Maximizing Potential: Solving for a in a Function with Two Particle Charges

Click For Summary

Homework Help Overview

The discussion revolves around a function used to calculate potential in a classical over-barrier model involving two different particle charges, qp and qt. The original poster seeks to find the derivative of the potential function with respect to one of the variables, a, and is interested in determining the conditions for maximizing this function.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the derivative of the potential function and the implications of having two variables, R and a. There are questions about the conditions for maximizing the function and the relevance of multivariable calculus in this context.

Discussion Status

The conversation is ongoing, with participants exploring different interpretations of the problem. Some suggest that the maximum occurs when the derivative is zero, while others point out the need to consider the gradient vector in a multivariable context. There is no explicit consensus yet, but various perspectives are being examined.

Contextual Notes

Participants note that R and a are variables in the function, while qp and qt are constants. There is also mention of the original poster's lack of experience with multivariable calculus, which may influence their understanding of the problem.

the-rocketman
Messages
3
Reaction score
0
I have this function (to calculate potential for classical over-barrier model if you're wondering) where qp and qt are both (different) particle charges:

V(a,R) = -(qp /R) - [qt / (R-a)]

What is dV/da?

The maximum of the function occurs when dV/da = 0, and I need to solve for a. So does solving for a yield R[1 + sqrt(qt/qp)]^-1?

Thanks
 
Last edited:
Physics news on Phys.org
the-rocketman said:
I have this function (to calculate potential for classical over-barrier model if you're wondering) where qp and qt are both (different) particle charges:

V(a,R) = -(qp /R) - [qt / (R-a)]

What is dV/da?

use the chain rule.
 
Hm... but it has 2 variables. I haven't had any multivariable calc.
 
what?
try to sketch the function. obviously, the function doesn't have a maximum for any constant R.
what is the question from the beginning?
 
R and a are not constants, they are the variables. the constants are the q values
 
the-rocketman said:
The maximum of the function occurs when dV/da = 0...
That isn't necessarily true for multivariable functions. Instead, you need to see when the gradient vector [dV/da, dV/dR] = 0 and use the discriminant to tell what type of critical point it is.
 
the-rocketman said:
Hm... but it has 2 variables. I haven't had any multivariable calc.

the process is the same. just imagine that R isn't a variable, so long as you want to find dV/da.

(the "d's" should be curly, like so: [tex]\partial[/tex])
 

Similar threads

  • · Replies 5 ·
Replies
5
Views
2K
Replies
2
Views
2K
Replies
6
Views
2K
  • · Replies 13 ·
Replies
13
Views
2K
Replies
1
Views
3K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 23 ·
Replies
23
Views
2K
  • · Replies 6 ·
Replies
6
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 1 ·
Replies
1
Views
3K