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Re: Electric fields and points of stability



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.

I should have mentioned before that there are four other places where
the electric field vanishes in this situation. They lie a little
toward the center of the square from the midpoint of each side.
These zeroes vanish if the point charges are replaced by line charges
perpendicular to the plane through the vertices. Of course, in that
case the zero at the central point becomes an axis along which the
E-field is zero.

Indeed, I wonder if Rick T's sketch is for the case of four line
charges rather than four point charges as it does not seem to
properly indicate the four additional zeroes. On the other hand it
may be that it simply neglects to show the field lines that leave
those zeroes headed toward the center of the square.

--
John Mallinckrodt mailto:ajm@csupomona.edu
Cal Poly Pomona http://www.csupomona.edu/~ajm

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