superposition

[kowalskil@alpha.montclair.edu]

Beth wrote:
> You can demonstrate it qualitatively with two charged rods and a charged 
> pith ball, hanging from an insulated string. You can estimate the direction 
> and strength of the force on the pith ball when one rod is near it, then 
> with the othe rod, then with both rods. I'm not sure if this is what you 
> are looking for, though.

Yes, we should be looking for experiments and demos. The one with a pith
ball, and the one I described yesterday (two dimensional simulation of
electrostatic field on carbonized paper are not likely to give accurate
results. But here is one which is much better in this respect. It deals 
with the field in a wire.

Take a resistor, nominally 100 ohms, and a very thin wire of known
length, for example, 1 meter, nominally 1 ohm. I say "nominally"
because the exact values do not matter. Connect them in series with
a battery (12V) and measure the potential difference in the wire.
Suppose it is 0.1 volts. Thus the average E1 in the wire is 0.1 V/m.
Disconnect the battery and use the second one (6 V). You can reverse
polarity, if you wish. This time your dV is 0.05 volts leading to
E2=0.05 V/m. Then put two batteries in series and measure E3 again.
The fact that E3=E1+E2 confirms the principle of supperposition in
the one-dim world; it avoids the issue of directions.

Martha wanted an example of non-superposition. Going outside of our
discipline consider somebody who has one drink in a bar each day
before driving. Then two drinks and a deadly accident. Also taxes
you pay, people you love, etc. Non-linearities are all over.

Ludwik