# Inertia of currents

1. Oct 2, 2006

### 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

2. Oct 2, 2006

### ZapperZ

Staff Emeritus
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.

3. Oct 2, 2006

### quasar987

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.

4. Oct 2, 2006

### cesiumfrog

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

5. Oct 17, 2006

### lark

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

6. Oct 17, 2006

### lark

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

7. Oct 17, 2006

### 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

8. Oct 17, 2006

### marcusl

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.

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/ohmmic.html#c1

Last edited: Oct 17, 2006
9. Oct 17, 2006

### leright

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.

10. Oct 17, 2006

### 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)

11. Oct 17, 2006

### 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.

12. Oct 17, 2006

### 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...

13. Oct 18, 2006

### 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?

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.

14. Oct 18, 2006

### 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 feild 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 seperate 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.

15. Oct 19, 2006

### leright

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.

Last edited: Oct 19, 2006
16. Oct 19, 2006

### cesiumfrog

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).

Last edited: Oct 19, 2006
17. Oct 19, 2006

### 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 seperate the field interaction of an electron and its mass.

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

18. Oct 19, 2006

### leright

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.

Last edited: Oct 19, 2006
19. Oct 19, 2006

### quinn

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?

20. Oct 19, 2006

### leright

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.

21. Oct 19, 2006

### 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,..

22. Oct 20, 2006

### leright

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

23. Oct 20, 2006

### 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.

24. Oct 23, 2006

### lark

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

25. Oct 23, 2006

### lark

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