# How does a Electric field (voltage) move

#### wes

Joined Aug 24, 2007
242
I just had a question about the movements of a electric field in a coil of wire (inductor ). When you apply a voltage to a coil, does the electric field (voltage) have to go around all the turns of wire,

so for say a 2 inch diameter coil and 2 inch high, with 10 turns, total wire length is 62 inches = 5.23 ft or 5.23 nanoseconds in terms of speed of light propagation through the coil. so would it take 5.23 nano seconds for a signal to reach from beginning to end. since it is going through all the wire length.

OR

does the electric field move through out the coil

so coil diameter is 2 inches and 2 inches high.

So the max amount of time needed for the signal to go from beginning to end is 160 picoseconds because the electric field doesn't move through the wire like the current does but instead moves in all directions at light speed and intersecting each turn causing current to flow.

so which is right?

#### russ_hensel

Joined Jan 11, 2009
825
Interesting question. I think a full answer would involve solving maxwell's equations. But a few points. The field is not on or off, so exactly what do you mean by arrive? Full steady state value ( time probably infinite ). Also a field is distributed in space, which parts of space are you concerned with. Also voltage and field are related but not the same ( check the units ) and you must consider both fields. Is your conductor perfect, if so no field inside the wire ( in the steady state ).

But as I say interesting.

Perhaps a voltage at the far end of the coil vs time is the answer you wish ( assuming a common ground ).

Would be interested to see what others say.

#### wes

Joined Aug 24, 2007
242
1st. the coils are NOT perfect.

What I mean by arrive is that when the field is switched on or maybe more accurately, Voltage applied (the source is connected to the coil), the time it takes for the field or voltage to start to cause current flow at the end of the coil (the other side of the source). It really is as simple as that, lol.

You know what, what you said is pretty much correct.

russ_hensel:
"Perhaps a voltage at the far end of the coil vs time is the answer you wish"

That is exactly what I am looking for, with the following coil specs depending on how the electric field causes current to flow in the coil, we get two different times that it should take before current starts flowing. Obviously only one of them is the real way it works.

Diameter = 2 inches
Length = 2 inches
turns = 10

Does the voltage reach (cause current flow) the end of the coil in
D * 3.141 = 62.82 inches = 5.23ft = 5.23 nanoseconds.
If this was correct then the voltage (electric field) had to move through all the turns in the coil.

OR

Does the voltage reach (cause current flow) the end of the coil in
L or D (since they are the same in size) = 2 inches = 166 picoseconds
If this was correct then the voltage (electric field) moved from the first turn up and to the side causing current to flow in the next turn and so on instead of needing to move inside the wires and around the turns as if they were pipes (just like how the electrons move through the wires.

Does this make more sense now?

#### nsaspook

Joined Aug 27, 2009
10,116
If the E field didn't follow the wire then how could a spot on a coil winding deep inside burn? (you need both fields for real power)
The E field follows the wire unless there is EM radiation into space.

#### strantor

Joined Oct 3, 2010
6,040
I am probably showing my ignorance here, but why are you associating the propogation of current through the coil to the speed of light? In my shaky understanding of current flow, the conductor is like a tube full of marbles; you insert a new marble in one end, and another pops out the other end instantly. there is no delay, no propogation time, from current entering one end of the coil to current reaching the other end of the coil. Am I way off base here/ have I missed the question?

#### nsaspook

Joined Aug 27, 2009
10,116
The electrons don't carry the energy and the movement of electrons in the wire has little to do with the speed of current propagation. The electrons are the charge carriers but the charge field moves at light speed on the surface of the wire.

Dangerous analogy time:

The electrons in a wire act like a superhighway that 'charge' (energy vehicles) travel on the surface of.

#### steveb

Joined Jul 3, 2008
2,436
so which is right?
It's a mixture of the two with the precise answer depending on the details of construction.

Without the details of exact materials and construction geometry, along with a corresponding sophisticated theoretical analysis of all that, the only thing you can say for sure is that the speed of the effects can not be faster than the speed of light over the dimensions of the device. Obviously, you can't have an instantaneous effect because that violates Lorentz invariance and the principles of relativity. Classical EM theory is a manifestation of relativity, after all.

However, there is no restriction on going slower than the speed of light. Hence, if the physics allows, direct propagation through a medium can be slower (in dielectrics, magnetic media and conductors), or waveguide effects can cause a nondirect route for the propagation of the fields. Either way, there is an implied longer delay time than that with direct light speed traveling of the electromagnetic waves.

The thing here is that there does not seem to be a clear way to say which effects will dominate. During the switch on transient, is the waveguiding effect along the wire the dominant behavior, or is it the free-space field propagation, or is it a mixture of the two? Note, that the first and last case implies a longer term effect, while the middle case will be the faster response. I suspect it is the last case, but I can't be sure.

Excellent question, by the way.

#### thatoneguy

Joined Feb 19, 2009
6,359
The speed of light in copper is lower than the speed of light in a vacuum.

In coaxial cables, it can vary from 0.6c to 0.9c

PC Motherboards are around 0.8c or so, this is due to the inductance and capacitance that is parasitic to the board once connections are made.

Pull out 3 taps along a long coil's length, put them as channel A, B, C on a 1Ghz Storage scope and turn on the power, storing the first millisecond.

It'd be kinda cool to do that with Hall effect sensors around the coil and plot them at the same time, but running out of channels could be a problem. Maybe use 2 scopes and set the trigger on both for the single "power on event".

I'd be interested in the results of this.

#### T.Jackson

Joined Nov 22, 2011
328
I have an electromagnet project for you shortly. You'll like this one.

#### wes

Joined Aug 24, 2007
242
Well the way I was thinking of it was since the electric field around the wire extends into space and since in the case of a coil, the other wires are close enough for the electric field to cause charge movement within those wires, so because of this the total time needed for charge movement (current flow) from the coil beginning to end is much less then you would normally think. Obviously the reason being that the the electric field wasn't guided like in a waveguide.

One of the things that also got me thinking about this was a capacitor. Think about it, you have two charged plates and each plate has this electric field around it and the other plate is the same, just with opposite charge. Each plate want's to equalize with other but the dielectric breakdown voltage is such that it can't until you connect a wire across it's terminals. What I got from this was that the electric field obviously expands out into the space around the plates. So wouldn't the same thing happen with a coil but since the wires are so close together , the electric field causes charge movement on them and this just repeats until the end of the coil which is connected to say a battery. This battery then supply's the current just like it usually does.

So yeah that's how I thought of it.
Sadly though, I don't have the equipment to test it, so instead I have to do these thought experiment's, lol

Joined Dec 26, 2010
2,148
Not only are there electric field couplings between turns, there are magnetic couplings as well, after all this is the whole point of winding a coil in the first place. With such intimate couplings between adjacent windings, I find it hard to imagine that the delay time would be equal to that of the same length of wire laid out straight.

I too would like to see a definitive answer to this point, which I am pretty sure came up before fairly recently.

#### crutschow

Joined Mar 14, 2008
30,452
The speed of light in copper is lower than the speed of light in a vacuum.

In coaxial cables, it can vary from 0.6c to 0.9c

PC Motherboards are around 0.8c or so, this is due to the inductance and capacitance that is parasitic to the board once connections are made.
....................
The delay is not related to the copper, it is due to the dielelectric constant of the surrounding material, which is the insulator between the center conductor and the outer shield in a coax cable, and the board material in a PC board. It is not from the parasitic inductance and capacitance. The inductance and capacitance actually determine the characteristic impedance of the line and that has no effect on propagation delay.

If you look at the propagation delay equations for a coax cable you will see a factor for the dielectric constant of its insulator. There is a similar equation for PCB propagation delay.

#### wes

Joined Aug 24, 2007
242
Not to get too far off the thread main point but why exactly is it that the speed of propagation in a coaxial is slower than in say copper? I know you said it has to do with the surrounding material dielectric constant Crutschow, but why? Does the signal frequency affect the propagation speed? Is the propagtion speed the same for AC and DC?

So yeah just had some questions, lol.

#### crutschow

Joined Mar 14, 2008
30,452
As I stated, the equation for the velocity of an electromagnetic wave includes a factor for the dielectric constant of the dielectric (including the absolute value of free space). You'd have to look at the derivation of Maxwell's equations to see why. (Incidentally he derived his equation for the velocity of an electromagnetic wave years before radio waves were actually generated and detected. When he realized the predicted velocity was near the then measured velocity of light he suggested that light was likely an electromagnetic wave, as we now know it is).

This velocity in a wire is independent of the AC frequency and is the same as DC step. There is no frequency term in the equation for the velocity.

#### nsaspook

Joined Aug 27, 2009
10,116
Slightly more off topic about the dielectric:

A interesting effect of the dielectric constant (displacement current polarization) in Maxwell's equations makes it possible to transmit and receive EM waves without a traditional antenna using only the dielectric properties of the resonator material.