1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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)


    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


    User Avatar
    Homework Helper
    Gold Member
    2017 Award

    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


    User Avatar
    Homework Helper
    Gold Member
    2017 Award

    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


    User Avatar
    Homework Helper
    Gold Member
    2017 Award

    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
    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.

    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}##
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted