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

[kmarinas86]

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.

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 "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.

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]

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.

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]

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

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 $$t=t_0$$, 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]

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.

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.

 

[Fernsanz]

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.

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]

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.

Word.