Coulomb's Law Placement of Charges in Equilibrium

[JSGandora]

Homework Statement

Consider the arrangement of two point charges equal in magnitude but opposite sign (+Q, and -Q), which are a fixed distance d apart. Can you find a location where a third positive charge
Q could be placed so that the net electric force on this charge is zero?

Homework Equations

Coulomb's Law

The Attempt at a Solution

The third charge obviously must be placed on the same line as the first two charges. Let the negative charge be to the right of the positive charge. If the third charge was to the left of the positive charge, the positive charge would repel the third charge with a greater magnitude than the negative charge would attract it, thus the third charge cannot be placed to the left of the positive charge.

If we placed the third charge to the right of the negative charge, the negative charge would attract it with greater magnitude than the positive charge would repel it thus it would also not be in equilibrium.

If the third charge was placed inbetween the two charges, the force by both charges would be in the same direction so the third charge would also not be in equilibrium.

The only logical answer for me is placing the third charge at a point at infinity. Is this the correct answer?

 

[Doc Al]

Can you find a location where a third positive charge
Q could be placed so that the net electric force on this charge is zero?

The only logical answer for me is placing the third charge at a point at infinity. Is this the correct answer?

Your reasoning is perfectly correct. But I would say that the best answer to the question (quoted above) is a simple "no".