Re: superposition (fwd)

["Donald E. Simanek" <dsimanek@eagle.lhup.edu>]

On Wed, 15 Jan 1997, John Mallinckrodt wrote:

> Donald,
>
> I still don't understand what it even *means* to attempt a superposition
> experiment when you are not controlling the placement of specific charges,
> but rather the potentials of different regions.  

Now I'm confused. I thought Herb Gottleib was suggesting something like
this:

An arrangement of two charges, +q and -q on the paper. I'd make them by
punching a small hole in the paper and affixing two washers and a bolt. 
Measure the field at some points. Now add another washer and a bolt
somewhere connected to, say the - polarity and measure the field at the
same points. Now remove the other washer that was connected to - polarity
and measure the field at the same points. Make the apapropriate inferences
about superposition.

Is there a flaw in this? The situation is complicated because you must
always have at least one + and one - electrode on the paper. Also by the
fact that you can't carry it out with conductive paint. The only flaw in
my method is that you've made a small hole in the paper, which acts like a
small insulating region. But that shouldn't affect the field and
equipotentials measured at points well away from that point (a few cm).
And I don't think the paper boundaries will matter, for they are a
constant for all the cases, and you won't measure too near them anyway.

Seems to me you could do it with field measurements (the two-point probe I
described), or with potentials. Both are expected to superpose: fields
with vector superposition, potentials with scalar superposition. 

> For example, consider 
>
>   1)  a dipole formed from two charges Q and -Q
>
> and 
>
>   2) another dipole formed from two more charges of the same magnitude Q
>      and -Q placed at different locations. 
>
> How would you go about demonstrating the superposition of these fields
> with the conductive paper?  You're not going to try to tell me that you
> will make the superposed case from four dots connected in pairs to
> opposite terminals of the power supply, are you?  If so consider these:
>
>  Case 1                       Case 2                    Superposition 
>
>  +                              +                        + + 
>   .<- test point               .                          .
>
>  -                              -                        - -
>
> I think you'll get pretty close to the same E in each case here.

I suppose you would. How about:


+
-         .
+

and 

-
+         .
-

I think our communication problem may be that I'm thinking of
superposition of the fields and potentials. I wasn't at all
thinking of *charge* superposition, though that's obviously underlying
all this.

If you wanted to do something to demonstrate charge superpositon... Hmm. 
Can we associate the charge of a conductive spot with its potential? If
so, we could have two spots, say +5 and -5 and another spot somewhere
attached to the slider of a rheostat connected between the terminals of
the power supply, so it could tap off any potential between +5 and -5.
Take it from there. Could use painted spots for this one. 

> Maybe you can give me a specific example which should work at least
> approximately and which is not so dependent on wise choices as to call
> into question the generality of the principle that you are trying to
> demonstrate. 

The two above may be what you want, John, off the top of my pointy head.
Of course, no one example establishes a principle, it only demonstrates
it's validity in particular instances.

In these cases, acceptance of the generality is heightened by measuring
fields and potentials over a variety of positions on the paper.

	-- Donald