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Coulomb's Law of two copper spheres

  1. Jan 21, 2005 #1
    Here's a question from my textbook:

    Two copper spheres, each having a mass of .4 kg, are separated by 2 m.
    (a) How many electrons does each sphere contain? The atomic mass of copper is 63.5 g/mol, and its atomic number is 29.
    (b) How many electrons would have to be removed from one sphere and added to the other to cause an attractive force of 1.00x10^4 N (roughly 1 ton)?

    I got (a) by dimensional analysis:
    (.4 kg Cu) x (1 mol/.0635 kg Cu) x (6.02x10&23 molec/1 mol) x (29 electrons/molec) = 1.10x10^26 electrons

    But, I am having trouble with part (b). I was thinking that you should use the equation:
    F=k(q_1)(q_2)/r^2 , but I'm not really sure how to proceed. I would appreciate any help. Thanks so much!
     
  2. jcsd
  3. Jan 21, 2005 #2

    rbj

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    [tex] F = \frac{1}{4 \pi \epsilon_0} \times \frac{|q_1| |q_2|}{r^2} [/tex]

    if the amount of charge removed from one sphere is the same as what is added to the other, then [tex] |q_1|=|q_2| [/tex]. you know what [tex]F[/tex] and [tex]r[/tex] is, so solve for [tex]|q|^2[/tex].
     
    Last edited: Jan 21, 2005
  4. Jan 21, 2005 #3

    Doc Al

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    Staff: Mentor

    You are on the right track. Realize that q_1 and q_2 have the same magnitude, so you can write F=kq^2/r^2 and solve for q. Then, knowing the charge per electron, you can figure the number of electrons that must have been moved.
     
  5. Jan 21, 2005 #4
    Thanks, but why should q_1 and q_2 have the same magnitude? And then how do you go from "q" to the number of electrons?
     
  6. Jan 22, 2005 #5
    They're both copper spheres and contain the same number of electrons..
     
  7. Jan 22, 2005 #6

    Gokul43201

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    The copper sphere were originally neutral, because they had as many electrons as protons.

    By removing some n electrons from sphere 1, you give it a net positive charge, Q1 = ne (where e = magnitude of charge on an electron/proton = 1.6 * 10^-19 C), due to the n excess protons it now has.

    Sphere 2, having gained these n excess electrons will now have a net negative charge Q2 = -ne, due to n excess electrons.

    Q1 = ne, Q2 = -ne, so |Q2| = ne.

    Does that answer both your questions ?
     
  8. Jan 22, 2005 #7

    dextercioby

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    If u get the "q" in Coulombs,then u can use the fact that electrons have negative charge to write
    [tex] q=-|q| [/tex]

    then
    q C---------------------->"x" electrons
    [tex]-1.6 \cdot 10^{-19}C [/tex] ------------------>1 electron.

    Solve for "x".

    Daniel.
     
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