Electric potential of an electron in a capacitor

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Discussion Overview

The discussion revolves around the electric potential of an electron in a capacitor, specifically addressing why the potential is measured from the negative plate rather than the positive plate. Participants explore the implications of different reference points for measuring electric potential and potential energy, as well as the arbitrary nature of directional choices in physics problems.

Discussion Character

  • Conceptual clarification
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant questions why the distance z is measured from the bottom plate, suggesting it seems counterintuitive since an electron gains energy moving to the top plate.
  • Another participant argues that the equations are valid regardless of the direction chosen for z, noting that a negative charge like an electron can be accommodated in the equations.
  • It is mentioned that the choice of direction is arbitrary, similar to how students handle positive and negative distances in problems involving gravity.
  • A participant points out that measuring potential from different plates yields different potential energy values, which can lead to confusion.
  • Another participant agrees that potential energy values depend on the reference point chosen, but emphasizes that the work done in moving the charge will yield the same potential difference regardless of the reference point.
  • One participant expresses uncertainty about the source of confusion, suggesting it may relate to the distance traveled from the starting position to either plate.
  • A later reply clarifies that potential energy is negative when measured from the top plate and becomes zero at the bottom plate, indicating a change in understanding.

Areas of Agreement / Disagreement

Participants express differing views on the implications of measuring potential from different plates, with some agreeing on the arbitrary nature of directional choices while others highlight the resulting differences in potential energy values. The discussion remains unresolved regarding the best approach to conceptualizing electric potential in this context.

Contextual Notes

Limitations include the dependence on the chosen reference point for potential energy and the potential for confusion arising from different directional conventions in physics problems.

user35711
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Why is the electric potential of an electron in a capacitor measured from the negative plate and not the positive plate here?
This is from Liboff Introductory quantum mechanics 1st(current is 4th) edition:
w2yTv.jpg

I don't understand why the distance z is measured from the bottom plate if the potential is of an electron which should gain Energy going to the top plate.
 

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In the equations the q is welcome to be positive or negative. When you plug in the negative charge of the electron I think you will see the equations make sense with the indicated direction of z.

There is no particular reason they had to choose z as up, and had they chosen the other direction the equations could be corrected with a minus sign. However up is a perfectly fine choice and the equations are written correctly for that choice.
 
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Cutter Ketch said:
However up is a perfectly fine choice
Direction choice is quite arbitrary as long as you stick with it. Students are often confused by a similar thing in basic problems of acceleration under gravity - when you drop an object, do you choose distance along its downward path to be positive (the way it's actually going) or negative (because up is often positive)? The answer will be correct, whichever you choose.
 
It's not the positive or negative sign that doesn't make sense. The complimentary value of the potential is given. If you measure from the bottom, you are giving a different value for the potential energy than when you measure from the top which is the distance potential the electron can accelerate through.
 
Agreed, there will be two values of potential energy, depending which plate you choose to be zero (reference). But the work done shifting the charge from one point to another will be equal to the Potential Difference, which will give you the same answer, whichever your axes are.
Potential is not defined in terms of "accelerating" an electron - it's the work done in moving the charge from a chosen point. I'm not quite sure where you problem lies but is it something to do with the distance traveled from start position to one plate or the other? You will get two different magnitudes and two different signs for this if not starting from the mid point.
 
You're right, I meant to say the energy in joules after moving charge q, not acceleration.
 
user35711 said:
You're right, I meant to say the energy in joules after moving charge q, not acceleration.
OK - so wouldn't you expect two possible results, depending on which side the charge ends up? Is it not just that simple?
 
What I didn't understand but now think I do is that the potential energy is negative when you start with the top plate and then goes to zero as you reach the bottom plate with the coordinates chosen.
 

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