I started a question for my students and realized that I'm not sure of the
answer to the next level. Can anyone help?
Place 4 equal charges on the vertices of a square. Sketch the electric
field lines for this configuration. Is there any location (other than
infinity) where the net force on a field charge would be zero?
This seems reasonable - yes, at the center of the square. The field
lines "converge" there and move out of the plane of the paper. The point
may be stable or unstable in the plane, and will have opposite stability on
the axis. That allows for a visuzlization of the field lines "meeting" at
the center in 2-D, even though they continue in a third dimension.
But that got me thinking - 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).
Does this violate the (textbook) rule that field lines start and end on
charges? If it does, are there any other comparable violations?
[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?]
This posting is the position of the writer, not that of SUNY-BSC, NAU or the AAPT.