This is an important subject. I hope there will be results. David
On Thu, Sep 24, 2009 at 2:14 AM, Harry Veeder <[email protected]> wrote: > > > ----- Original Message ----- > From: "Stephen A. Lawrence" <[email protected]> > Date: Thursday, September 17, 2009 10:13 am > Subject: Re: [Vo]:The Electric Field Outside a Stationary Resistive Wire > Carrying a Constant Current > > > 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. > > If an electric field exists outside and parallel to the current carrying > wire, and the wire is a loop it implies the electric field lines would > form a closed loop. However, this is not suppose to possible. > > Weber's theory predicts a force (distinct from a lorenz force) arising > from the relative motion between positive and negative charges such as > inside a current carrying wire where electrons move past protons. > > Harry > > > > > >
