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Inf. Parallel Plate Capacitors and Potential Energy

  1. Mar 13, 2015 #1
    Hopefully no one minds that I post a couple questions in a row as long as I'm following the rules:

    1. The problem statement, all variables and given/known data


    phyd.png
    Two infinite parallel plates labelled W and X are separated by 5.2 cm. The electric potential between the plates is 150 V. An electron starts from rest at time tW and reaches plate X at time tX. The electron continues through the opening and reaches point P at time tP

    c.) Find the electron’s kinetic energy and potential energy at point *P.
    d.) Find the minimum speed of the electron at time tw needed for it to escape to infinity.


    2. Relevant equations
    U = qV , energy conserved

    3. The attempt at a solution
    We can calc. the KE X easily: Ux = 0, Ex = Uw, Uw = 150V * -1.60*10^-19 C = 1/2 m(e) v^2 so we have v and there is no electric field once it is outside of the plates. A previous given answer indicates that the speed is constant once we hit X (I don't understand why other than that no outside forces are acting on the electron if we exclude gravity), so how can we calculate U and K at *P?
     
  2. jcsd
  3. Mar 14, 2015 #2

    Simon Bridge

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    Do we know the initial position of the electron?
    If the electron is accelerated through a potential difference of V then it's kinetic energy is V electron-volts.

    Per your question: do you know how to calculate the potential due to a single plate?
    Do you know the superposition principle?
     
  4. Mar 14, 2015 #3
    Yes it is at rest at W.

    I know the EF is σ/2e0 everywhere due to each plate and you can find V by integrating E through a distance. And I know you can also find V by adding the potentials from each plate. But we don't now the Surface density of the plates.
     
  5. Mar 14, 2015 #4

    Simon Bridge

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    You also know the potential difference between the plates is 150V... this gives you the kinetic energy at X.
    Per the charge density - just put it equal to ##+\sigma## for the +ve plate and ##-\sigma## for the -ve plate.
     
  6. Mar 14, 2015 #5
    Right, outside of the PPC the EF is 0 everywhere, so the ΔV would have to be 0 right? That means the potential doesn't change so the KE can't change as well (at point X and beyond).
     
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