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Potential difference between two points problem

  1. Jul 13, 2009 #1
    The problem statement, all variables and given/known data
    Find the potential difference between two points located at distances [tex]R_1[/tex], and [tex]R_2[/tex] from a point source.

    Solution
    Potential difference = [tex]V_{p_1, p_2} = V_{abs_1} - V_{abs_2}[/tex].

    Question
    Hows is the solution above true? What if the angle formed between [tex]P_1, Q, P_2[/tex] increases? Don't we have to take this into consideration? If the angle increases, then [tex]P_1[/tex] will be at a larger distance away from [tex]P_2[/tex] (at least until an angle of [tex]\pi[/tex]). Doesn't distance influence the potential difference?

    Thanks again,

    JL
     
  2. jcsd
  3. Jul 13, 2009 #2

    rl.bhat

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    Homework Helper

    Potential difference depends on the position of P1 and P2 with respect the the field, not on the path from P1 to P2.
     
  4. Jul 13, 2009 #3
    Is that a definition, or can it be justified?
     
  5. Jul 13, 2009 #4

    rl.bhat

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    Homework Helper

    Yes. It is the basic theorem.
    If you lift an object to certain height, rise in potential energy is = mgh, irrespective of the path through the object is taken.
     
  6. Jul 13, 2009 #5
    Both electric fields and gravity fields, which rl.bhat mentions, are called conservative fields, meaning that the path taken from A to B does not matter. Friction is non-conservative, by counterexample. Since the electric field is conservative, you can describe its potential with a scalar rather than a vector. You're right that distance affects potential difference sometimes, but this is taken into account when you calculate the individual potentials V1 and V2. But because it's a scalar potential, the angle does not matter, only the distance.
     
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