General question about solving force maximization problems

In summary, the speaker is struggling with an E&M problem involving positive charges on the x and y axes. They have derived an expression and differentiated it to find the maximum force, but their answer does not match the textbook's. They are asking for conceptual guidance on how to approach the problem.
  • #1
Ceenaya19
8
0
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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  • #2
Did you take the vector sum and maximize its magnitude, or did you ignore how each charge provides a force in a different direction?
 
  • #3
Two on y axis, and one on x axis.
So, the position is on the x axis. Please thinking again.
 

Related to General question about solving force maximization problems

1. What is a force maximization problem?

A force maximization problem is a type of optimization problem in which the goal is to find the maximum possible value of a specific force or set of forces acting on a system, subject to certain constraints.

2. What are some real-world applications of force maximization problems?

Force maximization problems have numerous applications in fields such as engineering, physics, and economics. For example, they can be used to optimize the design of structures like bridges and buildings, to maximize the efficiency of engines and machines, or to maximize profits in business decision-making.

3. How do you approach solving a force maximization problem?

The first step in solving a force maximization problem is to clearly define the objective or force that needs to be maximized, as well as any constraints that must be considered. This is followed by constructing a mathematical model of the problem and using techniques such as calculus and linear algebra to find the optimal solution.

4. What are some common challenges in solving force maximization problems?

Some common challenges in solving force maximization problems include dealing with complex and non-linear systems, incorporating multiple forces and constraints, and determining the appropriate optimization techniques to use based on the problem at hand.

5. How can force maximization problems be beneficial to society?

Solving force maximization problems can lead to more efficient and effective solutions in various industries, ultimately benefiting society as a whole. For example, optimizing the design of structures can lead to safer and more cost-effective buildings, while maximizing the efficiency of machines can lead to reduced energy consumption and environmental impact.

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