Harry Veeder wrote:
>
> Stephen A. Lawrence wrote:
>> Harry Veeder wrote:
>>> Maxwell's theory needs the field concept. The theory says and
>>> electric force can not be present without an electric field.
>>>
>>> If we follow Maxwell's theory to the letter, it says there will
>> be no
>>> electric field outside a current carrying wire.
>> I don't know what you're talking about here. If by "Maxwell's
>> theory" you mean Maxwell's four equations, as they are normally
>> written, and as they are embedded in the model of special
>> relativity (which is how thisis normally applied), then what you
>> said is simply false.
>>
>> If there is a current flowing through a resistive wire, then there
>> is an E field within the wire directed parallel to the wire. That
>> E field is what drives the current, and its value is proportional
>> to \rho*I where \rho is the resistivity per unit length of the
>> wire. The curl of the E field within the wire and near the surface
>> of the wire is zero, since
>>
>> Del x E = -dB/dt
>>
>> in rationalized CGS units. Since the curl is zero, if the field
>> points along the wire just withinthe wire, it must also point along
>> the wire just outside the wire.
>
> Isn't that only true for a stream of electrons in a vacuum?
No, that equation is true everywhere, in matter and out of matter.
If there were magnetic monopoles then the full form of the equation would be
Del x E = -dB/dt + J_b
where J_b is the magnetic current density. But without magnetic
monopoles, you can't have a magnetic current.
Note that the "auxiliary fields" D and H which appear in Maxwell's
equations are a computational convenience which simplify calculations in
matter; they are not necessary to the correctness of the equations.
>
>> Otherwise you'd get a nonzero integral of the E vector around a
>> small loop which is partly inside the wire and partly outside the
>> wire, whichwould imply the curl was nonzero.
>
>> For points near the wire, that field runs parallel to the wire.
>> This field is independent of the presence or absence of a charge
>> outside thewire.
>>
>> Arguments straight out of Purcell, based directly on Maxwell's
>> equationsand the Lorentz force law, lead to the conclusion that a
>> point charge located close to the wire will also induce a local
>> charge on the wire, which will result in a local field which is
>> perpendicular to the surfaceof the wire.
>
> I will try to defend of his bald assertion.
>
> After the introduction he considers three possible electric forces,
> Fo,F1,F2, on the test charge. He calculates that Fo > F1 > F2.
>
> Fo is due to the induced charge in the wire by the test charge, and
> he states right at the beginning of the introduction that this is
> well known. The reason why he appears to ignore it is that it can
> happen with or without a current. However his assertion is about
> force(s) which are entirely dependent on the current in the wire.
>
>
> F1 is the force due to net surface charges. He gives some examples to
> support his opinion that this is not as widely known. (You can
> criticize his examples, but this is only a side issue). While this
> force would not exist without current, it still depends on the atomic
> and molecular structure of the material. In other words one could
> imagine a nano-engineered wire which produces no net surface charge.
Hmmm -- OK I didn't read it in any detail; this may actually be
something new. Or it may not.
Certainly there must be a charge on the wire which depends on the
location along the wire; close to the positive end of the wire it's
going to be net positive, close to the negative end it's going to be net
negative. This, too, is a small effect and typically ignored.
>
> So we come to F2, a force which depends entirely on the current. Such
> a force is predicted by Weber's theory but not by Maxwell's theory.
I don't know what you mean by "Weber's theory" nor by "Maxwell's theory".
The modern theory of electrodynamics incorporates Maxwell's equations,
which are very similar to the way Maxwell formulated them (after he
added the displacement current term). They describe the behavior of the
fields. The behavior of particles is described by the Lorentz force
law, F = q(E - v x B). I don't know what piece might be attributed to
Weber.
As I pointed out above there certainly is an electric field outside the
wire; there must be. But it's usually ignored because it's small.
Here's an example where you can't ignore it:
Take a battery with widely separated terminals, and put a highly
resistive wire between them:
+ ------------------------------------------------------------ -
Now take another wire and put it next to the first one:
+ ----------------------------------------------- -
-------------------------------------------
If there's a field OUTSIDE the first wire, then the SECOND wire should
find itself with a net charge at its two ends. Does it?
Of course it does! Because that picture is really just the same as this
picture (unit width font please):
+ ----------------------------------------------- -
\ /
\| | | |/
| |---------------------------------------| |
| | | |
where our second wire runs between two capacitors, each of which is tied
to a battery terminal. What drives the charges along the wire between
those two capacitors? They travel along a wire which connected to
*nothing*, neither at the ends nor in the middle. Answer: The electric
field which runs *outside* the first wire.
>
>
>> This field vanishes if we remove the external charge. But did you
>> perhaps mean something else by "Maxwell's theory? (Incidentally I
>> said "As embedded in the model of SR" because without that extra
>> bit of icing you have no way of transforming the equations from one
>> frame of reference to another, and no answer to the question of
>> what happens when moving a uniform velocity.)
>
> Ok
>
> Harry
>
>>> Consequently, the theory leads one to expect an electric force is
>>> absent as well.
>>>
>>> Weber's theory is not built on the field concept, so this curious
>>> expectation does not arise.
>>>
>>> My analysis is based on reading of this preface to the book
>> suggested> by Taylor J. Smith.
>>> http://www.ifi.unicamp.br/~assis/Preface-Webers-Electrodynamics.pdf
>>>
>>>
>>>
>>> Harry
>>>
>>> ----- Original Message ----- From: "Stephen A. Lawrence"
>>> <[email protected]> Date: Monday, September 14, 2009 6:18 pm
>>> Subject: Re: [Vo]:The Electric Field Outside a Stationary
>>> Resistive Wire Carrying a Constant Current
>>>
>>>> Harry Veeder wrote:
>>>>> fyi Harry
>>>>>
>>>>> Foundations of Physics © Plenum Publishing Corporation 1999
>>>>> 10.1023/A:1018874523513
>>>>>
>>>>> The Electric Field Outside a Stationary Resistive Wire
>>>>> Carrying a Constant Current
>>>>>
>>>>> A. K. T. Assis, W. A. Rodrigues Jr. and A. J. Mania
>>>>>
>>>>> Abstract We present the opinion of some authors who believe
>>>> there is
>>>>> no force between a stationary charge and a stationary
>>>>> resistive wire carrying a constant current.
>>>> That's stated a lot, but it's just sloppiness. Anyone who
>>>> knows electronics realizes it's not really true.
>>>>
>>>> A good conductor carrying small current has *nearly* zero
>>>> voltage drop along any small length, and calling the drop
>>>> "zero" is usually "good enough". But really the voltage drop
>>>> along any segment is equal to I*Rwhere R is the resistance of
>>>> that segment.
>>>>
>>>> When the voltage drop along a (resistive) wire is nonzero, then
>>>> *any* path which leads from a higher voltage point on the wire
>>>>
>> to a
>>>> lower voltage point on the same wire must traverse the same
>>>> exact potential change, which means that there must be an
>>>> electric field *outside* the wire, running parallel to the
>>>> wire.
>>>>
>>>> This is well known but, as I said, usually neglected, because
>>>> it's usually too small to matter in real-world problems.
>>>>
>>>> The fact that there's an "image charge" induced in the wire as
>>>> well, which consequently must be having its effect on the
>>>> charge sitting outside the wire, is certainly the case and
>>>> could even be called "obvious", but it's not something I ever
>>>> thought of until I saw it mentioned in the abstract. :-)
>>>>
>>>>
>>>>> We show that this force is different from zero and present
>>>>> its main components: the force due to the charges induced in
>>>>> the wire by the test charge and a force proportional to the
>>>>> current in the resistive wire. We also discuss briefly a
>>>>> component of the force proportional to the square of the
>>>>> current which should exist according to some models and
>>>>> another component due to the acceleration of the conduction
>>>>> electrons in a curved wire carrying a dc current (centripetal
>>>>> acceleration). Finally, we analyze experiments showing the
>>>>> existence of the
>>>> electric> field proportional to the current in resistive wires.
>>>>
>>>>> complete paper available here:
>>>>> http://www.springerlink.com/content/q6634pp556m08500/fulltext.html
>>>>>
>>>>>
>>>>>
