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Re: Electric fields and points of stability



paul johnson wrote:

An equilibrium point exists at the center of the cube ONLY if all the
charges at the vertices have the same magnitude and the same sign.

I wouldn't have said that.

Doesn't it suffice to have diagonally-opposite corners
equal in sign and magnitude? You could have six of one
sign and two of the other.

Field lines from (or to) each charge lie symmetrically around each body
diagonal.

... if the sources are symmetricaly disposed.

As they approach the center, they veer away symmetrically on
either side so that the center is devoid of lines.

Yes, that's required for equilibrium, quite generally.

Does this violate the (textbook) rule that field lines start and end on
charges? If it does, are there any other comparable violations?

No. All the lines end on charges an infinite distance away whose sign is
opposite to the sign of the vertex charges.

I'm not sure I'd have said that, either.
If the lines go off to infinity, wouldn't it be easier
to say that they _don't_ end there?

It's not clear that the laws of physics require global
charge neutrality. In particular, consider the analogy
between electrostatics and gravity; you wouldn't want
to assume that lines of gravitational "force" terminate
on opposite mass/charges.

Rather than the "textbook" saying that all lines end on
charges, we could say _if_ they end, they end on charges.
You can easily have electric field lines that close on
themselves, not ending anywhere (hint: flux dot).

On the third hand, if you want to _add_ a hypothesis that
there is global charge neutrality, I don't think that would
conflict with observations. Indeed, charge tends to be
neutral when summed over relatively small regions. If you
try to build a charged cube (as described above) you'll wind
up with countercharges on the walls of your lab.

This posting is the position of the writer, not that of Urd, Skuld, or
Verdandi.

This posting is the position of the writer, not that of SUNY-BSC, NAU or the AAPT.