Inserting dielectric into isolated capacitor

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Discussion Overview

The discussion revolves around the effects of inserting a dielectric material into an isolated capacitor, focusing on the energy dynamics and polarization processes involved. Participants explore different scenarios regarding the timing of polarization and its implications for energy conservation and dielectric behavior.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant states that increasing the capacitance while keeping charge constant decreases the energy in the capacitor, raising the question of where this energy loss originates.
  • Two cases are proposed: in the first case, the dielectric slab polarizes immediately upon entering the electric field, while in the second case, it takes a long time to polarize.
  • In the first case, energy is used for both pulling the slab in and polarizing it, while in the second case, energy is solely used for polarization after the slab is in position.
  • Another participant suggests that the energy loss goes into polarizing the dielectric and notes that if held, one would feel the force exerted by the capacitor on the slab.
  • A participant questions whether the kinetic energy present in the first case results in less polarization compared to the second case.
  • One participant warns that the behavior of dielectrics can be complex, especially during transient states, and emphasizes that examples typically assume steady-state conditions.
  • It is noted that during the insertion of the dielectric, some portions may be polarized while others may not, complicating the overall understanding of the process.
  • Another participant asserts that the steady-state polarization should ultimately be the same in both cases, with the only difference being the time taken to reach that state.

Areas of Agreement / Disagreement

Participants express differing views on the implications of the timing of polarization on energy dynamics and levels of polarization, indicating that multiple competing perspectives remain without a clear consensus.

Contextual Notes

Participants acknowledge the complexity of dielectric behavior, particularly during transient states, and the potential for misunderstanding in this area. There are unresolved questions regarding energy conservation and the effects of kinetic energy on polarization levels.

SpartanG345
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U = (1/2)CV^2 = (1/2)Q^2 /C

Increasing C while keeping Q constant (isolated capacitor) will decrease the energy contained in the capacitor by and amount X
Where does this X energy come from?

Case 1 (slab polarizes immediately when it crosses the electric field of the plates)

The capacitor tugs on the slab, so does work on it,
If no friction, slab oscillates back and forth with constant
transferring between kinetic and potential energy.

Case 2 (slab takes a very long time to polarize)

The plate can be moved into position without the electric field of the capacitor doing any work. Once in position after along time the slab gets polarized. Thus all of the energy X must go into polarizing the slab.

In case 1, energy is used to pull in the slab as well as polarize the slab. There will be a point in case 1 where the slab is centred. At this point
X would have been converted to: Ke + Polarization energy (stored in the induced electric field)

Where as in case 2
X would have been converted to: Polarization energy only
Does this mean the case 2 slab will be more polarised (in the steady state)
 
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It goes into polarizing the dielectric.
If you'd been holding the slab, you would, indeed, have felt it.

In the case where the polarization takes a long time, the effect would just be initially as if the material were not a dielectric at all and the dielectric constant would change over time as the slab polarized.
 
Does this mean that in the first case there will be less polarization since when the slab in centered it will have some kinetic energy as well being polarized
 
You can get really tangled up with dielectrics. This is why your exercises and examples are all steady-state and static. Transient behavior can be very complicated.

As the dielectric falls between the plates, some of the dielectric will be polarized, some will be in the process of becoming polarized, and some will be unpolarized. There are no sharp boundaries, and the dipoles will affect their neighbors.

In the case of a very long polarization time, it is possible for the dielectric to fall completely through the plates without becoming polarized at all.

It is good that you are thinking about this because there are a lot of pmm proposals based on misunderstanding how dielectrics work.
 
Thanks for the reply, i updated my question a little.

What i am still confused about, is how there could be different levels of polarization, which is dependent on how the dielectric is introduced into the system. (case 1 and 2)

- based on energy conservation
 
The steady-state polarization should be the same in each case.
In the second case, you'd just have to wait longer for this to happen.
 

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