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Derivative particle problem

  1. Sep 8, 2005 #1
    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?

    Last edited: Sep 8, 2005
  2. jcsd
  3. Sep 8, 2005 #2
    use the chain rule.
  4. Sep 8, 2005 #3
    Hm... but it has 2 variables. I havent had any multivariable calc.
  5. Sep 8, 2005 #4


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    try to sketch the function. obviously, the function doesn't have a maximum for any constant R.
    what is the question from the beginning?
  6. Sep 8, 2005 #5
    R and a are not constants, they are the variables. the constants are the q values
  7. Sep 8, 2005 #6
    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.
  8. Sep 8, 2005 #7
    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])
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