How fast does an electon move?

[John Heath]

If I hold the magnet and copper disk still and just rotate the contacts to the copper disk it will generate a voltage . I saw it in a yahoo video.



A question. If I glue the meter to the copper disk and solder the leads to the outside and center of the copper disk will it generate a voltage on the meter that is rotating with the disk?

[IanB]

If I hold the magnet and copper disk still and just rotate the contacts to the copper disk it will generate a voltage . I saw it in a yahoo video.

This is because the wires leading to the contacts are moving through the magnetic field.

[IanB]

Consider an array of spinning tops: rotating the table they are spinning on, has no effect on the total angular momentum of the ensemble.  Each top continues to spin as it will (until friction takes its toll, of course).  You can change the arrangement of tops, but if the arrangement itself is circularly symmetric (hence the requirement for a round, axially magnetized part), there isn't even a change in the distribution of angular momentum that's sitting on the table!

This analogy is not quite perfect.

If I place an array of spinning tops around the edge of a stationary circular table, each top spinning at 300 rpm, say, and then subsequently I start rotating the table at 10 rpm, then in fact each of the tops is now spinning at 310 rpm relative to a stationary observer outside the table. This means the tops do have an increased angular momentum as measured by that observer.

[salbayeng]

John,
It has to slide to get any EMF, so soldering to 2 points won't work (unless the solder is molten!)
you need to have relative motion to work.
(I'm talking about motor action below as its easier to explain, but generator action is just the same)
 The critical feature of the setup is you must have one stationary arm (the return leg of the circuit through the meter) and one moving arm .  If both arms are stationery you generate a torque on the lower leg, exactly balanced by a torque on the return leg (These torques generate a couple but the rotation axis of the couple is horizontal, so no net motion about a vertical axis.)
You can spin the magnet about the vertical axis and nothing changes. Also there is no reaction torque experienced by the magnet (the return wire experiences the reaction torque.

As a generator: if you have the forward leg rotating, and the return leg also rotating, basically the integral of induced voltage around the loop sums to zero.

Faraday's original set up had a puddle of mercury with a wire arranged so it could circulate near the periphery of the puddle. A geometry very similar to the YouTube arrangement.

[salbayeng]

This is because the wires leading to the contacts are moving through the magnetic field.

Exactly right ,
It's a complete electric circuit.
You can move either the disk ,( the lower half of the electrical circuit).
Or move the "wires leading to the contacts" ( upper half of the circuit).
Both results will be identical.

(edit) and about 1/3 down here https://en.wikipedia.org/wiki/Faraday_paradox  , the section on modern explanations talks about this.

[salbayeng]

Getting back to the moving electrons with an apparent magnetic field.
Lets take  two parrallel streams of electrons, zooming down a vacuum tube, horizontally either side of the centreline.

If both move the same direction (e.g. as pairs) they will diverge due to coulomb repulsion, 
An observer moving with them will see no magnetic effect.
A stationery observer will see two magnets aligned parrallel to each other and they will be repelled by both magnetic and coulomb repulsion.
So beam divergence depends on the relative motion of the observer? doesn't sound right to me, but anyway, continuing on...

If moving in opposite directions  each electron will appear as a tiny magnet from the other's perspective (with north at the front and south at the rear??) . So assuming you are an observer on one electron, your won't see yourself as a magnet, and (assuming the other is approaching on your left),
as you approach you will slow down (coulomb repulsion) and then passing through the front of the others magnetic field you get deflected up.
As you go abeam you get deflected right due coulomb,
and behind the other electron you get accelerated (coulomb) and deflected down (Lorentz).  So as you pass a stream of electrons you will be wiggled up and down, and continually deflected right.
From your perspective (and momentum conservation) the other electron must also wiggle as it is a magnet experiencing a Lorentz force due to a moving charge (i.e. your electron) .

Of course the other guy sees you as a magnetic field, and himself as a charged particle.

(Edit) If the electrons are wiggling up and down they should be radiating synchrotron radiation ? That should be observable? https://en.wikipedia.org/wiki/Synchrotron_radiation

[John Heath]

That is interesting. This would mean a meter on the table with sliding contacts will measure volt but the meter glued to the disk with leads soldered to the copper disk will not. What happens when both the stationary meter with sliding lead and the rotating meter lead soldered are both at 12 o'clock? The stationary meter would measure a voltage but the rotating meter would measure 0 volts . That would make for a cool picture to see one meter say .1 volt and the other rotating meter say 0 volts while measuring the same points on the disk at the same time at 12 o'clock on the rotating copper disk.

[salbayeng]

John,
If I take some figure 8 cable, connect to a DMM, then short the other end of the cable, it will always read  zero no matter how you wave the cable around in a magnetic field, that should be obvious .
You could glue that cable and meter to any motor shaft and it still reads zero.
You could solder the end of that cable somewhere on the rim of your homopolar motor,  and it still reads zero.
You could solder some other part of  of the cable to some other place on the homopolar disk, and it still reads zero.
You could cut the piece of  wire that bridges two points soldered above, still reads zero, and this is exactly the meter glue to homopolar motor arrangement.

and
If I take some figure 8 cable, connect to a DMM, then short the other end of the cable, it will read  zero.
if I place this cable into a strong magnetic field,  then split the cable with a knife, and slowly pull the red wire apart at constant velocity, while keeping the black stationary, then I will read a fixed voltage on the DMM, lets say after I have spread the wire out to a foot or so, I rapidly solder a new red wire in adjacent to the black wire, and cut the original red wire, I now move the new red wire away from the black and read a constant voltage, so if you do this repeatedly (and do the wire changeover sufficiently fast,) you will read a constant DC output.

A different variation would be to have an axle with say ten rigid wires arranged as spokes, the DMM negative lead connect to the axle, The positive lead has two jumper climps.  So as the spokes revolve in a magnetic field you attach one crocodile clip to the nearest spoke, and as another spoke approaches you attach the other croc clip to this, then remove the first croc clip, and transfer this to the third spoke when it approaches, this way you have at least one lead attached to a moving spoke at all times and you will get a constant DC output.
Let's repeat with a 100 spoked wheel, and use wire brushes to pick up the nearest spoke,  again you will get a constant DC output.
You could extend this to a thousand spoked wheel, which is essentially a solid disk.

[John Heath]

Let's repeat with a 100 spoked wheel, and use wire brushes to pick up the nearest spoke,  again you will get a constant DC output. You could extend this to a thousand spoked wheel, which is essentially a solid disk.

I see a fly in the soup here. Instead of moving the clip from spoke to spoke I will use a FET analog switch to move from spoke to spoke. As a analog FET switch requires zip in the way of energy to switch from spoke to spoke a voltage resulting from this would be free energy assuming the copper disk is not rotating . Check mate. As there is no free lunch . free energy , in physics there should not be a voltage. I will be clearer in details to make sure we are one the same page.

The magnet is not rotating. The copper disk in not rotating. The 100 spokes soldered to the outside of the disk are not rotating.

The only thing that is rotating , effectively , is the 100 analog switches selecting one spoke at a time in a clockwise direction. 

You are saying this will produce a voltage?

[IanB]

A voltage is not energy (i.e. power output). Also a switch does require energy to change state, whether an FET switch, or even a diode.

[T3sl4co1l]

Spokes will not generate a voltage no matter how many of them you select from.  Relative motion is required.

Otherwise, there would be static voltage on the spokes, and switching them in with transistors would work.  Indeed, switching them wouldn't even be necessary, you could just sit there and soak.

Tim

[T3sl4co1l]

A perhaps related paradox is adiabatic expansion/compression:

Intuitively speaking, compression/expansion of a gas feels natural, when you have many particles (a gas) in a box.  The gas presses on the walls at all times, and no matter how fast the walls move, they are exposed to a quasi-continuous force.

But it seems to intuitively fail for a single particle.  Suppose you move the piston at such a speed, so that the lone gas particle does not interact with it during the move.  In one moment, the gas particle bounces off the piston in one position, and in the second moment (after the move), it bounces off at a different position.  Yet it's still going the same velocity, and therefore is at the same temperature, so hasn't been adiabatically expanded or compressed.

Have you just violated adiabatic conditions, then?

Assume the chamber walls do not exchange heat energy with the gas, i.e., it's a closed system with insulating walls.

The resolution is thus:

Thermodynamics is only concerned with the eventual result of change.  "Eventual" as in, infinite time.  But implicit in this assumption is that, any possible change can only happen continually.  And it is the sum of those derivatives that matters.  Thermodynamics is about integrals of a system over all time.

Moving the wall "instantaneously" (as far as the gas is concerned -- it doesn't need to be a contrived instantaneous event, it can be a real continuous physical movement as long as the gas bounce period is known) violates this condition, because the system is now discontinuous.  So it violates the assumptions, not the conclusions!

In E&M, when Faraday's law tells you that the voltage is the derivative of flux, it's not something that can be constructed in piecewise manner -- it's a true, physical derivative.  You can't have voltage without relative motion, whether it's change of the field (as in a transformer) or geometry (as in a motor).

Tim

[salbayeng]

Tim
I think you skipped this bit "So as the spokes revolve in a magnetic field ",
The reason you need the croc clips is because the spoke moves too far away to reach anymore, and you need to clip onto the next spoke as it comes past.

[John Heath]

it's not something that can be constructed in piecewise manner

I hear you and agree. FET switches are rotating in a piece-wise manner not real rotation so it is not the same.

I am going to make a bazaar statement then do my best to dig a way out of that hole.

The bazaar statement.

The true volt drop from the middle to the outside of the copper disk in a magnet field is millions of volts without the need to rotate.     

Onward with shovel in hand. I will charge an air plate condenser to 100 volts. I can measure the voltage from plate to plate as 100 volts.  However if I move inside the condenser between the plates I can no longer make this measurement as I and my meter are inside the voltage gradient of the condenser. I will always measure 0 volts between the condenser plates from the inside the condenser between the plates. There is an example of this in sky charge. Our sky charge is around 100 volts per meter. That is 200 volts from head to toe. If you measure from head to toe the reading is 0 volts. It is 0 volts as we are in the voltage gradient of our sky therefore it is a measurement that can not be made.

The magnetic field creates a voltage gradient around the copper disk of high voltage but this voltage can not be measured as you have to enter the same voltage gradient to make the measurement. However a small amount of movement takes us slightly out of this voltage frame of reference allowing us to measure a tiny amount of this 1 M volts gradient from the center to the outside of the copper disk.

This requires a blind belief that special relativity has is right that a magnetic field is just a Coulomb force caused by relative movement. 

[nuno]

To the OP:
http://www.physlink.com/education/askexperts/ae69.cfm
http://amasci.com/miscon/speed.html

[salbayeng]

Hi John, it is customary to use an emoticon when having a leg pull. else people might think you are serious.

I will charge an air plate condenser to 100 volts. I can measure the voltage from plate to plate as 100 volts.  However if I move inside the condenser between the plates I can no longer make this measurement as I and my meter are inside the voltage gradient of the condenser. I will always measure 0 volts between the condenser plates from the inside the condenser between the plates.

Actually not true , you can measure the voltage of a capacitor while inside the electric field of said capacitor.
You can also measure the voltage induced in a coil rotating with axis perpendicular to a magnetic field while sitting in that coil.
You can measure the strength of "gravity" while sitting in a gravitational field.

These issues are all basically "geometry" issues , in order to assign a number to a measurand, you may need to perform some kind of integral over a path. Take a simple example, with say constant current flowing down a resistive wire, the path integral is simply the distance along the wire between the meter probes.
The homopolar motor has a really odd geometry (the "physical" area is constant, but the "electrical" area always increases, think of a hamster wheel, if the wheel is 100mm diameter and 50mm wide, the physical area  available is 1670sqmm., but if the hamster does one revolution per second, the area he sees increases by 1670sqmm every second) . If you can get your head around how a hamster can be simultaneously running at 570m/hr and be stationary then you are halfway to understanding a homopolar motor.

Have you ever wondered why it is that you can't hear yourself in the earpiece of a telephone? It is because there is a coupling transformer, the wire with the microphone signal goes into transformer, round and round the core several times then gets sent out on the pair of wires connecting your phone to the other guy. The incoming signal to your phone goes round and round through the same transformer before getting to the earpiece, effectively cancelling out your own voice. Basically the path integral from the microphone to the earpiece is zero, inspite of the large fluctuations in the magnetic flux of the transformer.  Because the microphone wire and earpiece wire travel the same path there is no net signal.
It analogous (but not equivalent) to not measuring  a voltage while sitting on a homopolar rotor, while "the other guy" can measure a voltage.
(note to E.E.'s reading this, I'm aware how sidetone cancellation actually works).

[John Heath]

My use of a condenser was not the best example for this case. A sphere 1 meter in diameter. Another sphere 2 meters in diameter. The two spheres are 1 meter apart. It will be around 10 p farad between the spheres. Charge the two sphere to 1 million volts. At 10 p farad we can keep track of how much energy was put into the spheres. Now place the 1 meter sphere inside the 2 meter sphere without shorting them out. Once the little sphere is inside the big sphere it can not be shorted out even if the little sphere touches the inside of the big sphere. I repeat for clarity. The little sphere inside the big sphere can not be discharged even if it touches the big sphere. Now take the little sphere out of the big sphere and place them back the way they were 1 meter apart. A measurement will show the the energy 1 M volt at 10 p farad is still there and can be discharge. This one you can take to the bank as I have a video of it. I will dig it up so you can have a gander.

Found it

[salbayeng]

Tim, re "adiabatic" ,
There are other areas of physical science where "adiabatic" can be invoked to explain a lossless transformation.

An example inspired by a recent post, and a good way to trap unwary physics students.
First pose a problem:  A parallel plate capacitor , with 10mm separation is charged to 100v, you then seperate the plates to 100mm, what voltage is on the plates now?
Most people will jump straight in with 10v (the wrong answer BTW)
 A physical demonstration is much more fun. Take a grounded brass plate (or any avaliable grounded metal surface. Place a sheet of mylar on it (50 to 100um), Take another brass disk with a porcelain knob attached, place it on the mylar, charge it to 100v , lift it off the mylar (holding the knob), and touch iy against a colleague and watch him jump. (you can get around 20kV) This was a part tricky a century ago, the two brass plates were covered with dissimilar insulators, you would rub them together to get a decent potential then lift one off.

[salbayeng]

Re: Two charged spheres.
(n.b. a condenser is the hot part of a refrigeration system,  in historical contexts we still talk of "condensers" when Leyden Jars are relevant. But in a modern context, no-one says the "galvanic pile" in their laptop is going flat, if you want to use condensortivity to measure condensortive effects you need to be consistent and the units are milli-microfarad (we didn't have pico back then))

The thing with the capacitance of charged spheres is that geometry and potential energy are intermixed with the whole arrangement. Also people mix up potential and potential difference. Coulombs law requires charge conservation, but if you move the pieces around you change the geometry, if you change geometry you change capacitance, if you change capacitance you change the voltage, you also need to add or remove mechanical energy when you change the capacitance of a charged system.  Many of these science-fair demos rely on sleight of hand where the operator is changing geometry and or inputting/removing mechanical energy and you can't see this.
The simplest demo is the pulling apart of capacitor plates, which has a counter-intuitive  result, in this the geometry "increases" , but to do this you have to apply tension, and then you are adding energy to the system, hence the charge is constant, voltage goes up, electric field is constant, and energy stored in that field increases.

I'm not sure in your example if the 1MV is between the two spheres, or the potential w.r.t earth (that makes a big difference!)
But there are some things that happen,
(a) as you open the big sphere some of the charge on the outside races around to the inside, so the voltage drops to 700kV??, the capacitance also increases. As soon as you pull the latch the two halves will fly open (repulsion of likes), so energy is removed from the system
(b) when you put the little sphere inside you need to push it in (if opposite charge) or hold it back, so adding/removing energy.
(c) with the sphere inside, there is much more inter-sphere capacitance, so the potential difference will be much less (if opposite charged)
(d) at this point I think, if you short out the outer sphere, so it has zero voltage, but there will be still energy inside the sphere
(e) if you then pull out the inner sphere (you need to add energy to this), magically there is now a voltage on both spheres!

There all sorts of things you can do, but it's only magic if you ignore the geometry and energy transfer effects.

(edit: some typos)

[John Heath]

Yes moving the spheres around changes the energy for a preferred coulomb position and the charge voltage. However if careful not to discharge the sphere then when returned to there original position the energy and voltage will be the same. This is why I said 1 M volt at 10 p farad to keep track of the energy. This being said a sphere within a sphere can be consider a condenser yes/ no. And as seen by the video the condenser can not be discharge when the small sphere is inside the big sphere. The same can be said of our sky charge at 100 volts per meter. It can not be measured or discharged as we are inside the voltage gradient. A resistor or copper wire 1 meter long facing up will measure 0 volts in a vacuum voltage gradient of 100 volts per meter. I see the copper disk in the Faraday paradox as the same in that the magnetic field has caused a voltage gradient in the copper disk but we can not measure in has one enters that voltage gradient when you try to measure the copper disk.

there is a voltage gradient across a resistor and there is a voltage gradient in the vacuum that the resistor is in. The resistor gradient can be measured but not the vacuum voltage gradient. We feel gravity but this is because the ground stops us from falling . If falling the gravity gradient can not be measure as per the equivalence principle. In any event that is my 2 cents on the Faraday paradox.

[salbayeng]

It is possible to measure the earths atmospheric electric field , typically by the use of some form of rotating probe, for example two electrodes 100mm apart rotated about a horizontal axis will yield 10v pk AC signal in a E-field of  100v/m.

The instrument is called a "field mill" http://a-tech.net/ElectricFieldMill/

There are commercial E-field sensor systems https://www.campbellsci.com.au/electric-field-sensor  for example that provide alerts for an impending thunderstorm , or local corona activity (useful in areas with explosive dust hazards)

[John Heath]

Interesting link. Thanks for posting. The wiki article is short. Maybe some googling can shed more light on an e field mill. 

[John Heath]

Found a nice video on its construction with more detail.