Re: Electric fields and points of stability

[Rick Tarara <rtarara@SAINTMARYS.EDU>]

Using the field generator in the E&M animation package (see below) I
generated and pasted the field arrangement from the 4 charges in the corners
of a square and have posted it at:

<http://www.saintmarys.edu/~rtarara/4charges.jpg>

Just to help the visualization.

Rick

*********************************************************
Richard W. Tarara
Professor of Physics
Saint Mary's College
Notre Dame, Indiana
rtarara@saintmarys.edu
********************************************************
Free Physics Educational Software (Win & Mac)
www.saintmarys.edu/~rtarara/software.html
NEW:  Mac versions of Lab Simulations
********************************************************
----- Original Message -----
From: "John Mallinckrodt" <ajm@CSUPOMONA.EDU>
To: <PHYS-L@lists.nau.edu>
Sent: Monday, October 14, 2002 1:12 PM
Subject: Re: Electric fields and points of stability


> > ... what if you place charges on the vertices of a cube.  Now does
> > an equilibrium point exist?  It seems that it should - at the center
> > of the cube - but what happens to the field lines at that point?
> > (There is no additional dimension to remove them).
>
> They come out toward the middles of the faces of the cube.
>
> > Does this violate the (textbook) rule that field lines start and end on
> > charges?  If it does, are there any other comparable violations?
>
> There is no violation; this is a completely standard case.  Whenever
> the electrostatic field is zero at some point in space, you will find
> that field lines approach the point from some directions and leave it
> from others so that the net flux out of any surface surrounding the
> point (but no charges) is zero.
>
> > [More food for thought - 3-D, 4-D visualizations.  The potential can be
> > plotted as a 3-D surface for the 2-D case.  Local min/max correspond
> > to "quasi-equilibria".  I'm struggling to visualize a 4-D surface for the
3-
> > D potential.  I usually do this as a "stack" of 3-D surfaces, but I'm
just
> > not seeing this one.  Any suggestions?]
>
>
> I wouldn't try to think of it as a 4-d surface.  It's just a scalar
> field in three dimensions like density, temperature, etc.  You could
> imagine coloring points in space by their potential using
> "translucent paint" so that you could "see into" the volume of
> interest.  Some scientific visualization packages allow you to do
> this sort of thing and also to examine arbitrary two-d slices.
>
> In this case you'd see a slightly more complex version of a saddle
> point.  The potential decreases as you move toward the center from
> any vertex of the cube and continues to decrease as you move from the
> center toward the middle of any face of the cube.
> --
>     A. John Mallinckrodt        http://www.csupomona.edu/~ajm
>     Professor of Physics      mailto:ajm@csupomona.edu
>     Physics Department         voice:909-869-4054
>     Cal Poly Pomona              fax:909-869-5090
>     Pomona, CA 91768-4031     office:Building 8, Room 223
>
> This posting is the position of the writer, not that of SUNY-BSC, NAU or
the AAPT.

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