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How can I derive the equation for electric potential at a distance r from a charge Q?

  1. Aug 29, 2009 #1
    1. The problem statement, all variables and given/known data
    Find the electric potential a distance of .5 x 10^-10 m from the proton of a hydrogen atom


    2. Relevant equations
    V= kQ/r


    3. The attempt at a solution
    I know how to answer the question, because I know which equation to use. What I do not understand is, where the equation comes from ?
    Could somebody bullet point the derivation of the equation (algebra, not calculus please )


    Regards and Thanks!
     
  2. jcsd
  3. Aug 30, 2009 #2

    tiny-tim

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    Hi FelixISF! :smile:
    It comes from the field (the force), which in this case is a Coulomb's law field.

    The field has to be the gradient of the potential.

    The field is -kQ/r2 in the r-direction, so the potential has to be kQ/r (plus a constant). :wink:

    (That's calculus, of course … I don't understand what you mean by an algebra derivation :confused:)
     
  4. Aug 30, 2009 #3
    Re: How can I derive the equation for electric potential at a distance r from a charg

    I don't see how you go from -kQ/r^2 to kQ/r... Apart from the mathematical relation ship of the field being the gradient of the potential, I don't get the intuition behind it.
    so field = -kQ/r^2 and potential = kQ/r
    Now, there must be a relation between potential and field with which you can transform the field equation to the potential equation.. Do you understand what I am asking for?
     
  5. Aug 30, 2009 #4
    Re: How can I derive the equation for electric potential at a distance r from a charg

    Use the equation [tex]V=\int_{\infty}^{r}\vec{E}\cdot \vec{dl}[/tex] where V is the electric potential. In the case of a point charge you can substitute [tex]\vec{dl}=dr[/tex] and [tex]\vec{E}=E[/tex], so your integral becomes [tex]V=\int_{\infty}^r E \; dr[/tex].
     
  6. Aug 30, 2009 #5

    tiny-tim

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    In other words, potential energy is another name for work done (by a conservative force),

    so electric potential difference = PE difference per charge = work done per charge = force times distance per charge = kQ/r2 times ∆r
     
  7. Aug 30, 2009 #6
    Re: How can I derive the equation for electric potential at a distance r from a charg

    thanks, that made it clear for me!
     
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