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Electrons moving in electric field

  1. Sep 2, 2016 #1
    1. The problem statement, all variables and given/known data
    Suppose electrons enter the electric field midway between two plates at an angle θ0 to the horizontal, as shown in the figure, where L = 5.1 cm and H = 1.1 cm. The path is symmetrical, so they leave at the same angle θ0 and just barely miss the top plate. What is θ0? Ignore fringing of the field.

    21-66alt.gif

    2. Relevant equations
    F = qE

    3. The attempt at a solution
    Not sure where to start but I'm assuming I have to break things into components and that there's trig involved...
     
  2. jcsd
  3. Sep 2, 2016 #2

    Simon Bridge

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    Very good - that is an excellent start.
    You have actually done problems like this before.
    Hint: the electron is a projectile fired at an angle to the horizontal in a uniform vertical force field
     
  4. Sep 2, 2016 #3
    Indeed you can solve it by using projectile motion. By getting the ratio of maximum heights (H) and the range (L), you can determine the angle.
     
  5. Sep 3, 2016 #4
    Got the answer! Thanks!
     
  6. Sep 3, 2016 #5

    gneill

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    Can you demonstrate that mathematically? Somehow I doubt that it is so o_O
     
  7. Sep 5, 2016 #6

    Simon Bridge

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    For the benefit of someone else with the same issue, please post what you did.
     
  8. Sep 5, 2016 #7
    The motion of electrons can be calculated by using the equations of projectile motion.
    The electrons reach the maximum height at
    H= v2*(sin(θ))2/2*g
    and leave the plate at the range of
    R=v2sin(2θ)/g
    (Note: H is the distance between two plates, R is the length of plate, v is the initial velocity of electron, g is the acceleration acts on the electron )
    by getting the ratio, we can eliminate the v and g by division thus leads to
    H/R= sin2(θ)/2sin(2θ)
    from the identity of trigonometry we know that 2sin(2θ)=2sinθcosθ
    Therefore,
    tanθ=2H/R. Put in the values of H and R we get
    θ=tan-1(2H/R)
     
  9. Sep 5, 2016 #8

    gneill

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    Nice. I didn't see that as what you were implying from your hint.
     
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