General question about solving force maximization problems

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SUMMARY

The discussion revolves around solving a force maximization problem involving two positive charges on the y-axis and a single positive charge on the x-axis. The participant derived an expression for the superposition of electric forces and attempted to maximize it by differentiation. However, their solution did not align with the textbook answer, prompting a request for conceptual guidance. Key considerations include the vector nature of forces and the importance of maximizing the magnitude of the resultant force.

PREREQUISITES
  • Understanding of Coulomb's Law and electric forces
  • Knowledge of vector calculus, specifically differentiation
  • Familiarity with the concept of superposition in physics
  • Basic grasp of force diagrams and their components
NEXT STEPS
  • Review vector addition and how to calculate the resultant force from multiple sources
  • Study the principles of force maximization in electrostatics
  • Explore examples of similar force maximization problems in electrostatics
  • Learn about the implications of charge configuration on force interactions
USEFUL FOR

This discussion is beneficial for physics students, particularly those studying electromagnetism, as well as educators seeking to clarify concepts related to force interactions and maximization techniques.

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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