Michael Foster wrote:
Stephen A Lawrence wrote:
You've said two different things here: "the strength of the
field will drop", and "the voltage drops". The dielectric will
_certainly_ affect the voltage, just as interposing a charged
parallel plate capacitor would affect the voltage (which would
reduce it by the voltage to which the capacitor had been
charged). As an aside, that is how a polar dielectric acts to
increase the capacity of a parallel plate capacitor versus using
an air dielectric: for any particular net charge on the plates,
interposing it reduces the voltage between the plates;
consequently the ratio of charge to voltage increases.
What it won't do, however, _if_ it's a large flat sheet and the
field is perpendicular to it (and it carries no net charge), is
have a significant effect on the electric field on either side
of it ... any more than a large parallel plate capacitor would.
If you disagree please explain either (a) how a polar dielectric
in an E field differs in its field from a charged capacitor or
(b) how either one of them has a large effect on the field
outside the "plates".
Let's make sure we're talking about the same thing. I'm a little
concerned that we're talking past each other about different but
related subjects. Forget about the terms "voltage" and "field
strength". What I'm addressing is the physical force of attraction
or repulsion between electrically charged objects, whatever
terminology you want to apply to it.
That's field strength -- the local electric field is all that a charged
object can "sense".
A voltmeter, which is connected via conductors of some sort to two
different points in space, measures the difference in potential energy a
unit of charge would have at those two points; that's voltage. A
typical voltmeter lets a significant amount of current flow in the
course of its operation and hence only works with circuits -- won't work
with "static" charges. Somebody -- I think it was you? -- mentioned an
electrostatic voltmeter; sounds pretty spiffy, but I've never seen one:
the best I can do here is an opamp on the front of a Radio Shack
volt-ohm meter and that's still not high enough impedance (and low
enough capacitance!) to measure static charges.
Electroscopes using a couple of leaves of aluminum foil (or gold, if
you're using a "real" one), on the other hand, are a different story,
and I have played with a home made version a bit, several years ago. I
_think_ an electroscope measures the voltage difference between the top
and bottom of the bottle but I'd have to think about it a while to be
sure... (and they measure humidity, and ionization in the air, and
other stuff, all at once, which makes them a bit hard to use precisely,
to say nothing of the fact that, if you charge the electroscope and then
look for a deflection in the leaves to tell you about variations in the
local field, the electroscope itself is producing a significant and
oddly shaped field all on its own, and so messing up other parts of the
experiment...)
Let me propose a practical model. We have a charged metal object,
a sphere, for example. It has been charged to, say, 20kV. The
sphere is electrically isolated and there is no current source
beyond the initial charge.
OK there's already a problem here. You can specify the amount of charge
on the sphere -- 0.1 coulomb, whatever -- but without knowing the
geometry of the whole situation and, in particular, the placement of
negative charges and the point you pick for "ground", you _don't_ know
the voltage.
If you have an equal but negatively charged sphere close by, and no
other charges near, the voltage between the spheres will be relatively
low. If you pull the two spheres apart (and hence do work on them) the
voltage between them will rise, roughly in proportion to the distance
between them. The voltage is the amount of energy a unit of charge will
gain when it moves from the positive to the negative pole -- or the
positive pole to ground -- and that depends on how far it goes, as well
as depending on the field strength. And, of course, it depends on the
point you choose for "ground".
So, the point is you can't meaningfully say it's charged to "20kV". But
enough nits; let's move on...
There is no significant corona leakage
within the time frame of our demonstration. To be classical, we
have a pith ball hanging by a length of thread nearby and it is
attracted to the charged sphere, as evidenced by the angle at which
the thread inclines from the vertical toward the sphere. The pith
ball has been placed at a distance that will not allow it to touch
the charged sphere.
Are you saying that an uncharged polar dielectric object with a
high K placed between the charged metal sphere and the pith ball
will have no effect on the attraction between the pith ball and
the sphere? In other words, will the angle of the thread and the
distance between the pith ball and the sphere remain unchanged?
As far as I can see that must be correct. Note, though, that there are
some very touchy issues when it comes to actually doing the experiment.
First, if your insulator actually _conducts_ at all, even at gigohms per
square, you may get an "image charge" effect: negative charges will be
attracted from the edges of the material toward the middle by the
positively charged sphere, and that will locally have a large effect on
the E field. As an extreme example, if you use a (large, flat) sheet of
aluminum foil instead of an insulator, the pith ball will lose a lot of
its interest in the charged sphere. (But then grounding issues intrude
-- if you touch the Al, thus momentarily grounding it, it pulls some
charge from your body with which to _really_ neutralize the E field of
the sphere, and again you're not testing what you expected...) This
effect can be avoided or reduced by bending the insulator around the
charged sphere, but the experiment gets harder in that case.
Second, if the humidity is down around zero (as it tends to be this time
of the year where we live) your "neutral" insulator may very well not be
neutral to start with, which can totally mess up the experiment.
I've played with these things a bit, just using simple stuff lying
around the house (charged balloons, paper pieces, an old Zerostat,
wires, steel balls, and such); that works pretty well during the dry,
dry winter in the Northland. But, I don't recall ever sliding a plastic
sheet between two attracting objects. So, I'm just quoting theory at
this point.
