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Electrostatic Potential Energy

  1. Feb 9, 2009 #1
    1. The problem statement, all variables and given/known data

    What is the electrostatic potential energy of an isolated spherical conductor of radius 24 cm that is charged to 3.9 kV?


    2. Relevant equations

    Electric potential

    U = (kQ)/r



    3. The attempt at a solution

    U = ((8.99 * 109 ) * (3.9 * 103)/(0.24)

    Could someone walk me through how to do this? Its a simple problem I know...but i'm not understanding it, thanks!
     
  2. jcsd
  3. Feb 9, 2009 #2

    LowlyPion

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    You may be confusing kV with Coulombs here.

    The Voltage is your electrostatic potential energy and is supplied by the kQ/R relationship.

    But they didn't give you the charge on the sphere.
     
  4. Feb 9, 2009 #3
    The answer has to be formatted in Joules.. so its work, but i'm not exactly sure how to get work from an energy field.
     
  5. Feb 9, 2009 #4

    LowlyPion

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    So then you're wanting to know how much work is required to charge a sphere?

    So Work = V * q

    As you bring the charges to the sphere, there will be work for each charge carried in from ∞. The average ΔV will be 1/2*V that the charges will need to be brought in against. That means for all the charges the total work will be 1/2*V*Q - where Q is the total charge.

    But we also know that V = kQ/R, so rewriting we have

    W = 1/2*V*(V*R/k) = 1/2V2*R/k

    Or if you looked at it like a capacitor - a spherical one floating in space - then you can start from Q = V*C and since the potential energy in a capacitor is 1/2Q2/C you can rewrite that as 1/2*k*Q2/R = 1/2*V2R/k
     
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