I only meant to give an example of how the superposition principle
could fail if there were "many-body" forces. Using a term that depended
on angle is only one possibility of course. However, I find that
elementary students get the message easily from this statement, because
they immediately see that once you have three non-colinear charges the
geometry automatically includes the angle.
My statement about circularity was just to note that, for static
charges, Gauss' Law and Coulomb's Law are mathematically equivalent. So
the linearity of Maxwell's equations is built in to agree with the
experimental observations. If there were "many-body" terms in the force
law for static charges, then Maxwell's equations would have to be changed
(that might be an interesting exam problem for a grad E&M course)
Mark
Dr. Mark H. Shapiro
Physics Department
California State University, Fullerton
P.O. Box 6866
Fullerton, California 92834-6866