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Ohm's law, why current induces electric field and cause effect direction 
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#1
Jun3010, 12:30 PM

P: 58

Hi,
Lately I've been concerned about the Ohm's law [tex]J=\sigma E[/tex] and the physical interpretation of this law depending on what is considered the cause and what the effect. More concretely, it is quite natural and intuitive for me the interpretation of this law in one direction: a electric field [tex]E[/tex] over a ohmic conductor will cause a current [tex]J[/tex]. No one would have problems working out that electric force acting upon electrons will cause them to move, i.e. setting up a current. We can certainly say that the electrical field is the cause in this case and the current is the effect, the result. However, in the reverse direction, namely that a current [tex]J[/tex] injected somehow in a ohmic conductor will cause a electric field [tex]E[/tex], is by far more counterintuitive. Anyhow the current is generated previously by other means (for instance photoelectric or thermoionic effects) and injected into the conductor an electric field will arise. What is the explanation that acounts for that electric field caused just by movement of electrons in a conductor (which is nothing but a cristaline structure "covered" by a cloud of electrons)? I would gladly read your explanations. Thanks. 


#2
Jun3010, 12:45 PM

P: 1,036

It is counterintuitive indeed, but they are mutually inclusive, neither being the cause nor the effect.
I view it in the following way to see it better. By definition a constant voltage source is one that maintains a constant voltage despite varying load resistance. Let's say a current enters a conductor, the charge carriers in conductors are electrons. They have energy, but lose a portion of that energy when they collide with the lattice structure. When an electron in the conduction band collides with an electron in the valence band, energy is transferred. So a current is a transfer of energy among electrons, where the actual motion/displacement of an electron is small, but the propagation of energy is near light speed. The energy loss due to lattice collisions constitutes resistive loss. Thus the conduction electrons carry energy, a portion of which they lose due to resistance i.e. lattice collisions. By definition, the energy lost per unit charge is the voltage drop. Hence current entering a conductor incurs energy loss due to resistance/lattice collisions, resulting in a drop in voltage. The converse also holds. A conductor with no current is instantly connected across a small voltage. The E field results in charge motion i.e. current. Ohm's law is bilateral, where J & E are inclusive. Which one comes first is a moot question. You are thinking the right way. Claude 


#3
Jun3010, 01:46 PM

P: 58

So the question is still in the air: why an electrical field appear just because electrons are moving? (Don't lose of sight the "electrical" nature of the force im asking about which is the electrical field that appears in Ohm's low, not any other mechanical forces) 


#4
Jun3010, 05:34 PM

P: 1,036

Ohm's law, why current induces electric field and cause effect direction
The "thermal energy" associated w/ an electron is given by 0.5*m*v^2 = k*T, where m is mass, v is velocity, k is Boltzmann's constant, & T is temperature (absolute). If "resistance" is not a "mechanical" entity, then what is it? I'd like to know. Thanks in advance. Claude 


#5
Jul110, 01:01 AM

P: 58

Please, I'm not expecting simple or naive answer; I expect a physical explanation on why moving charges in a ohmic conductor induce an ELECTRIC field, i.e., a field that would cause a test charge placed inside the conductor to move purely by electric force [tex]F=qE[/tex]. 


#6
Jul110, 12:10 PM

P: 1,011




#7
Jul110, 12:36 PM

P: 58

Or do you mean that it should be viewed more like a compresionrarefaction process like a sound wave? That is, the first avalanche of electrons moving fast get really close to the frontend of standingstill electrons; then, because of proximity this standing still electrons will move forward getting closer to the next ones and so on. Is this a correct visualization? Thanks again 


#8
Jul110, 01:03 PM

Emeritus
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PF Gold
P: 29,239

Note that I can shoot electrons in vacuum (we do that all the time in a particle accelerator) and after the accelerating structure, it can simply coast without any applied field. So you have current, but no applied field that cause this current, nor does it induced the SAME field in reverse. It will have other fields, such as magnetic field or time varying electric field, but this electric field is NOT the same electric field as referred to in Ohm's Law, i.e. constant axial field in the direction of motion. Zz. 


#9
Jul110, 02:14 PM

P: 58

Are you suggesting that we can have the current with or without electric field depending on how we generate that current? i.e., are you suggesting that we can't read the Ohm's law in the direction [tex]J[/tex] implies [tex]E[/tex] but we can read it in the direction [tex]E[/tex] implies [tex]J[/tex]? If you are claiming this then we should warn electrical engineers around the world because the relation V=IR is not valid when the current is the first cause (for example when the current is generated in a photodiode); and obviously this is not the case 


#10
Jul110, 03:13 PM

P: 58

It is quite clarifying and supports my previous picture of sound wave to explain the propagation of the electric field. This also explain that electric field induced when the current is the "first cause" is exactly the same as the one obtained from Ohm's law, because in any case the current has to be the dynamic solution of an existing electric field. So now it's clear for me: the Ohm's law is a true constitutive relation which relates two quantities no matter which one is the "first cause" Thanks AJ Bentley 


#11
Jul110, 10:44 PM

P: 1,036

The answer to the OP question "how is it that if the current is first that it can produce an E field?" is that the injected charge carrriers provide the said E field.
Remember that electrons & holes being charged, possess an E field of their own. Let's say we have a conductor, a good one but not a superconductor. Let's say it is connected across a current source suddenly. The holes & electrons enter the conductor. Upon arrival, they bang into the lattice resulting in heat dissipation known as resistance. Each charge carrier can approach a limited average velocity owing to collisions. Hence a charge distribution will be effected. At the end where electrons enter, an accumulation of e results in an E field since e possess such a field. Likewise with holes. h+ at the opposite end. If you prefer, a hole entering is equivalent to an e exiting. So one end has an accumulation of h+, the other has e. There is an E field whose lines start on a hole & end on an electron, as well as a potential. The potential V, is just the line integral of E over the path. In a superconductor, SC, there is no resistance, hence no E field. When e enter a SC, they incur no collisions, & their tendency is to diffuse apart from one another. When they reach the surface, they cannot continue outward since energy is needed. So a charge accumulation exists on the surface of a SC. Hence, in the absence of interior charge unbalance, there can be no E field on the interior of the SC. Did this help? Claude 


#12
Jul210, 02:31 AM

P: 58

Second, and once again, the Efield is not produced as a result of charge accumulation. An accumulation of electrons radiates an Efield in all directions, not just in the direction of current, so an accumulation would accelerate electrons which are behind it and would slow down electrons which are before it, i.e. would spread electrons out of the accumulation in all directions. Furthermore you are seeing the current inside the conductor as a succession of charged zones which is not true since the conductor carrying a current is homogeneous As I said I have found the answer I wrote in my previous post. Thank you anyway. 


#13
Jul210, 02:42 AM

P: 58

Second, and once again, the Efield is not produced as a result of charge accumulation. An accumulation of electrons radiates an Efield in all directions, not just in the direction of current, so an accumulation would accelerate electrons which are behind it and would slow down electrons which are before it, i.e. would spread electrons out of the accumulation in all directions. Furthermore you are seeing the current inside the conductor as a succession of charged zones which is not true since the conductor carrying a current is homogeneous As I said I have found the answer I wrote in my previous post. Thank you anyway. 


#14
Jul210, 06:49 AM

P: 1,036

Why would peer reviewed uni texts say that if it were not so? What are your references? I never expalined a directed current based on charge accumulation. The charge accumulation accounts for the E field inside the good conductor (not SC). Please don't put words in my mouth. I try to help you by giving free advice which takes years to acquire, & you rudely rebuke me with straw man arguments, correcting me on issues I never raised. Just out of curiosity, how far along did you get regarding education. Are you a practicing scientist/EE? Just curious. You have a lot of sass & moxie with little chops to back it up. The problem with these forums is that everybody thinks they know more than everyone else. You exemplify that attitude. Claude 


#15
Jul210, 07:12 AM

Emeritus
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PF Gold
P: 29,239

I've just shown you an example where I could have a current without the use of an external electric field to generate that current. Want another example? Look at the current from a photoemission process. Look ma! No electric field! I still want to see this experiment where you shoot electrons into a conductor, and this process, in turn, generates the corresponding E field that is similar to the Efield that causes the current in the reverse process. I shoot electrons into metals all the time (it's part of my job)  we call it either a beam stop, or a Faraday Cup. In none of these do you generate the identical Efield in the conductor that is described by Ohm's Law. Zz. 


#16
Jul210, 09:10 AM

P: 1,011

Ohm's "law" is very quaint. For example, [tex]\mathbf{J}=\sigma\mathbf{E}[/tex] applies only for a uniform field in the direction of the current. What kind of "law" is that? There is no "righthand law" in physics. Lefthanded materials exist. We have something called "the righthand rule". Ohm's "law" should be called "Ohm's rule". I did a Google search, and it turns out many concur. 


#17
Jul210, 10:40 AM

Mentor
P: 11,625

If the conductor is anisotropic, the current density and electric field can be in different directions at a given point. In this case you have to use a tensor for the conductivity. 


#18
Jul210, 12:01 PM

P: 367

Quite often, equations will be written in an "aesthetic" form. The left hand side (LHS) may sometimes be the cause, other times it may be the effect, yet other times the equation will simply be a mutual relation. In the present case of Ohm's law, [tex]J=\sigma E[/tex], J is the effect and E is the cause. I suppose this makes perfect sense writing the equation this way because it places the dependent variable on the LHS and the independent variable on the RHS, i.e. it is in the from y(x)=mx. Not to get offtopic, but I believe a few examples might be helpful to some.... Newton's second law: F=ma F is the cause and a is the effect; forces cause bodies to accelerate, not vice versa. Why is it commonly written in the opposite form as Ohm's law? Easier to remember, looks nicer.... who cares? The most famous equation in all of physics: [tex]E=mc^2[/tex] This is simply, what I called above, a mutual relation. Rest energy is mass, mass is rest energy. 


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