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Re: [Phys-L] more about basic DC circuits

  I want to add a few more comments to the so-called "Law of Conservation of Current" by P. Knight. A conventional understanding of conservation law for a characteristics of an isolated system is its constancy IN TIME regardless of processes within the system  which may change the system beyond recognition in all other respects. Even from this formal viewpoint, Night's statement "The current is the same at all points in a current carrying wire" is not conservation law because it shifts the definition from temporal domain to spacial domain. Physically, this statement holds only as a very special case of DC in a stationary state. Otherwise it is just wrong as has already been shown in this conversation. We could add another couple of simple examples. When we charge a capacitor in an RC-circuit, even maintaining current constant within the wire, there is no current between the capacitor plates. The current flow is interrupted at the plates. In such cases
Night's statement can be remedied by introducing the "displacement current", but the latter contains explicit contribution of varying electric field. Another example does not even need a C-unit - we can just use a simple uniform R-circuit under an AC of sufficiently high frequency, such that the corresponding wavelength is less than the size of the circuit. In this case the physical current will not be the same at all points of the wire, and accordingly, the wire itself will not remain electrically neutral - its different stretches will have different charge, varying with time. This shows that Night's second statement: "The law of conservation of current is really a practical application of the law of conservation of charge" - is also generally wrong. In most cases the conservation of charges DEMANDS the current to be inhomogeneous even in a homogenous wire (Gauss' law, or its differential formulation - the continuity equation).

Moses Fayngold,
NJIT    



On Monday, December 16, 2013 10:44 AM, "Rauber, Joel" <Joel.Rauber@SDSTATE.EDU> wrote:

It may be nit-picking, but those are some particularly itchy nits; particularly on PHYS-L

I might add, what appears more egregious to me, is page 867 (assuming my pagination is the same as JD's, not sure as mine is not the "with Modern Physics").  This page is the title page for chapter30 entitled "Current and Resistance".  The book has the title page of each chapter displaying in blocks the "fundamental" ideas of the chapter.  And front and center is a block "Conservation of Current".  And there is a section sub-heading with that name.

In Knight's defence, He defines the Law of Conservation of Current as follows:  "
The current is the same at all points in a current carrying wire." A very limited piece of applicability for a conservation law.

He immediately afterwards states, "The law of conservation of current is really a practical application of the law of conservation of charge."; which is a good clarification.  He then describes junctions and states the usual SUM-in = SUM-out junction rule for currents, referring to it as Kirchoff's junction law.

I view "the current is the same at all points in a current carrying wire" as a special case of Kirchoff's junction rule where you pick a point on the wire as a node which has one incoming lead and one outgoing lead.  Therefore any point on  a single wire could be viewed as a node where current going in is the same as that going out;  hence the current is the same along the length of the wire by imagining applying Kirchoff's junction
rule at all points on the wire.

I really wish he hadn't elevated the status of the current junction rule to that of a conservation law.  This seems to put it at the same status as conservation of momentum and the other fundamental conservation laws.

The using up energy statements are just unfortunate and seem to reinforce confusion between what JD refers to as "physics energy vs. DOE energy"

Take a peek at Fig. 30.9

JR

-----Original Message-----
From: Phys-l [mailto:phys-l-bounces@phys-l.org] On Behalf Of brian whatcott
Sent: Sunday, December 15, 2013 9:35 PM
To: phys-l@phys-l.org
Subject: Re: [Phys-L] more about basic DC circuits

On 12/15/2013 8:14 PM, John Denker wrote:
The last true/false quiz provoked an interesting discussion.

So let's take another step in that direction.  I'll make it really
easy, by telling you where you can look up the answers.

Q3:  True or false:  Electrical current is conserved.  This
  means current cannot be "used up".
    Knight, page 892 and page 896.

Q4:  True or false:  In a circuit, energy can be "used up".
    Knight, page 896.


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Yes, charge is conserved.
Yes, electrical energy is used up by dissipation in to other forms - in heating for example.
But no, He didn't mean current is conserved, and no,  he didn't mean energy is not conserved.

It is just nit-picking, of course.

Brian W

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