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Re: Capacitor charge, were is it?
I just thought I might add a little more to my previous post, concerning
the use of the phrase "charge in the dielectric", pointing out how it's
also used in the literature, but with qualifications that use it as
an abstraction to help work out the math, rather than a literal charge.
On Sat, 26 Oct 1996, Tesla List wrote:
> >From wesb-at-spectra-dot-netSat Oct 26 23:43:15 1996
> Date: Sat, 26 Oct 1996 16:33:02 -0400 (EDT)
> From: Wes A Brzozowski <wesb-at-spectra-dot-net>
> To: tesla-at-pupman-dot-com
> Subject: Re: Capacitor charge, were is it?
>
>
>
> On Fri, 25 Oct 1996, Tesla List wrote:
>
> > From: huffman <huffman-at-fnal.gov>
> >
> > I'm having trouble with the idea of charge being stored in the dielectric.
> > This may not be totally Tesla related but I would like some comments,
> > stones, etc.
>
> I'm a day late on a reply here, but I don't yet see any responses to this,
> so hopefully I won't be junking up the list with a reply that will already
> have been answered by someone else. The problem is that some folks use the
> term "charge" with respect to a dielectric, when they really mean to use
> "polarization". I suspect that some people confuse the two, but that others
> mix them up intentionally because not everyone here has had the opportunity
> to take an electromagnetic fields course, and referring to charge can help
> everyone picture what they're talking about. What's usually being described
> is energy being stored in the dielectric. Often it will be said that there
> is charge in the dielectric, when actually the energy is stored by
> polarizing the dielectric. This is the electric field analogy to the
A common quantity used in fields texts is that of charge density, that is
the amount of charge per unit volume, or charge per unit area. In order to
extend the mathematical toolkit as far as possible, this concept gets
extended into dielectrics as the effective amount of charge that would
be needed to create the same electric fields as are produced by polarizing
the dielectric. This is often described as the Polarization Charge Density,
to distinguish it from an actual charge density. Reitz and Milford do a
decent job of describing this on pp70-73 of "Foundations of Electromagnetic
Theory". On p 124 of "Engineering Electromagnetic Fields and Waves", Johnk
refers to this as a "so-called polarization charge density", pointing out
that it's an artificial quantity, however useful it may be in getting the
answers to real fields problems. Both of these references use the abstraction
of an imaginary charge distributed throughout the dielectric.
But this isn't the only way to look at it. as long as we're creating an
abstraction that simply makes it easier to solve a problem, we can look for
the abstraction that's most useful in solving the problems we're
interested in. Chelkowski, in "Dielectric Physics", instead uses the concept
of a charge that appears at the very surface of the dielectric, but is bound
and unremovable from the material. This can also give the same results as
reality for certain classes of problems, but with greatly simplified math.
By the way, for anyone looking for a refresher in electromagnetic fields,
I've never seen a better book than Johnk's. Instead of the usual fields
book format of first beating electrostatics to death, then beating
dielectrics to death, then slowly working through magnetic fields,
induction, and finally Maxwell's equations and waves, Johnk splashes you
almost immediately with Maxwell's equations and gives a broad, working
overview of everything. Before page 100 you're already in waves, and the
first 25 pages weren't even handling fields, but making sure you have a
good working grasp of vector mathematics and the various coordinate
systems. He takes extra effort to make sure you can visualize what's
happening and what the various mathematical operations used actually
mean. If you've ever had trouble visualizing what the curl of a vector
field actually is, his little visualization trick will come across as one
of the slickest things you've ever seen.
After the overview is done, Johnk then goes back, filling in the details,
in the order of the standard format. The neat thing about it is that you
can get the overview, then skip ahead to only the topics you're interested
in, and get it done in a minimum of time. If you try skipping things in
a standard format book, you'll almost certainly skip things that will be
needed later on, and the reading will get murkier and murkier as you go on.
This book's a gem.
> > a capacitor is charged, then carefully dismantled. The two metal plates
> > were handled, shorted together, then reassembled getting the charged
> > capacitor which can be shorted out yielding a large spark.
> > There must be something going on here that is not obvious. 8?/
>
> What's happened is that the dielectric is of a type that retains its
> polarization for a time, analagous to a piece of iron that's been
> temporarily magnetized. While it retains its polarization, it still contains
> energy. You're getting some of it back when you short the plates. What you
> should also find is that after the dielectric has had time to unpolarize,
> you should be able to short the plates together again and get another spark.
One thing I should have pointed out about this one is that the phenomenon's
called Dielectric Absorption, which is also what causes that interesting
little weirdness when you short out a charged capacitor, unshort it, and
find there's still a little voltage across it. The experiment originally
mentioned with disassembling a charged capacitor was observed by Benjamin
Franklin in 1748, in his experiments with Leyden Jars. Anyway, the term
Dielectric Absorption is the term to look for in the indices of all those
textbooks for a good description. In "Electrostatics and its
Applications", Moore gives a nice, very lightly technical description of
the whole thing.
Anyway, my posting yesterday was just a shot from the hip on a subject
that's not been covered much here, and I thought a few elaborations and
references might be helpful for those for those who found the subject
interesting.
Wes B. YAPD (Yet Another Proud Dinker)