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Re: messy electrostatics



Here is a “psedo-paradox”, actually a little teaser to challenge
a student. Consider two point charges, Q1=+10 nC and
Q2=-10nC, separated by a distance of d=0.1 meters. The
electrostatic potential energy, U=k*Q1*Q2/d= -9 microjoules.

But a point charge is only a mathematical abstraction. So we
decided to place the same charges on small metallic spheres,
for example, R1=R2=0.1 mm. Will the electrostatic energy be
about the same or not? A student may say “about the same”
because d>>R. You may accept it, if you wish. Or you may ask
“why was the work done to bring Q1 and Q2 from infinity to
the spheres ignored in your consideration?”

This will immediately focus on the issue of the “level of
reference”. The electric potential energy of one sphere with
respect to another is not the same as their total electrostatic
energy with respect to infinity. It takes the infinite amount
of work to create a point charge (R-->0 corresponds to
F-->infinity). To avoid this embarrassing issue we often
calculate relative potential energy (one point with respect
to another). Fortunately Mother Nature tolerates this in
many problems.