Inertia of Currents: Exploring Resistance & Superconductivity

[lark]

Something I keep on wondering about - wouldn't currents have some inertia, some tendency to keep on moving, even if there is no inductance? After all, electrons have inertia and they would tend to
keep on moving in the same direction even when there's no electric
field pushing them ...

Is this an effect that would be incredibly small compared to anything that goes on with real currents?

I think superconductors are like that - once a current is started, it keeps on going unless stopped somehow - because there is no resistance. But, in non superconducting material, the resistance would stop the electrons
very soon?

Laura

 

[ZapperZ]

I think superconductors are like that - once a current is started, it keeps on going unless stopped somehow - because there is no resistance. But, in non superconducting material, the resistance would stop the electrons
very soon?

Laura

The reason why current in a superconductor continues to move is not due to inertia of the charge carriers. It has more to do with long-range phase coherence in which these carriers are described by non-dispersive plane waves. So if you buy into the QM description, the charge carriers are spread out all over the material as supercurrents.

Zz.

 

[quasar987]

Something I keep on wondering about - wouldn't currents have some inertia, some tendency to keep on moving, even if there is no inductance? After all, electrons have inertia and they would tend to
keep on moving in the same direction even when there's no electric
field pushing them ...

Here is my (classical) interpretation of currents, and how it answers your question:

In a conductor, the electrons are going at very high speed in random directions, such that the average speed of the electron is 0. The electrons are also colliding with one another constantly. When you apply an electric field in the conductor, the electrons start accelerating in the direction of the field. But they only have time to build a small velocity before colliding with another electron. At which point the acceleration starts anew and the particle picks up speed in the direction of the field before the next collision, and so on. What we call the drift velocity then, is the average over time of the average velocity in the direction of the field (over all electrons).

When the field is turned off, the electrons loose the driving force that was pushing them in the direction of the field after each collisions, which resulted in a non-nul average velocity. So the drift velocity becomes 0 again, i.e. there is no current.

 

[cesiumfrog]

Laura, you may be interested to google "Lenz law", "self-inductance" or "back-emf".

 

[lark]

Laura, you may be interested to google "Lenz law", "self-inductance" or "back-emf".

I didn't mean inductance effects - I meant the inertia of the electrons which are moving a little more in one direction than another. It wouldn't
just go away if the voltage goes away. The electrons wouldn't have a
force on them any more, though.

I expect the truth is that this inertia of the electrons moving is very very
small compared to the mass of the metal they're in.

But if the current was very high, say if you had a plasma with a lot of current - or the solar wind is a kind of current, perhaps - or currents moving in the Earth's upper atmosphere, maybe they would have a significant inertia.

Laura

 

[lark]

Laura, you may be interested to google "Lenz law", "self-inductance" or "back-emf".

I didn't mean inductance effects - I meant the inertia of the electrons which are moving a little more in one direction than another. It wouldn't
just go away if the voltage goes away. The electrons wouldn't have a
force on them any more, though.

I expect the truth is that this inertia of the electrons moving is very very
small compared to the mass of the metal they're in.

But if the current was very high, say if you had a plasma with a lot of current - or the solar wind is a kind of current, perhaps - or currents moving in the Earth's upper atmosphere, maybe they would have a significant inertia.

Laura

 

[lark]

Apparently the inertia of the charge carriers does matter in some situations - I went searching with Google and I came across an article about their inertia changing how a plasma acts.

Laura

 

[marcusl]

I didn't mean inductance effects - I meant the inertia of the electrons which are moving a little more in one direction than another. It wouldn't
just go away if the voltage goes away.

Actually it does. quasar987 steered you in the right direction. The electron drift velocity is tiny compared to random thermal motions in a metal at room temperature, and when the electric field is removed it disappears in a time comparable to the relaxation time or mean time between collisions--about 10^(-14) seconds in copper. Since a collision erases any memory of drift, that's how long any "inertia" effect could last after the field is removed.

This link may be instructive
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/ohmmic.html#c1

 

[leright]

Actually it does. quasar987 steered you in the right direction. The electron drift velocity is tiny compared to random thermal motions in a metal at room temperature, and when the electric field is removed it disappears in a time comparable to the relaxation time or mean time between collisions--about 10^(-14) seconds in copper. Since a collision erases any memory of drift, that's how long any "inertia" effect could last after the field is removed.

This link may be instructive
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/ohmmic.html#c1

Lark is referring to superconductors though...a superconductor has zero resistance. Therefore, if there is an existing current, and voltage is removed, the current will be maintained...however, the reasoning for the maintained current is much more complicated than simple inertial effects and QM needs to be considered, as Zz expertly pointed out.

 

[quinn]

Actually if you study the diffential equations for electrical currents inductance IS inertia.

Inductance is related to the second derivative of charge and inertia is the second derivative of position, or another way- inertia is the first derivative of mometum and inductance is the first derivative of current.

(Current is moving charge, which is a constant charge carrier with a velocity)

 

[marcusl]

Inductive "inertia" is supported by energy stored in the magnetic field. If it were electron inertia, current in a coil would behave the same if wrapped around air or iron.

 

[quinn]

incorrect.

I said that inductance is inertia, and that inductance is related to the 2nd derivative of charge. It is true that an air core electromagnet acts different than a ferrite core electromagnet and thus a constant of porportionality, namely permeability.

inertia is simplely the resistance to change, and inductance surely covers that...

 

[LURCH]

But Lark is quite obviously talking about the physicle inertia (resistance to acceleration) of the ellectrons themselves. Can inductance (resistance to change in charge) be the explained by this?

Apparently the inertia of the charge carriers does matter in some situations - I went searching with Google and I came across an article about their inertia changing how a plasma acts.

Do you have a link? I find this an interesting question. If the ellectrons are moving through (i.e.) a wire, and then they stop, their momentum must result in the waire being "bumped", however slightly, in the direction they were drifting. But I'm not sure if the article you found is reffering to that (the inertia of ellectrons), or the inertia of the "charge-carrying particles" in a plasma (which would be protons, right?) or the inertia of charge itself, which would be inductance. I've been following allong with the doings over at PPPL, http://www.pppl.gov/ , so I'd really like to read that article.

 

[quinn]

I don't see how inductance isn't physical inertia...

An electron at constant velocity will tend to stay in motion due to its inertia and will not change speed until it is acted upon, either by collision or field interaction. The end result is the same, the electron will stay in an inertia reference frame (constant velocity).

The problem here is that people want to separate an electrons actions into "mass caused" and "field caused". Both can carry mometum and thus resist change.

It is true that when a current changes in a wire it imparts a (small) momentum transfer to the physical wire and it is caused by the mass of the electrons and the field of the electrons.

 

[leright]

I don't see how inductance isn't physical inertia...

An electron at constant velocity will tend to stay in motion due to its inertia and will not change speed until it is acted upon, either by collision or field interaction. The end result is the same, the electron will stay in an inertia reference frame (constant velocity).

The problem here is that people want to separate an electrons actions into "mass caused" and "field caused". Both can carry mometum and thus resist change.

It is true that when a current changes in a wire it imparts a (small) momentum transfer to the physical wire and it is caused by the mass of the electrons and the field of the electrons.

maybe I'm just not 'getting' your point, but in my eyes inductance has nothing to do with inertia. It may be somewhat analogous, but it is not the same, I don't think. Inductance is simply an induced voltage in a conductor (or an induced e-field) due to changing magnetic flux, where the changing flux occurs due to changing B-field (transformer EMF) or changing surface area (motional EMF) through which the B-field is penetrating. The induced voltage occurs in such a way as to drive a current around the conductor in the direction that produces a magnetic field that opposes the changing flux. It's as simple as that. Nature fights changes in magnetic flux by inducing voltages and currents.

Now, changes in current in a conducting loop cause changes in magnetic flux, which in turn causes an EMF that produces a current that opposes the change in current, and this might be what you are talking about when you say inertia is inductance. I'm not quite convinced. The ideas are vaguely similar though.

So you are correct in saying they are ANALOGOUS (but wrong by saying they are EQUIVALENT), since derivatives of current (changing velocity of electrons...) or, equivalently, second derivatives of charge, are resisted by Faraday's law of inductance. If there is a changing current (accelerating electrons) this will be resisted by inductive effects. This is like acceleration of masses being resisted by inertial effects. So, inductance resists changes in current (or electron acceleration) and inertia resists changes in mass acceleration. However, this doesn't mean inductance and inertia are equivalent phenomena!

Sorry if this doesn't make any sense...it is very late and I'm tired.

 

[cesiumfrog]

However, this doesn't mean inductance and inertia are equivalent phenomena!

Hmm.. we know magnetism can be derived just from the relativistic mechanics of electric charges.. Can Lenz' law be derived from the mass-inertia of electrons? If not, the first alternate mechanism I can imagine now is that trying to accelerate a number of charges too quickly might tend to make them bunch up (opposed by electric repulsion). Maybe the answer is in experiments with plasma (ie. currents with different mass charge-carriers).

 

[quinn]

It does mean they are the same. Sorry.

The phenomenon is resistance to change of velocity, AKA inertia. An electron resists change in velocity. It is impossible to separate the field interaction of an electron and its mass.

q*[L*(d2/dt2)q] = m dp/dt = force

 

[leright]

It does mean they are the same. Sorry.

The phenomenon is resistance to change of velocity, AKA inertia. An electron resists change in velocity. It is impossible to separate the field interaction of an electron and its mass.

q*[L*(d2/dt2)q] = m dp/dt = force

hmmm...q[L*(d2/dt2)q] does not equal force...it's actually equal to work, or the path integral of the force over a closed path that is caued by the changing current.

q[L*(d2/dt2)q] is certainly not equal to force. Hell, m dp/dt isn't even equal to force...dp/dt is though.

You can't say inertia is the same thing as inductance just because they behave similarly or the equations look similar. I agree that they are analogous, but I am not yet convinced they are the SAME. I've heard of inductance being called "electrostatic inertia", but nobody EVER claimed it to BE inertia in the same sense as inertia of massive bodies. You may be right, but you haven't convinced me yet.

 

[quinn]

Mistakes happen when answering quickly.

I do apolgize for the quip response. It is very true that I screwed up on that answer. Sorry.

My assursion remains the same.

Is there not a resistive force felt when bending a flexible tube with flowing water in it?

 

[leright]

Mistakes happen when answering quickly.

I do apolgize for the quip response. It is very true that I screwed up on that answer. Sorry.

My assursion remains the same.

Is there not a resistive force felt when bending a flexible tube with flowing water in it?

You are simply throwing equations around, claiming they are similar in form, and ASSUMING they are the same phenomenon. From the explanation you've given me, you can say they are ANALOGOUS phenomenon, but I don't see how you could ever claim them to be the SAME.

Unless you can justify your position in more detail then I am not going to agree with what you're saying.

As cesiumfrog stated, are you able to derive Lenz's law and inductance from inertia due to mass? IF you can do this then you are perhaps correct.

 

[quinn]

Well,.. one could always just take the former equations that I have been quoting and divide by length thus rendering a intrinic quantity for parameter... inductance per meter, capacitance per meter,.. thus rendering a equivalent equations for a simple harmonic oscillator and an LRC circuit... perhaps you just think this is more tomfoolery,.. but,... you can debate it all you want, the fact remains that inertia and inductance are equivalant,..

 

[leright]

If anyone else wants to back these statements up then please do so...

 

[leright]

At this point I am saying electrical inductance is like mechanical inertia and I'm leaving it at that. They are not the same. Until you can provide a more compelling argument then this is where I stand.

 

[lark]

Do you have a link? I find this an interesting question. If the ellectrons are moving through (i.e.) a wire, and then they stop, their momentum must result in the waire being "bumped", however slightly, in the direction they were drifting. But I'm not sure if the article you found is reffering to that (the inertia of ellectrons), or the inertia of the "charge-carrying particles" in a plasma (which would be protons, right?) or the inertia of charge itself, which would be inductance.

That was Physics of Plasmas, May 2005
12, 054504

It was talking about inertia of both electrons and ions in a current from a
static electric field, how it plays a role in acoustic instabilities in the
plasma. (not inductance)

try searching for "electron inertia" online, various things come up that might relate to this.

Laura

 

[lark]

maybe I'm just not 'getting' your point, but in my eyes inductance has nothing to do with inertia.

Inductance can't come from the mass of the charge carriers, because
the self-inductance of a solenoid, for example, is just
the permeability constant times turns/unit length squared, times
cross-section area of the solenoid.

It doesn't have anything to do with what the charge carrier in the
solenoid is. It could be protons or ions whirling around in a plasma.

Laura

 

[marcusl]

If anyone else wants to back these statements up then please do so...

Here's how I see it. Start with your favorite definition of inertia. Here are a couple:
1. inertia (în-ûr¹she), in physics, the resistance of a body to any alteration in its state of motion, i.e., the resistance of a body at rest to being set in motion or of a body in motion to any change of speed or of direction of motion. This is known as Newton's first law of motion. (http://www.neutron.anl.gov/hyper-physics/inertia.html )

2. The concept of inertia is today most commonly defined using Isaac Newton's First Law of Motion, which states: Every body perseveres in its state of being at rest or of moving uniformly straight ahead, except insofar as it is compelled to change its state by forces impressed. [Cohen & Whitman 1999 translation]
The description of inertia presented by Newton's law is still considered the standard for classical physics. (http://en.wikipedia.org/wiki/Inertia)

N.B.: no mention of self-inductance anywhere! If we want to understand inertial effects of current flow in a wire, we'd better look at motion of individual electrons under a (really powerful) microscope.

Electrons in a copper wire at room temperature undergo a collision about every 4x10^(-14) sec [relaxation time], during which they lose all "memory" of their previous motion. There are about 10^23 electrons per cc, all moving randomly, so average motion is zero. An electric potential applied across the ends of the wire produces an axial electric field that accelerates each electron (for a short time!) following a collision. The average motion or net "drift" is what we call a current.

Change or remove the electric field and the electrons will resist any alteration in their state of motion, i.e., ... any change of speed or of direction of motion according to Newton. That's inertia. But only for 4x10^(-14) seconds! Then the motions are randomized again and inertial effects are over. A changing magnetic field can influence the motion by generating an emf, thereby inducing electron flow, as Mr. Faraday discovered. You can say that it behaves like inertia because you can't tell the difference by looking at your oscilloscope and ammeter, but you're just doing an experiment that's too crude to see the differences. Inside the wire at the microscopic level the continuing current is being driven from outside. In fact whether the changing magnetic field is generated by the original current as in a solenoid or by an external electromagnet and power supply, it's still an external forcing function and not inertia. Inertial effects disappear in about 4x10^(-14) sec in copper at room temperature IMHO.

 

[leright]

Here's how I see it. Start with your favorite definition of inertia. Here are a couple:
1. inertia (în-ûr¹she), in physics, the resistance of a body to any alteration in its state of motion, i.e., the resistance of a body at rest to being set in motion or of a body in motion to any change of speed or of direction of motion. This is known as Newton's first law of motion. (http://www.neutron.anl.gov/hyper-physics/inertia.html )

2. The concept of inertia is today most commonly defined using Isaac Newton's First Law of Motion, which states: Every body perseveres in its state of being at rest or of moving uniformly straight ahead, except insofar as it is compelled to change its state by forces impressed. [Cohen & Whitman 1999 translation]
The description of inertia presented by Newton's law is still considered the standard for classical physics. (http://en.wikipedia.org/wiki/Inertia)

N.B.: no mention of self-inductance anywhere! If we want to understand inertial effects of current flow in a wire, we'd better look at motion of individual electrons under a (really powerful) microscope.

Electrons in a copper wire at room temperature undergo a collision about every 4x10^(-14) sec [relaxation time], during which they lose all "memory" of their previous motion. There are about 10^23 electrons per cc, all moving randomly, so average motion is zero. An electric potential applied across the ends of the wire produces an axial electric field that accelerates each electron (for a short time!) following a collision. The average motion or net "drift" is what we call a current.

Change or remove the electric field and the electrons will resist any alteration in their state of motion, i.e., ... any change of speed or of direction of motion according to Newton. That's inertia. But only for 4x10^(-14) seconds! Then the motions are randomized again and inertial effects are over. A changing magnetic field can influence the motion by generating an emf, thereby inducing electron flow, as Mr. Faraday discovered. You can say that it behaves like inertia because you can't tell the difference by looking at your oscilloscope and ammeter, but you're just doing an experiment that's too crude to see the differences. Inside the wire at the microscopic level the continuing current is being driven from outside. In fact whether the changing magnetic field is generated by the original current as in a solenoid or by an external electromagnet and power supply, it's still an external forcing function and not inertia. Inertial effects disappear in about 4x10^(-14) sec in copper at room temperature IMHO.

My thoughts exactly. Inductance behaves like inertia, but they are certainly not the same thing.

Than you for taking the time to argue this.

 

[Creator]

Something I keep on wondering about - wouldn't currents have some inertia, some tendency to keep on moving, even if there is no inductance? After all, electrons have inertia and they would tend to
keep on moving in the same direction even when there's no electric
field pushing them ...

Laura

Laura...
I sent you a post yeaterday...answering this question very succinctly. Apparently, someone...possibly a moderator removed it without informing anyone ..and without any reason ..
Anyone know why it was removed?

Creator

 

[lark]

Change or remove the electric field and the electrons will resist any alteration in their state of motion, i.e., ... any change of speed or of direction of motion according to Newton. That's inertia. But only for 4x10^(-14) seconds!

But in a plasma that isn't true - I looked around a little and apparently
E&M works differently in plasmas because of the mass inertia of the particles - which includes ions and electrons.

Laura

 

[marcusl]

But in a plasma that isn't true - I looked around a little and apparently
E&M works differently in plasmas because of the mass inertia of the particles - which includes ions and electrons.

Laura

The case I treated, as mentioned in the post, was electrons in copper at room temperature. You are correct that those numbers don't apply to a plasma which, as you point at, has both ion and electron charge carriers. It also has low density and long mean free path compared to a metal, and a host of special effects.

It's not true that E&M works differently, however. E&M is E&M !

 

[lark]

The case I treated, as mentioned in the post, was electrons in copper at room temperature. You are correct that those numbers don't apply to a plasma which, as you point at, has both ion and electron charge carriers. It also has low density and long mean free path compared to a metal, and a host of special effects.

It's not true that E&M works differently, however. E&M is E&M !

It works differently in the sense that things like Ohm's law have to be
changed - I was looking around at plasma physics stuff and finding things about how an extra term gets added to Ohm's law. And there is "magnetic reconnection" in a plasma that is somehow related to the mass-inertia of charge carriers. So what I mean is, if you were writing down differential equations for current in a plasma they would look different.

Laura

 

[lalbatros]

Lark,

Currents indeed have inertia.
However they are not usually observed because of the high collision frequencies. In between two collisions, electrons (in copper for example) are indeed accelerated and their inertia does determine this acceleration. But with high collision rate the effect is not observable.

In particles accelerators, the particle beam is a current. Its inertia is observed easily: just by observing how much material the beam must cross before stopping. (but this is usually not the objective of these expensive experiments).

I plasma physics, more precisely in tokamaks, a current is induced in the plasma ring by an external magnetic field. When the plasma density is high, the plasma (fully ionised gas) behaves roughly like an excellent conductor and no inertia can be observed. However, in some circumstances, specially at low density, the most energetic electrons in this current see their collision frequency decreasing as their speed increase. These electron accelerate until they get out of the machine. These are called "run-away" electrons and can damage measurement devices. They show clearly their inertia: nothing can stop them in the plasma until they get out of the machine (within the tokamak a strong magnetic field keep most particles moving along the magnetic field lines inside the tokamak)

Michel

 

[questionmark]

inductance of seawater

an interesting case may be when you have an electric circuit comprising of two widely-separted electrodes placed into seawater passing an electric current between them driven by a source. the ions in the seawater are the charge carries for the seawater-part of the circuit, whilst electrons are the charge carriers for the remainder - in the cables. the ions have a much larger mass than the electrons. will the circuit have more/less/the same inductance compared to the case where a circuit with the same loop-area is contructed only using cables - i.e. no ions in the circuit?

 

[nikolatesla20]

Hm. All of these posts are interesting.

I too have always compared electrical inductance to physical inertia. I will agree they are not necessarily the same thing.

However, if we simply look at the behavioral level:

1. Current is applied thru a coil. The coil builds up a magnetic field. Upon removal of the current, the magnetic field collapes, thereby generating a reverse current (back EMF). This causes a large voltage to be generated (because the current has not where to go), releasing the stored energy (stored magnetic field).

2. A Physical object starts from a rest position to 60MPH. After reaching 60MPH, it makes contact with a solid graphite wall (the side of a mountain). It receives a large force in the opposite direction, causing a large release of energy (release of stored momentum).

They may not be mathematically equivalent, but they sure are mathematically comparable, even comparable at the physical observational level. And if we graphed the energy in each situation, we would see a similar graph with a large spike on the end. (Graph voltage for the coil, and graph force in lbs for the physical object).

I think the thing to realize however, is yes, the "inertia" of the inductor is not from the moving electrons. It is from the generated magnetic field. In the same vein, physical inertia is not from the body, but from stored energy in its motion. In this case I tend to think of inertia as "gravitational inductance"...

-niko

 

[leright]

Inductance has nothing to do with electrons staying in motion once they are in motion, which is what inertia describes...It has something to so with a current in a conductor being induced due to a time varying B-field. I don't see how this relates inertia to inductance.