> > The first is about Coulomb's Law

> > DEL . D = rho

> > Meaning, the divergence of the electric field is equal to the charge
> > density.

> > Now, if I understand properly, D (at a given point in space and time)
> > is the number of electric field lines passing through that point.  D is
> > also the Electric field divided by the permittivity at that point.  (It
> > seems that the greater the permittivity, the more charges you can fit
> > in the same volume for the same cost in energy)

> > Here is question one:  Does the quantity D, meaning "number of electric
> > fields passing through a point" have any meaning?

> Physically, no. This concept of "lines" of force arose when iron
> filings were sprinkled on a permanent magnet. Each particle becomes
> a miniature magnet with its own N/S poles and the "lines" form
> as the particles align with each other. Ships at sea have the entire
> ocean upon which to roam, yet 400 years ago the ships of the line
>   http://www.***.com/
>  battle lines.

> > That is, it can be
> > defined, mathematically, of course, in terms of limits as the volume
> > goes to zero and dividing by the volume.  But does this mathematical
> > definition work if the number of field lines is an integral value?
> > Oh, yes, now you may see what I'm getting at.  Are electric field lines
> > quantized?

> No. Nor are magnetic field lines. the number of lines will reduce
> with increasing size of the particles. Use nails instead. This will
> not change the strength of the field. We use the term "field" as in
>  'vector field' to mean the vectors are aligned in parallel (locally)
> Field 1:
> ///////
> ///////
> ///////
> field 2:
> ------
> ------
> ------
> field 3:
> \\\\\\
> \\\\\\
> \\\\\\
> field 4:
> |||||||||||
> |||||||||||
> |||||||||||
> Field 5:
> ______________
> ______________
> ______________
> Field 6:
> ................
> ................
> ................

> In the above, my diagrams are quantized only because we have
> that limitation in typescript.
> It is the length of a vector that defines its "strength"

> > That is, are there a specific large-but-finite number of
> > electric fields associated with every charge?
> One field, infinite lines seperated by an infinitesimal distance.
> The field can curve and come to a point, but I can't draw that here.

> > It seems to be what
> > Maxwell's equations suggest...  Yet at the same time, I've gone through
> > most of my education understanding that the nature of Coulomb's law had
> > to do with potentials.

> Yes. The "strength" or "potential" of a magnet can be thought of in
> terms of the weight it can support, as with maglev trains. The relation
> between the electrical current in the windings of an electromagnet
> and this strength is electrodynamics, a nice word Einstein used in
> "On the Electrodynamics of Moving Bodies" and then said nothing
> about beyond describing Galilean relativity in the first paragraph and
> calling it the "Principle of Relativity" so that he had a fancy title and
> an excuse to fumble-mumble his stupidity and say the PoR was
> only an approximation.

> > That is, rather than interacting directly, charged particles enact a
> > change in their environment (raising or dropping of electrical
> > potential in the region)

> If you move a magnet, it takes its field with it, right?
> If you move a magnet past a copper conductor, the magnetic
> field passes THROUGH the conductor and produces electric
> poles at the ends of the conductor, which we label as + and minus.
> That's a generator, you can make an LED glow.

> 1) Movement + magnetic field => electric field.

> You can also drive a current through a conductor that is in a
> magnetic field and move the conductor or magnet.
> That's a motor.

> 2) Electric field + magnetic field => movement.

> You can 'move' (i.e. change) an electric field to make a
> magnetic field.
> That's an electromagnet.

> 3) Electric field + movement = magnetic field.

> By CHANGING the electric field, a magnetic field
> is created.
> By CHANGING the magnetic field, a electric field
> is created.
> There is movement in a transformer. They hum.

> Now imagine you have a changing magnetic field but NO
> magnet, which produces an electric field but NO conductor.
> That's radio, light, x-rays, gamma rays...
> No aether was used in this explanation.

>  Then the particles, depending on their charge
> > respond to these changes in electric potential.  Maxwell's equations
> > happily handle this concept in that E = -DEL V, or the electric field
> > is precisely the gradient of this potential.

> > Now, I know it's become the fashion to assume that if two things are
> > mathematically equivalent, then both must be true, but it seems to me
> > that it must be either one or the other.  Either the true phenomenon is
> > a bunch of field lines connecting between the particles, in which case,
> > much of quantum mechanics can probably be explained through the quantum
> > nature of these field lines, or the particles create and react to
> > electric potentials, which is, I believe, the traditional explanation.

> > -Jon
> > http://www.***.com/ ; >