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Minimum work to transport electron?

  1. Dec 6, 2015 #1
    1. The problem statement, all variables and given/known data
    A charge Q = -820 nC is uniformly distributed on a ring of 2.4 m radius. A point charge q = +530 nC is fixed at the center of the ring. Points A and B are located on the axis of the ring, as shown in the figure. What is the minimum work that an external force must do to transport an electron from B to A?
    (e = 1.60 × 10^-19 C, k = 1/4πε_0 = 8.99 × 10^9 N · m^2/C^2)

    https://www.physicsforums.com/attachments/work-png.93021/?temp_hash=3fc763fb95a2d9ab71f3bf4a54a23c14

    2. Relevant equations
    V = (k*q)/(sqrt(R^2 + z^2))
    work = (V_b - V_a)*q
    work = (k*q_1*q_2)/r

    3. The attempt at a solution
    V_B = (9*10^9*530*10^(-9))/(3.2) = 1490.625 V
    V_A = (9*10^9*530*10^(-9))/(1.8) = 2650 V
    V_B - V_A = -1159.375 V

    (V_B - V_A)*q, where q = 1.60*10^-19 C
    (-1159.375)*(1.60*10^-19) = -1.855*10^-16 J

    I'm not sure if I'm supposed to use -820 nC or 530 nC for the q value when calculating V_B or V_A.
     

    Attached Files:

  2. jcsd
  3. Dec 6, 2015 #2

    TSny

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    Does the ring also contribute to the potential at point B?
     
  4. Dec 6, 2015 #3
    I was assuming that if the ring contributes to the potential at point A, it would to point B as well.
     
  5. Dec 6, 2015 #4

    TSny

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    The same amount at both points?
     
  6. Dec 6, 2015 #5
    So.. How do I know how much potential there is at point B?
     
  7. Dec 6, 2015 #6

    TSny

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    Look at your list of relevant equations.
     
  8. Dec 6, 2015 #7
    Do I use the equation V = (k*q)/(sqrt(R^2 + z^2)) for both points A and B? With R = 2.4 and z = 1.8 for A, and z = 3.2 m for B?
     
  9. Dec 7, 2015 #8
    Coulomb's law, F=kQ1Q2/r^2
    Work=Fr
    Since F is not constant between A and B, we have to calculate based on small distances dr so that F is constant within it.
    dW=F(r)dr

    Edit
    You have to apply Gauss law too for the ring.
     
    Last edited: Dec 7, 2015
  10. Dec 7, 2015 #9
    Why would he want to use Gauss's law for this question? Work is equal to change in potential energy since ##\Delta K=0##, i.e. ##W=\Delta U=q\Delta V##, in this case ##q## is the electron. Note that for continuous charge distributions(Like the ring of charge): ##V=\frac{1}{4\pi\varepsilon_0}\int\frac{dq}{r}##
     
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