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Electric Potential Energy of a Charge Distribution

  1. Jan 18, 2012 #1
    1. The problem statement, all variables and given/known data
    Examine the diagram provided,
    Sphere 1: q=3.0x10-4C
    Sphere 2: q=-3.0x10-4C
    Sphere 3: q= 3x10-4C
    digram.jpg
    a) Find the total electric potential energy of the charge distribution
    b) Find the total electric potential at point Z

    2. Relevant equations
    EE=kq1q2/r +kq2q3/r+kq1+q3/r... etc

    V=kq/r

    3. The attempt at a solution

    a) EE= kq1q2/r +kq2q3/r+kq1+q3/r
    EE=(9x109)[(3.0x10-4*(-3.0x10-4)/3) + ((-3.0x10-4*(3.0x10-4)/3) + ((3.0x10-4*3.0x10-4)/6)]
    EE= -405 J (Does anyone else get the same answer? I tried to do it continuously in my calculator so I don't lose digits)

    b) V= K(q1/r+q2/r+q3/r)
    V=(9x109)[(3.0x10-4/4.24)+(-3.0x10-4/3)+(3.0x10-4/4.24)]

    V=3.7x105 V or J/C
     
  2. jcsd
  3. Jan 18, 2012 #2

    SammyS

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    Those answers look good to me.
     
  4. Jan 18, 2012 #3
    Ok thanks!
     
  5. Apr 2, 2012 #4
    Those are tough to calculate all at once. It took me a few tries but I did end up with the same answers.
    For anyone else who likes to take things one step at a time, here you go:

    a) E = k[(-3x10^-8)+(1.5x10^-8)+(-3x10^-8)]

    b) V = k(4.15094x10^-5)

    (and at the end, when your multiplying the final sum by Coulomb's Constant (k=9x10^9), make sure to put brackets around that too. Seems to make a difference.)
     
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