----- Original Message ----- From: mix...@bigpond.com Date: Thursday, October 1, 2009 5:40 pm Subject: Re: correction /Re: [Vo]:The Electric Field Outside a Stationary Resistive Wire Carrying a Constant Current
> In reply to Harry Veeder's message of Thu, 01 Oct 2009 02:20:00 - > 0400:Hi, > [snip] > >> The "'positive' in between" is what makes the equations work > out. I > >> think you > >> are having a problem because you expect the net EMF to integrate > to > >> zero (begin > >> point = end point), which it would do if you take the "step" > into > >> account. Note > >> that the EMF does not change monotonically around the complete > >> loop. It does > >> along the wire (assuming a constant resistance/length ratio), > >> however there is > >> at least one step when you hit the electrodes. (In the case of a > >> battery perhaps > >> more accurately one step at each electrode). > >> Regards, > >> > >> Robin van Spaandonk > >> > >> http://rvanspaa.freehostia.com/Project.html > >> > > > >Explaining the steady current in terms of EMFs does not lead to a > >contradiction > >so this is not where my problem lies. However, if the steady > current is > >rigorously explained in terms of electric fields a contradiction > seems>to arise. > > How is EMF different from "electric field"? IOW why do not have a > problem with > the former, but you do with the latter? An ElectroMotive Force is a concrete arrangement of matter that comes into being either by happenstance or by design and is capable of pushing charges around. A 9 volt battery or a gas powered electrical generator or a thunderstorm are examples of EMFs. Even if we assume electric fields are real -- in the sense of being more than just abstract mathematical tools for making calculations and predictions -- they owe their reality to a concrete arrangement of matter. In addition to this ontological difference, there is also a logical difference which is born out when you try to explain the current ONLY in terms of electric fields. > >The steady current requires that the electric field lines > >around the loop (i.e. from '-' to '-') form a closed path, > otherwise the > >current would be fleeting instead of steady. > >On the other hand this > >contradicts the rule that electric fields cannot form a closed > loop when > >the B field is not varying as is the case with a *steady* current. > > ...but individual field lines don't form a closed loop. They end on > positive and > negative charges in between. That's what the discontinuity is all > about that I > mentioned in my previous post. It's where the voltage step happens. > > This is most clearly seen where the separator is a capacitor, and > no current > flows through the dielectric of the capacitor. All you really have > is a "bent" > wire connection with two ends. Current flows from one end to the > other. > This is also true in a battery, but the break isn't as obvious as > it's at the > atomic level, where electrons and ions separate. Actually there are > more like > two breaks in a battery, one at each electrode, resulting in two > currents, an > external electron current, and an internal ion current. > > Regards, The electrons must be recirculated in order to maintain a steady current. If an electric field is the same as an EMF, then the electric field must form a closed loop, otherwise electrons would pile up at the '+'electrode where the electric field ends in your depiction. Of course a closed electric field loop is not allowed in theory, so the concept of an electric field cannot be used in a logically consistent manner to *fully* explain the current. Therefore an electric field IS NOT the same as an EMF. Harry
