Current & Ohm's Law: Continuous vs Discrete?

[Schfra]

When we talk about current and ohm’s law, do we pretend that current is continuous rather than discrete in the same way that we do with charge distributions?

 

[lekh2003]

When we talk about current and ohm’s law, do we pretend that current is continuous rather than discrete in the same way that we do with charge distributions?

Current is continuous. In concept, current is a moving charge over time. Of course, current can stop flowing, but we assume that the charge distribution over time is constant for practical purposes.

 

[Dale]

When we talk about current and ohm’s law, do we pretend that current is continuous rather than discrete in the same way that we do with charge distributions?

Yes.

 

[sophiecentaur]

When we talk about current and ohm’s law, do we pretend that current is continuous rather than discrete in the same way that we do with charge distributions?

When you do a calculation about the force distribution along a beam or the tension in a rope, do you feel the need to include the particular nature of the materials involved? Do not be fooled into thinking that including electrons in any circuit calculations will help you at all in the understanding.
Are you bothered at all that no calculation you have ever done with a computer has avoided quantisation and that it does not match the algebraic equation you may have started off with? Relax (numerically, that is).

 

[Schfra]

Current is continuous. In concept, current is a moving charge over time. Of course, current can stop flowing, but we assume that the charge distribution over time is constant for practical purposes.

So if we had a conductor that was composed of a very small number of theoretical particles each with a very large charge, then would we say that the conductor was non-ohmic because the current would fluctuate between 0 and some value for associated with the charge of one of these particles?

 

[Drakkith]

So if we had a conductor that was composed of a very small number of theoretical particles each with a very large charge, then would we say that the conductor was non-ohmic because the current would fluctuate between 0 and some value for associated with the charge of one of these particles?

For small time scales, yes. But it would still hold for larger time scales where the discrete nature of the charges can be modeled as continuous.

 

[Schfra]

For small time scales, yes. But it would still hold for larger time scales where the discrete nature of the charges can be modeled as continuous.

What if some particle of charge Q partially passes through a point in a wire as shown in the attached image?

Also does the particle have to reach the point at which current is being measure or pass it?

 

[sophiecentaur]

So if we had a conductor that was composed of a very small number of theoretical particles each with a very large charge, then would we say that the conductor was non-ohmic because the current would fluctuate between 0 and some value for associated with the charge of one of these particles?

Of course. Ohm's law is followed by- solid metals at a constant temperature. Metals have a huge number of available charge carriers and each one (on average) takes the same amount of energy to get it through the wire (or whatever) So the energy needed is proportional to the number of charges passing. And that's Ohm's law. Ions can also carry charge but I haven't come across highly charged ions carrying current in a 'linear' way.
The nearest thing to what you are suggesting that I can think of is the experiment with a pith ball, oscillating between two charged plates, transferring charge on each cycle of the oscillation.

 

[sophiecentaur]

What if some particle of charge Q partially passes through a point in a wire as shown in the attached image?

Also does the particle have to reach the point at which current is being measure or pass it?

This is a nonsense idea. Without a doubt. It has nothing to do with Ohm’s law. Your attempt at extending a law which actually depends on a Quantum Effect has no validity at all. The valid intermediate models that bridge the gap between Electrical batteries and meters and QED do not include visible sized particles.

 

[Schfra]

This is a nonsense idea. Without a doubt. It has nothing to do with Ohm’s law. Your attempt at extending a law which actually depends on a Quantum Effect has no validity at all. The valid intermediate models that bridge the gap between Electrical batteries and meters and QED do not include visible sized particles.

Should current not ever be thought of as charged particles passing a point in some unit time, and does the idea of current apply exclusively to continuous charge distributions?

 

[ZapperZ]

Should current not ever be thought of as charged particles passing a point in some unit time, and does the idea of current apply exclusively to continuous charge distributions?

Please note that in many particle accelerators, the charges come in bunches and not a continuous flow. In such cases, we have "average currents" and "peak currents", which designate some value over a period of time. There's no ambiguity here on what is meant by the term "current" in such cases.

BTW, the title of this thread is a bit misleading. By invoking "Ohm's law", you have made implicit assumptions on various things (for example, the parameters described in the Drude model). So trying to marry this with such discrete and discontinuous charge flow doesn't make sense.

Zz.

 

[Dale]

Should current not ever be thought of as charged particles passing a point in some unit time, and does the idea of current apply exclusively to continuous charge distributions?

So, if you are doing classical EM then J is a continuum. You can approximate a discrete charge distribution by using Dirac delta functions, but used inappropriately it can lead to some internal inconsistencies.

If you are doing quantum electrodynamics then the question becomes even more interesting. A single electron, say in an excited state in a H atom, has in some sense a current density which is a continuous distribution throughout space.