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Apropos' to this discussion (specifically the Earnshaw theorem),
I always include the following problem in any E&M course:
A point charge Q1 = ___coulombs and a second point charge
Q2 =___coulombs are separated by ___ meters. (Fill in any
numbers and signs [of charges] - there will be a solution.)
It is desired to add a third point charge so that the three charge
system will be in equilibrium under only electrostatic forces -
ie; the Coulomb force on each charge (due to the other two) is
to be zero.
1) Where should this third charge be placed?
2) What sign should this third charge be?
3) Calculate the required magnitude of this third charge.
4) Is this system in stable equilibrium? Prove your answer.