(Solution) - Multiple charges at different locations are said to be in -(2025 Original AI-Free Solution)

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Multiple charges at different locations are said to be in equilibrium if the force acting on any one of them is identical in magnitude and direction to the force acting on any of the others. Suppose we have two negative charges, one located at the origin and carrying charge ? 9e, and the other located on the positive x-axis at a distance d from the first one and carrying charge ? 36e. Determine the location, polarity and magnitude of a third charge whose placement would bring the entire system into equilibrium.