Re: superposition (fwd)

[John Mallinckrodt <ajmallinckro@CSUPomona.Edu>]

On Wed, 15 Jan 1997, Donald E. Simanek wrote:

> On Wed, 15 Jan 1997, John Mallinckrodt wrote:
>
> > Well...  I'm afraid this simply won't work.  With the conductive paper we
> > effectively set up boundary value problems--e.g., V is fixed on some
> > painted spots, grad V is perpendicular to the edges of all painted spots,
> > and grad V is parallel to the edges of the paper and to the edges of any
> > regions in which we scrape off the conductive coating.  The paper solves
> > the PDE's for us.  But superposing the fields that result from two
> > different sets of boundary conditions is not at all the same thing as
> > solving for the fields that result when we somehow "combine" boundary
> > conditions.  (Frankly, I don't even understand how you would propose to do
> > the latter.)
>
> Actually, if you do experiments and take data not too near the edges, it
> works quite well (having done it). The departure from the non-bounded case
> shows up only within about 2 cm of the edge of the paper. If that were not
> so, they couldn't get anyone to buy these materials for the usual
> field-mapping experiment. :-)

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.  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.

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. 

Best,

John
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