electrons actually they move relatively slowly what moves fast is the electromagnetic field that is guided by the wire that moves at c.
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Although the flow of electricity in a wire is often referred to as the movement of electrons actually they move relatively slowly what moves fast is the electromagnetic field that is guided by the wire that moves at c.
That's a good point, although the rest of us have been assuming that, the OP might not realise it.
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Let's say that at the end of a wheel there is a wire that measure electricity speed, this spinning wheel is quite big, diameter 500 meters, rpm is 100000, so the speed of this wheel will be 5236000 m/s, which is more than 1% the speed of light. So in theory, they can measure if electricity can go faster than light?
A rotating system is not an inertial frame so it is possible for one observer to measure light in another location to be faster than c, although if the observer were on the rim of the disc they would only measure it to be c. This is similar to the effect of a gravitational field.
For light, the speed is always the same for any observer (inside or outside the train, inside or outside the wheel, etc). But for the electricity on wire, if the observer is on the rim of the spinning disc, the speed of electricity is same as when the wheel is not spinning. If the observer is outside the wheel, the speed of electricity could be faster than c. If they do this experiment, it would be an amazing discovery.
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Although the flow of electricity in a wire is often referred to as the movement of electrons actually they move relatively slowly what moves fast is the electromagnetic field that is guided by the wire that moves at c.
The speed of the electron in a copper wire, which is one of the best conductors of electricity is always less than c. In fact, it is the wave surrounding the conductor that is actually at c .
Alan
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What about speed of electricity on a wire? Can it be added to the train's speed?
Yes, if the wire is on the train then relative to the ground the electricity is speed in wire + speed of train.
I disagree but because you have been thanked 96 times I am most likely wrong.
If I understand him correctly then Colin is wrong. We have to keep in mind that the speed of the electricity relative to the ground is less than the speed of light, always! If someone in the rest frame of the wire measures the speed of electricity then when transformed to the ground frame then speed will still be less than the speed of light.
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We have to keep in mind that the speed of the electricity relative to the ground is less than the speed of light, always! If someone in the rest frame of the wire measures the speed of electricity then when transformed to the ground frame then speed will still be less than the speed of light.
Ok, I see what you mean. Looking again at the Fizeau experiment I can see how even with the wave travelling in a medium and the medium travelling at <c then the transform/velocity addition is still necessary.
Perhaps you can help with this one:
For light, the speed is always the same for any observer (inside or outside the train, inside or outside the wheel, etc). But for the electricity on wire, if the observer is on the rim of the spinning disc, the speed of electricity is same as when the wheel is not spinning. If the observer is outside the wheel, the speed of electricity could be faster than c. If they do this experiment, it would be an amazing discovery.
Jack
In addition to a rotating system not being an inertial frame, I am sure that there is a limit of c on the speed of the rim as seen by an outside observer. Also, the same translation rule, as in the train example, should apply when adding the transmission speed of the electricity.
Perhaps Pete can throw some light on this [:)]
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Is there any experiment to google? (only about electricity on wire, not light).
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The speed of the electron in a copper wire, which is one of the best conductors of electricity is always less than c.
This is an understatement!
If you put enough current through a copper wire to almost melt it, the electrons are only drifting at a couple of mm per second.
As you say, it is the electrical field that travels at something like the speed of light (for typical conductor geometries, pulses travel at about 2/3 the speed of light).
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it is the electrical field that travels at something like the speed of light (for typical conductor geometries, pulses travel at about 2/3 the speed of light).
It's the dielectric that determines the velocity factor, not the conductor. A VF of 66% is typical for PTFE or polythene, but in an air spaced line the VF is about 95% - 99%.
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The drift speed of an individual electron in a current-carrying copper wire is about equivalent to fast walking pace. The electrical signal, on the other hand, propagates at close to light speed. One can think of it as a bit like a Newton's cradle. The power source pumps in electrons, which all cannon into one another, ejecting electrons and creating a near-instantaneous current at the other end of the wire.
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I thought it would be a good academic exercise for us to do the calculation:
Let's imaging a notional conductor, a cylindrical piece of wire.
Its cross-sectional area is A, the length is d and there are n charge carriers, e, moving at velocity v.
Therefore the total mobile charge, Q, in the cable is given by Adne
Time, t, for this charge to move along the conductor = d/v
Since current, I, = Q/t we can substitute for the above:
I = Adne / d/v = Avne
So v = I / Ane
Now i need some numbers for my notional copper wire including - number of charge carriers etc...
Who would like to take up the baton...
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Or you could read this.
http://resources.schoolscience.co.uk/CDA/16plus/copelech2pg3.html (http://resources.schoolscience.co.uk/CDA/16plus/copelech2pg3.html)
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The drift speed of an individual electron in a current-carrying copper wire is about equivalent to fast walking pace.
Not by a very long chalk, the drift velocity of a 1A current in a 2mm copper wire is 23 microns per second.
//en.wikipedia.org/wiki/Drift_velocity
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Thank you; can we please complete my calculation above to show how we know this?
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The calculation is on the wiki page above.
n =8.5E28
e =1.6E-19
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I thought it would be a good academic exercise for us to do the calculation:
Let's imaging a notional conductor, a cylindrical piece of wire.
Its cross-sectional area is A, the length is d and there are n charge carriers, e, moving at velocity v.
Therefore the total mobile charge, Q, in the cable is given by Adne
Time, t, for this charge to move along the conductor = d/v
Since current, I, = Q/t we can substitute for the above:
I = Adne / d/v = Avne
So v = I / Ane
Now i need some numbers for my notional copper wire including - number of charge carriers etc...
Who would like to take up the baton...
So if we take the cross sectional area A = 0.003m, velocity v = 1 m/s, number of charge carriers n (in copper) = 8.5 x 1028 per m3. Then we need d to derive the volume of the wire to proceed. If we just assume it is 1 cubic metre anyway this simplifies things. Electron charge is 1.6 x 10-19C. So now we have the figures to calculate current and subsequently drift velocity. Then all we need do is change the value for current to see how this affects drift velocity. We could even calculate a hypothetical current needed to bring drift velocity close to c, just for fun.
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For v = 1 m/s you appear to get 40.8 million amps. This may be wrong! Very likely so.
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Whoops!
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I know that if we switch on a torch on a train, the speed of light cannot be added to that of the train. What about speed of electricity on a wire? Can it be added to the train's speed?
It depends on
1) what you intend with "speed" (speed of what?)
2) what you intend with "electricity"
Just to make an example, the phase velocity of electromagnetic waves in a wave-guide can be greater than c. Even the group velocity of an electromagnetic wave, in a suitable medium, can be faster than c.
What instead must always be less then or equal c is signal velocity
http://www.mathpages.com/home/kmath210/kmath210.htm