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Problem about uniformed charged ring and a charge in the center

  1. Jul 23, 2009 #1
    1. The problem statement, all variables and given/known data
    A charge Q = - 710 nC is uniformly distributed on a ring of 2.4 m radius. A charge q = + 350 nC is placed at the center of the ring. Points A and B are located on the axis of the ring, as shown. In Figure below, an electron is projected along the axis of the ring from infinity. The electron reaches and comes to a momentary halt at a point on the axis which is 5.0 m from the center of the ring. The initial speed of the electron at infinity is closest to:
    http://img31.imageshack.us/img31/3900/q6g1.jpg [Broken]

    a) 1.4*10^7 m/s
    b) 9.1*10^6 m/s
    c) 6.9*10^6 m/s
    d) 4.6*10^6 m/s
    e)2.3*10^6 m/s
    2. Relevant equations
    U=ke*q1q2/r1r2
    V=ke*Q/sqrt(x^2+a^2)
    http://img38.imageshack.us/img38/7096/picture1oxd.jpg [Broken]

    3. The attempt at a solution
    1/2 mv^2=ke*q1q2/r12+ke*Q*qe/sqrt(x^2+a^2)

    plug in number, solve for v and i don't find any answer similar with my result, is there something wrong with my solution ?
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Jul 23, 2009 #2

    rl.bhat

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    Homework Helper

    In the problem what is the role of point A and B?
     
  4. Jul 23, 2009 #3
    i believe it is use for the next question
     
  5. Jul 23, 2009 #4
    I have got 1.58*107, what is somewhat similar to first choice. Your formulas look reasonable. My calculations are:

    Ring radius 2.4 m
    distance from center to halt point 5 m
    distance from ring to halt point 5.5 m
    q (charge at center) -7.10E-07 C
    Q (charge at ring) 3.50E-07 C
    Electron charge -1.60E-19 C
    Electron mass 9.11E-31 kg
    Vacuum permittivity 8.85E-12 C^2 N^−1 m^−2
    Potential energy from the ring -9.09E-17 Dj
    Potential energy from the central change 2.04E-16 Dj
    Total potential energy 1.14E-16 Dj
    Velocity 1.58E+07 m/s
     
  6. Jul 23, 2009 #5
    By q1q2 do you mean q*qe ?
     
  7. Jul 23, 2009 #6
    i am very appreciate ur help, it is just i did not have the result like u
    there is a little bit problem with ur solution, that is q (charge at center) is 3.50e-07 C and Q(charge at ring) is -7.10e-07 C, not other way around
     
  8. Jul 25, 2009 #7
    My mistake. The right answer is choice A then.

    Ring radius 2.4 m
    distance from center to halt point 5 m
    distance from ring to halt point 5.5 m
    q (charge at center) 3.50E-07 C
    Q (charge at ring) -7.10E-07 C
    Electron charge -1.60E-19 C
    Electron mass 9.11E-31 kg
    Vacuum permittivity 8.85E-12 C^2 N^−1 m^−2
    Potential energy from the ring 1.84E-16 Dj
    Potential energy from the central change -1.01E-16 Dj
    Total potential energy 8.35E-17 Dj
    Velocity 1.4E+07 m/s
     
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