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Proton trajectory grazing a charged sphere

  1. Mar 3, 2017 #1
    1. The problem statement, all variables and given/known data
    upload_2017-2-11_10-28-38-png.112937.png

    2. Relevant equations
    potential energy = -kQq/r
    potenial = kQ/r


    3. The attempt at a solution
    i am not quite sure how does l play a part in this experiment since it is far away l is insignificant and the only initial energy is kinetic energy and final is kinetic and electric potential energy i can calculate the final electric potential energy and initial kinetic energy is given so hence at most i can only calculate final kinetic energy but how is that going to help me find l
     
  2. jcsd
  3. Mar 3, 2017 #2

    ehild

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    It is a central force field, there is one more conserved quantity, what is it?
     
  4. Mar 3, 2017 #3

    gneill

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    Staff: Mentor

    Moderator note: Thread title changed to better describe the problem. Previous title was too general (forum rules on thread titles).
     
  5. Mar 3, 2017 #4
    is it the work done on the proton?
     
  6. Mar 4, 2017 #5

    ehild

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    Why should it be constant during the motion of the proton?
     
  7. Mar 4, 2017 #6

    ehild

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    In a central force field, like that, the angular momentum also conserves.
     
  8. Mar 5, 2017 #7
    oh wow that is really smart is it because the force is constantly radially out ward hence no net torque on proton about the centre of sphere
    so ,
    initial energy = final energy
    2000eV = 1000ev + 1/2 m vf2
    vf = √(2000ev/m)

    then by what you said conservation of angular momentum i am assuming you meant about the centre of sphere

    hence
    m ri x vi = m rf x vf
    ri x vi = rf x vf
    letting distance o to o' be s
    √(l2 + s2) √(4000ev/m) sinθ = R √(2000ev/m)
    √(l2 + s2) l/(√(l2 + s2)) = R /√2
    l = R/√2
    am i right for part a by the way thanks for the amazing insight really inspiring question
     
  9. Mar 5, 2017 #8

    ehild

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    It is right, good work!
     
  10. Mar 6, 2017 #9
    omg thanks so much that one hint of yours helped me so much i was initially initially thinking of calculus
     
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