Three identical conducting spheres are located at the vertices of an equilateral triangle \(ABC.\) Initially the charge of the sphere at point \(A\) is \(q_{A}=0\) and the spheres at \(B\) and \(C\) carry the same charge \( q_{B}=q_{C}=q.\) It is known that the sphere \(B\) exerts an electrostatic force on \(C\) which has a magnitude \(F=4~\mbox{N}.\) Suppose an engineer connects a very thin conducting wire between spheres \(A\) and \(B.\) Then she removes the wire and connects it between spheres \(A\) and \(C.\) After these operations, what is the magnitude of the force of interaction **in Newtons** between \(B\) and \(C?\)

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