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Work to move charges from Infinity to origin

  1. Aug 15, 2010 #1
    1. The problem statement, all variables and given/known data

    Eight 3.0 μC charges are located at the corners of a unit cube centered about the origin with 1mm edges. How much work does it take to bring a 5.0 μC charge from infinity to the origin?

    2. Relevant equations

    U= k*q1*q2/r

    3. The attempt at a solution

    r= ((1*10^-3)^2+(1*10^-3)^2+(1*10^-3)^2))^(1/2)m
    =1.73*10^-3m

    U=(9*10^9)*(3*10^-6)*(5*10^-6)*8 / (1.73*10^-3)
    =623.54 J

    U at Infinite = 0

    Work = 623.54 J



    I have tried to explain why I have simply multiplied one result by 8 below.

    The charge will have to have some path to get to the center of the cube and as a result there will be some time where it will be closer to some charges(a) than 1.73*10^-3m which would require more work to move the charge(b) closer than this. This extra work will be counter-acted as there will be negative work equal to this for the charge(b) to move away from the charge(a) once again.

    Ok so this is the answer that I have obtained, unfortunately this is not one of the multiple choice options available. So I am not confident that I have completed the problem correctly, any feedback would be most welcomed.
     
  2. jcsd
  3. Aug 15, 2010 #2

    ehild

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    The cube is centered about the origin. How far is the centre of a cube from the corners?

    ehild
     
  4. Aug 15, 2010 #3
    Eight 3.0 μC charges are located at the corners of a "unit cube centered about the origin with 1mm edges"

    r= ((1*10^-3)^2+(1*10^-3)^2+(1*10^-3)^2))^(1/2)m
    =1.73*10^-3m

    Wouldn't that be the distance?
     
  5. Aug 15, 2010 #4

    ehild

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    No. Make a picture. What does it mean "centered about the origin? "

    ehild
     
  6. Aug 15, 2010 #5
    Ok I think I have seen where I have made the mistake, thank you for your 'guidance' :)
     
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