----- 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
