is The electric force between two charges changes, if we bring a third closer to them
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How is the coulomb force between two charges affected by the presence of a third charge?
The electrostatic force between two point charges will not be affected by the presence of a third charge (or any number of charges) because it is a two body interaction. However the total force on any one of the charges will be the vector sum of all the electrostatic forces acting on that charge (according to superposition principle).
Think of a system of two charges A and B. Now a third charge C is added. Let us consider the total electrostatic force on A. The total force on it of the charges will be lesser or greater than before ( i.e. before C is added). But that does not mean that the force on A due to B has changed. It only means that a force (due to C) acts on A in addition to that due to B and the total force on A can be found out by the vector sum of the forces due to B and C on A (considering the angles between them).
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