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Homework Help: Electron move through capacitor

  1. Nov 5, 2014 #1
    1. The problem statement, all variables and given/known data
    An electron enters a region between two capacitor plates with equal and opposite charges. The plates are L=0.1 m by d=0.05 m, and the gap between the plates is h=0.002 m. During a short time interval of dt=0.002 s, while between the plates and far from the edges, the change of momentum is dp=<0,-9x10-17,0> kg m/s. Ignore gravitational effects here since they are so weak compared to electric effects.
    (a) What is the electric field vector between the plates (far from the edges)? (hint: momentum principle)
    (b) What is the charge (magnitude and sign) on the upper plate?
    (c) What is the potential difference dV = Vtop - Vbottom ?

    I figured out how to solve the problem, however, I have some questions.
    1) Do I use 1.6x10-19 or do I use -1.6x10-19 ? I know the negative makes more sense since it's an electron but my friend were arguing that signs does not matter.
    2) How do I tell if the charge I got is for the upper plate or lower plate? I used the equation: E = Q / A epsilon0 to find the charge Q.
    3) I'm not entirely sure that my work is correct. I might have done something wrong somewhere.
    2. Relevant equations
    dp = F dt => F = dp / dt
    F = qE => E = F / q

    E = Q / A epsilon0 => Q = E A epsilon0

    dV = -E dl
    3. The attempt at a solution
    F = -9x10-17 / 0.002 = -4.5x10-14

    E = 4.5x10-14 / -1.6x10-19 = 2.8x105 V/m (not sure if this should be plus or minus because the sign of charge of electron)

    Q = 2.8x105x0.1x0.05xepsilon0 = 1.24x10-8 ( not sure if this charge belongs to upper plate or lower plate )

    dV = -2.8x105 x 0.002 = -562.5 Volt
  2. jcsd
  3. Nov 5, 2014 #2

    rude man

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    Since no coordinate system was furnished with the problem it doesn't matter which signs you use. Furthermore, the sign of the E field, that of the upper plate charge, as well as that of the potential difference are all indeterminate.
  4. Nov 5, 2014 #3


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    Rudy's correct if you're really critical. I'm inclined to see the mentioning of a negative dpy as an indication that you are supposed to consider the electron is pulled towards the bottom plate. I.e. take the positive y-direction upwards.

    That way you get ##\vec E## pointing upwards and a negative Vtop - Vbot.

    The expression you use in b) is for Q on both plates, meaning Qbot is + what you found and Qtop = - idem.

    (physically, all you found is a charge difference, but because the exercise mentions equal and opposite charges, there is no doubt left).

    My compliments for a clear and well-formulated post.
  5. Nov 6, 2014 #4

    Simon Bridge

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    Off the specific questions:

    (a) the literal calculaton would give a minus sign because you have a positive number divided by a negative number ... so keep the signs.
    Think about the role the sign plays in the electric field. Remember, E is a vector - you are asked for the vector, so you answer should be a vector - vectors have a magnitude and a direction. What is the magnitude in this case? What is the direction?

    (b) If the charge on the upper plate is Q then the charge on the lower plate is -Q ... does it matter to the problem description which is which?
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