I've added some minor clarifications to my example of two wires: Stephen A. Lawrence wrote: > > 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: > > + -------------------------------------------------------- -
The wire is connected to both terminals, so current flows through it. (That may not have been clear.) > Now take another wire and put it next to the first one: > > + ----------------------------------------------- - > ------------------------------------------- The second wire is not connected to anything, at either end; it's just hanging in the air, close to the first wire but not touching it. > > 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. These are simple parallel plate capacitors, which consist of two metal plates separated by a gap filled with air (or vacuum, if we are doing this on the Moon). > 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 >>>>>> >>>>>> >>>>>> > >
