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Directional Derivative of Potential energy

  1. Mar 11, 2013 #1
    I'm facing some problem in understanding few basic concepts of classical physics.

    http://www.fotoshack.us/fotos/67357p0020-sel.jpg [Broken]


    I cannot understand what does "ij" indicate in "Vij" and how does F=-∇iVij. Why ∇i, why not only ∇.

    Please help anybody. I'm practically getting frustrated googling for answers.

    N.B. Equation 1.29
    http://www.fotoshack.us/fotos/74847p0019-sel.jpg [Broken]
     
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Mar 11, 2013 #2

    mfb

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    i and j in Vij are indices for particle numbers. As an example, V23 is the potential between particle 2 and particle 3.
    ##\nabla_i## refers to the change of the position of particle i.
     
  4. Mar 12, 2013 #3
    Thanks for the "ij" explanation but what about my other question i.e., why F=-∇iVij and why ∇i, why not only ∇.
     
  5. Mar 12, 2013 #4

    mfb

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    There is no obvious meaning of ∇. Derivative for what?
    What is meant here is the change in potential for particle i.
     
  6. Mar 12, 2013 #5
    So what does the line "the subscript i on the del operator indicates that the derivatives are with respect to the components of ri" mean.
     
  7. Mar 12, 2013 #6

    jtbell

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    It means that the derivatives are with respect to xi, yi and zi, not xj, yj and zj.
     
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