Suppose two particles each having charge $q$, are placed at a separation. What charge $Q$ should be placed at the midpoint between them, so that all the three may remain in equilibrium
closed as too localized by dmckee♦ Aug 26 '12 at 19:15
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This is a standard question asked in pretty much any first course on electrostatics. As such, rather than give the full answer, I'll point out that equilibrium is achieved when there is no net force on any particle. When it comes to forces on static charges, Coulomb's Law is the only equation to choose from. Try balancing the forces using this.
As an added bonus, see if you can prove the instability of the system. Which way does a perturbed force push/pull a particle that has been slightly displaced in this system?