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I Potential energy in 3D

  1. Aug 1, 2017 #1
    To find potential energy in 3 dimensions why do we take partial derivative and not total derivative?
     
  2. jcsd
  3. Aug 1, 2017 #2
    Which formula do you mean?
     
  4. Aug 3, 2017 #3
    Derivatives of what?
     
  5. Aug 4, 2017 #4

    jbriggs444

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    Science Advisor

    Guessing at the context...

    If you have the potential field (e.g. gravitational potential per unit mass as a function of position), you can take three partial derivatives to arrive at the associated vector field (e.g. gravitational acceleration as a function of position).

    If you have the vector field (e.g. gravitational acceleration as a function of position) and an assurance that the field is conservative then you can arbitrarily assign a zero potential somewhere, and take a path integral along an arbitrarily chosen path to obtain the associated potential field (e.g. gravitational potential per unit mass as a function of position).

    What would it mean to take the total derivative of a function of three variables? The only way I see to do it would be to choose a path (or at least a tangent to a path). Taking a partial derivative amounts to picking a tangent that is aligned with a chosen coordinate axis.
     
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