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Conservation of energy in a capacitor

  1. Feb 28, 2015 #1
    Consider a parallel plate capacitor in vacuum, we hold a test charge below one plate and release it at some point in time, we observe that the charge is accelerating towards the other plate, that is the charge is gaining kinetic energy.

    My question is how does the loss of energy from the capacitor affect them? (the energy is transfered to the charge thus it's no longer stored in the capacitor)

    My initial assumption was that the charge distribution on the plates would change so that the electric field would lessen in magnitude and thus the total voltage goes down, but then after repeating the same process a large amount of times no matter how the chrages rearranged themselves inside the plates there is no way for the field to go down to zero, the chrages cannot escape from the capacitor as the plates are not connected in a circuit which leaves the option of the total capacitance going down but capacitance is a geometric property and since the geometry of the system hasen't changed the capacitance cannot go down.

    Clearley then one or more of my assumptions is wrong, so how do we observe the effect of conservation of energy on the plates of the capacitor?
  2. jcsd
  3. Feb 28, 2015 #2


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    Are you talking about the capacitance going down, or the imbalance of charge between the plates going down?
  4. Feb 28, 2015 #3
    I'm talking about two charged plates forming a capacitor, what I don't understand is how does the loss of energy affect the plates and the charge distrubution within
  5. Feb 28, 2015 #4


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    Let me see if I have this right. We have a parallel plate capacitor consisting of two plates separated by some distance with a vacuum between the plates. Our test charge is not within one of these plates, but between them.

    If that's correct, then the energy was initially stored as potential energy of the test charge and this is where it comes from. I wouldn't say that it was stored in the capacitor, as the charge isn't stored in the capacitor. We could put test charges near one plate and let them accelerate towards the other plate all day long and the energy of the capacitor wouldn't change (assuming we didn't let the test charges be absorbed by the other plate).
  6. Feb 28, 2015 #5
    Yep that's the system, according to your answer I think I don't understand energy, the potential energy of the charge is due to the field produced by the plates and when it moves it's converted to kinetic energy, essentialy the plates are the ones providing that energy aren't they?
  7. Feb 28, 2015 #6


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    The energy of the charge is a result of the field of the plates and the charge, not just the plates. You can't just look at the plates here.
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