General question about solving force maximization problems

AI Thread Summary
The discussion centers on a problem involving two positive charges on the y-axis affecting a single positive charge on the x-axis, with the goal of finding the x-position for maximum force. The user derived an expression for the forces and attempted to maximize it through differentiation, but their answer does not align with the textbook. Key advice includes considering the vector nature of the forces and ensuring that both magnitudes and directions are accounted for in the calculations. The user is encouraged to reassess their approach to include the vector sum of forces. This highlights the importance of understanding vector components in force maximization problems.
Ceenaya19
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I'm doing this E&M problem for fun (I'll be taking the class this fall), but now it's just starting to get frustrating. I can't really post the problem because there is a diagram, but I'm not really looking to be given the actual solution anyway, so I'll describe it to you:

Two positive charges on the y-axis are acting on a single positive charge on the x-axis. The problem asks me to determine the x-position at which the single positive charge experiences the maximum force. I derived an expression to describe the superposition of the two positive electric forces on the single positive charge; then, to maximize it, I differentiated it, set it equal to zero, and solved for "x".

My answer does not match the answer in my textbook, but I can't think of any other way to do this problem; I always assumed that maximization was straightforward. So, could someone please point me in the right direction, conceptually? Thanks.
 
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Did you take the vector sum and maximize its magnitude, or did you ignore how each charge provides a force in a different direction?
 
Two on y axis, and one on x axis.
So, the position is on the x axis. Please thinking again.
 
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