Ohm's law, why current induces electric field and cause effect direction

ZapperZ

Perfect.

1. I have a "current source", i.e. free electron beams from my particle accelerator. After the last accelerating structure, it is now simply coasting, i.e. no electric field, but the electrons are still moving, so it has a current.

2. I shoot them into a piece of copper (it is what you would qualify as an "ohmic conductor", no?).

3. I then measure the field across it. What do I get?

4. I actually do this! I mentioned WAY early in my responses of something called the "Faraday Cup". In fact, 2 summers ago, I assigned an undergraduate summer intern to actually build a super fast Faraday Cup to measure very short electron bunches. Therefore, I strongly suggest you look up what a "Faraday Cup" is, and come back to me and tell me that you actually can get the same E-field as described in Ohm's Law across the conductor. You do NOT! You don't have to believe what I said, you are welcome to look it up.

5. In Ohm's law, you have a field E, that creates a current I, in the SAME CONDUCTOR. In your "experiment", there is NO "I" in the conductor (refer to my earlier post on the mean free path). The "I" or current in your scenario is external to the conductor and only comes in because it hits the conductors. Any kind of E-field that is generated in the conductors is NOT in correspondence with the external current. This is NOT Ohm's Law!

6. I study the process of secondary emission, which involves electrons with energy ranging from 200 eV all the way to hundreds of keV, hitting materials ranging from conductors to insulators. So the mechanism of electron transport once it hits a material is something I don't just read on, but it is something I experiment on! I truly would like you to do that exact experiment that you just described before you make such claims, because some of us actually HAVE done such experiments!

7. You posted this in the physics part of PF, not in the engineering part. Presumably, you wanted some fundamental physics issues being resolved here. I've tried, several times, to refer you to the Drude model with the hope that you might learn that there's a more fundamental description of the physics that produces Ohm's law, and discover for yourself the difficulty of having a current in a conductor without any preexisting E-field.

8. I can't make you learn and I think I've tried several times. It is no longer any of my concern to try and correct the errors in your understanding. You originated this thread and asked a question, but it appears that you already have made up your mind of the answer. All you appear to want to do is carry out an argument. I'll end my participation here, because I've already wasted too much time on a futile effort.

Zz.

Fernsanz

Are you the one who decides what is Ohm's law and what isn't? The current in my scenarios is external? What the hell is a current that travels across the resistor? If i have a current in a SC loop and in t=0 I insert a resistor in the loop, what the hell is external? The E-field that will arise across the resistor is not the one Ohm's law? Which part of the Ohm's law says if an electrical field along a conductor is the Ohm's law or not? Will the resistor violate the relation V=IR while the current in the loop semicondcutor-resistor is dacaying? No, it will not violate, so V=IR, so that's Ohm Law.

Do you even know my job? It will be interesting when I inform my mates that when we anlyze the effetc of space radiation in the circuits of the satellite (for example electrons being pumped into satellite ohmic conductors) we are worngly using the Ohm's law V=IR because the electrons come from outside. Ridiculous

You will never admit you are wrong becasue, as has become clear, any E-field that it is generated you will say it is not the Ohm's law. Stick yourself to explain how the hell that "kind of" electrical field is generated; I will decide if it is Ohm's law or not at my own.

It seems you can't stop typing "Drude model"!!! Read what I said about it in my previous post because you haven't even read it. Drude model has nothing to say here!!

You can not teach what you ignore. Yes please, end you participation here and let others who have answers participate.

kmarinas86

I emphasize the following:

The problem with the topic of this thread is that because of its constraints you stubbornly do not consider other physically valid scenarios, and thereby you limit yourself to explanations for which there are better alternatives. The sound analogy is the best one you got, and both cabraham and I both mentioned something of that nature much earlier in this thread. The first seven responses of this thread go exactly this:

What do you mean by "Thanks again"? Did you think I was cabraham?

Both cabraham and I contributed to this explanation, per above. Yet you only give credit to him. You even responded more thankfully to my explanation, but you thought I was someone else. Nevermind about this then. We've got a plausible explanation that doesn't go into many details as to why electrons behave this way. Do you want another explanation or deepen this one? Do you want to define the differential equations that are required to describe the second-order and higher-order effects of the E-field? Do you want to discussion in this thread to advance? Or do you want some kind of "totally exclusive and equally plausible explanation" for this? Seems like work doesn't it?

The 8th post was from ZapperZ. At this point, all hell in this thread broke loose. After a recent set of questions by ZapperZ, this following conservation was spawned:

ZapperZ thinks an applied field is not restricted to an "internal source", yet cabraham thinks otherwise. If an E-field is external, does that meant it is not "applied field"? It seems really arbitrary to assume either way. This thread is littered with disagreements that stem from mere terminological differences. The above is just one example.

ZapperZ is about to leave this thread for good, if he has not already:

Let's face it. You are more an applied physicist than a theoretical physicist. Why would someone like you care to put priority on the opinions of those who lean more toward the science of theoretical physics over those who lean more toward the practice of applied physics? You insist in using the conventions of engineers. Physics has more advanced explanations than are typically used in practice. Aren't you asking about something that your years of experience has not told you yet?

AJ Bentley

My two-pennyworth.

IMO
The classical ideas of fields and the movement of charges (not specifically electrons) don't sit well in the study of electrodynamics.

I rather like the approach taken by Prof Mead of 'explaining' electricity as a quantum effect from the outset. What's more, he points out (not in so many words) that when we study physical systems, we inevitably begin with a simple situation.
Typically we would avoid friction effects (often by setting ourselves up in a separate universe for the experiment!). For that reason, he elects to only consider superconductors.

It sounds crazy but it works. Within the first chapter of his book 'collective electrodynamics' he disposes of the E field and the B field as totally unnecessary artificial constructs and just uses the scalar and vector potentials along with simple QM concepts to completely reconstruct the subject.
He doesn't destroy Maxwell's work, he simply redirects it along the lines Maxwell would have gone if he'd been aware of facts we now know.

I can't recommend it strongly enough.

Just to give you the Flavour:-
He points out that the voltage across the ends of a loop (scalar potential) and the Vector potential A around the loop together satisfy the de Broglie relationship of frequency to wavenumber. By considering charge as a wave, it's therefore possible to specify the potentials as a four-vector throughout space - they depend only on J (also a four vector with the charge density.)
E and B - you don't need - you can easily calculate a value for them at any point if you want - but it turns out that most of the time you don't need to.

cabraham

Above there is a waveform of an R-L circuit whose current builds up to V/R over many time constants. May I re-emphasize that Ohm's law is valid in the resistor from time 0 out to steady state.

At t=0, Vr = 0, I = 0.

When I = 0.1*V/R, Vr = 0.1*V.

When I = 0.5*V/R, Vr = 0.5*V.

As the current builds up in the resistor the voltage builds up in unison. At every point in time, Vr = I*R. At t=0, there is no current, I=0. The entire voltage, V, is acoss the inductor, while Vr (voltage across resistor) is zero. Then the current builds up. During this time the voltage across the inductor is decreasing & the voltage across the resistor is increasing.

Ohm's law is in effect the entire time, transient as well as steady state.

Again, the resistor voltage increases simultaneously w/ the current, such that the ratio of Vr/I is always equal to the resistance R.

Regarding E fields & currents, the fact that charges drift in the presence of an E field is indisputable. But whenever an E field imparts kinetic energy to a charge, the E field energy is reduced, as conservation of energy is always happening. The E field energy lost is replaced by an energy conversion process, i.e. chemical reaction in battery (redox), mechanical power input to generator, etc. So E fields when exerting force on charges give up energy, & if not replenished cannot sustain a cuuent.

Likewise a current injected into a conductor can produce an E field but again, this E field does not impart force to the network current.

Neither J nor E can drive the other. The power source gives rise to both. Without energy conversion, neither J nor E will be sustained. When a battery is connected across a lamp, what drives E & J? It is the redox chemical process. If a cap is charged, then disconnected from the source, the cap can be switched across the lamp & it will momentarily light up, then fade.

If a current source like the inductor is switched into a lamp, it will glow momentarily, then fade. Just as J produces E, E can also produce J. But to sustain J & E, energy conversion must take place. The solid state physics aspect is intriguing, but sophomore level EE circuits & junior level EE fields is all that is needed. I think some make it way harder than needed. Any comments/feedback welcome.

Claude

kmarinas86

Okay, now I see that "Vr" is your resistive voltage drop. OK.

I just discovered that you can use subscripts.

V_R.

It's a lot better that show it that way.

I totally agree with this.

This does not sound right at all. Why should current injected into a conductor be any different than a lightning strike electrocution causing a current to be forced through one's body?

What if the power source consists of changing J and changing E?

This could be due to changing J and changing E at quantum level.

Totally agreed.

Needed for what? People have different plans, so maybe what they need depends on what they need to do.

Gordianus

Ohm´s law used to be simple and the Drude model explained very well the electric behaviour of metals. Now, having read many posts I feel totally confused. Do we really need QM to predict how much current flows in a wire?
My simple mind always believed the electric field was the stimulus and the current the result.
I´ve been teching elementary electricity and magnetism and I´ve never seen so much confusion around Ohm´s law.

cabraham

This type of prejudice is quite common. But consider what it takes to generate an E field. Charges must be displaced, i.e. separated. First, the mere separation of charges involves moving them , which constitutes current. Second, work must be done to achieve this. Third any E field which imparts force & energy to a charge carrier must lose the same amopunt of energy it imparted. CEL is immutable (conservation of energy).

An ac generator is a little more involved than a battery, so we'll look at the latter. If a battery powers a circuit consisting of conductors & a lamp, one can say that the current in the conductors & lamp is related to the E field per Ohm, i.e. J = sigma*E. But the current in the battery is oriented in the opposite direction. Let's use positive current convention.

In a passive element, current enters the terminal that is the more positive of the two, & exits the more negative terminal. The charges drift in the presence of E field per F = q*E.

But in the battery, positive current exits the positive terminal & enters at the negative terminal. This completely opposes the notion that "the E field drives the current". In the battery, the current is oriented in a direction against the E field. Electrons are moving from the pos to neg terminals inside the battery. This is the exact opposite of what happens if the E field "drives" the current.

So what "actually drives the current?" It is the chemical redox reaction, lead acid, nickel cadmium, or whatever. Energy is spent creating the E field. This E field does indeed impart energy to the conductors & lamp resulting in charge motion, i.e. current. But the E field is diminishing with every electron it moves. The chemical redox reaction keeps replenishing the E field, & current keeps going.

Brilliant minds have analyzed this Ohm's law question since the mid 19th century. "Does J drive E, or vice-versa"? The answer arrived at for more than a century & a half is "Why does one of them have to be the cause of the other? What if both J & E are caused by another entity?" This is the only logical answer. The cause of anything mechanical, electrical, chemical, nuclear, etc. is the transfer of energy. An inductor energized & shorted has energy per 0.5*L*I^2. If the current is diverted from the short to a resistor, this energy is dissipated as heat. First there was J w/o E, then E appeared, then both decayed to zero. The energy associated with each was converted to heat.

Likewise a charged capacitor open has energy per 0.5*C*V^2. When placed across a resistor, we get a J where we formerly had only E. But they soon both vanish. Again, think energy, not J or E being "first". Either can be first, but the cause is always the delivery of energy, while the effect is the receiving of energy.

Nothing else makes any sense at all. Cheers.

Claude

kmarinas86

So what caused the delivery of the energy.....

Here's a better idea. Our understanding of cause and effect (i.e. as a before and after thing) is an old and outdated understanding. New understanding of cause and effect is that everything results from change. A cause=A change. Everything that is conserved has always existed and will continue to exist in the same quantities. You must explain the transfer of energy as the result of changes without violating conservation. So this change is actually the change of something or more than one something. So the magnitudes of changes are what determine an effect. Cause is therefore more about the rate of change, the change of that rate of change, and so forth. Cause is therefore an ensemble of change, and therefore it cannot ascribed to an unchanging property or object. All that unchanging properties or objects do (assuming they exist) is put permanent limits on the boundaries of change.

kmarinas86

J/E is equal to conductivity. Since resistivity is equal to inverse conductivity, the verdict is quite clear. A current is produced by shorting an electric field. This creates a low-resistance path through which charges may travel. If E does not exist, then what is J? On the other hand, E may exist without J in a system with zero conductivity, but without J it cannot increase or decrease. The truth is that they all cause and effect each other simultaneously. What do you think causes the pathway to short? Perhaps its the build up of an electric field at a cathode. Perhaps it is infinite regress.

kmarinas86

So what makes you think that this by itself explains how much amps are going to come out of the battery? What is the with the obsession with a "singular" cause? The philosophy of "singular" cause is utter baloney nonsense!

Everything that science is capable of explaining is "caused". What do you think triggers the chemical redox reaction? Something must change outside the cathode to trigger the current yo.

ZapperZ

I know of Carver Mead's work quite well, In fact, if you do a search on PF, I've cited his PNAS paper on his Collective Electrodynamics several times. This is because he cited superconductivity as being the clearest manifestation of QM at the macroscopic scale. His reformulation of E&M fields is actually quite interesting and refreshing.

However, his work cannot derive, for example, Ohm's law, nor can he arrive at an explanation for "resistivity" in metals. Maxwell equations can't either. This is because this is not an issue of electromagnetic field, but rather a materials property (it is why such derivations are very seldom done in E&M classes, but rather, in solid state classes). Mead was able to describe, using his picture, various phenomena of superconductivity because the charge carrier responsible for that phenomenon has long-range coherence. The supercurrent does not interact with the microscopic details of the bulk material, what David Pines termed as a state of "quantum protectorate". So in essence, dealing with just the supercurrent made it "easier".

This is not the case with ordinary metals in the normal state. The question is, how are charges transported from one location to another, resulting in what we call a "current". We know that the charge carriers undergo several interactions: (i) electron-electron interactions, (ii) electron-ion (or phonon) interactions (iii) electron-impurities interactions), etc. (refer to, say, Valla et al., PRL 83, 2085(1999)). At room temperature, in a typical metal, the electron-ion/phonon interactions dominates, resulting in the fact that a free electron trying to move, will not make it way past the mean-free path. That's it. Without any external field, any electrons moving through such a material will thermalize. This is the origin of resistivity. One can derive from First Principles the resistivity of various materials using such a model.

This area is such a well-studied subject in condensed matter physics, because transport phenomenon is one of the most important aspects of that field. I could easily point out to the QFT approach to such a phenomenon (to answer the question from another member who wanted to know if such a thing has to be handled quantum mechanically) using what we call as the propagator, and arrive as the single-particle spectral function. Here it is even clearer that, analogous to the random walk problem, each charge carrier WILL experience multiple interactions impeding its motion. It is why this is a many-body physics problem. It is why the "electron" that we detect in a material does not have the same "mass" as the bare material. In heavy fermionic system, the charge carrier can have a mass more than 200 times the bare mass!

In all of these, there is a clear cause-and-effect, especially in how one gets Ohm's Law, how charges move through a material, etc.

Zz.

Fernsanz

A really good post.

But, for the sake of simplicity and to focus on the essence of the problem, let's get rid off bateries and sources. Just imagine a current flowing in a superconductor loop with no resistance. Then, at some time, let's label it [tex]t=t_0[/tex], I insert an ohmic resistor in the loop. At that very instant I will see a voltage i.e. an electric field across the resistor. Of course, both the current and the voltage will quickly decay to 0 since there is no source to keep it flowing but that is irrelevant for our question: how did that E-field arise?

cabraham

I never believed in a singular cause. I was just emphasizing that the energy has to be conserved, & must originate somewhere, i.e. redox. The OP question was related to J & E, as to one causing the other. I was merely explaining that they are interactive, mutual, & require energy conversion/source to sustain.

As far was what determines how many amps are supplied by the battery, Sir Oliver Heaviside laid that to rest in the 1870's.

In a previous post you stated

"The truth is that they all cause and effect each other simultaneously"

That has been my position since forever. Reread my posts on this forum or any other & that is what I/ve been saying for years. I've never bought into the belief that 1 specific variable is the cause of another under all conditions.

Claude

Fernsanz

I attach this fantastic paper I've found with title: "Electric Field and Plasma Flow: What Drives What?"

It is no exactly the same question that the OP one but very very similar. This is exactly the type of argument I was expecting. As clearly stated by the author, definitions of cause and effect, who goes first and who goes after, can be rigurously obtained with no philosophical burden.

I suspect that, as the subject of the paper is magnetohydrodynamics, something similar can be done for our subject, if it has not been done already. In fact his paper contain the words "Ohm's law" and touch the subject very close.

I would love an analogous paper to exist for Ohm's relation.

PS: The paper concludes, among other things, that flow also drives electrical field; hence, the equation can be interpreted symetrically depending on what is considered the stimulus and what the response. This is just the case for Ohm's law also.

Attached Files

ElectricfieldAndFlow.pdf (130.9 KB, 14 views)

Fernsanz

That is because most people take statements as they are given with little critical attitude towards it, if any. If you dig just a for a moment into many things we think we know well you will end up with more questions than certainties. And that, in turn, will lead you to gain deep insight on subjects most people haven't even realized. Ohm's law is an example as it is the question "why water evaporates below 100ºC when everybody knows that below 100ºC it is liquid". Just an example to comment on your appreciated post.

I hope that, in the end of this thread your view of Ohm's law be really deeper and different. Less simple it seems at first glance. I don't think your mind is simple, by the way.

kmarinas86

Word.