Increase in electric potential energy

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Discussion Overview

The discussion centers on the concept of electric potential energy in a system of two like charges, A and B, and how their interactions affect the potential energy of the system. Participants explore the implications of charge movement within an electric field and the attribution of potential energy to individual charges versus the system as a whole.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant suggests that as charge A moves towards charge B, A's electric potential energy increases, but questions whether B's potential energy also increases due to its movement towards A.
  • Another participant clarifies that the potential energy increase is related to the configuration of the system rather than being attributable to either charge independently, drawing a parallel to gravitational potential energy.
  • A third participant explains that the potential energy of the system is determined by the work done to bring the charges from infinity to their final positions, emphasizing that the potential energy is a function of their separation distance.
  • One participant questions whether the potential of both charges increases as they approach each other, suggesting a simultaneous change in their positions within each other's electric fields.
  • Another participant asserts that there is only one potential associated with the configuration of both charges, rejecting the idea of separate potentials for A and B.

Areas of Agreement / Disagreement

Participants express differing views on the attribution of potential energy to individual charges versus the system as a whole. There is no consensus on whether both charges experience an increase in potential energy or how to interpret the concept of potential in this context.

Contextual Notes

Some assumptions about the nature of electric potential energy and the behavior of charges in an electric field remain unresolved. The discussion does not clarify the implications of different charge types (like versus opposite) on potential energy changes.

Miraj Kayastha
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If a positive charge A moves towards another stationary positive charge B then the A's electric potential energy increases. But shouldn't the electric potential energy of B also increase as it is also in a way moving towards the A inside the A's electric field?

So shouldn't the total increase in electric potential of the system be the double of the increase in anyone of the charges?
 
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1) The potential energy might decrease if the charges A and B are opposite.

2) Assuming A and B are of like charge, the increase in potential energy is held in the configuration of the system A and B together. The potential energy is not attributable to either A or B independently. This is also true for the gravitational potential energy. However, in the case of two objects of disproportionately different sizes, it is often convenient to neglect the motion of one of the objects (the larger one, since it accelerates so little). And in this case, one often talks about "the potential energy of the smaller object" since that's the only motion we care about, when in fact the potential energy is contained in the configuration of the system.
 
The potential energy of the system (of charges A and B) in its final configuration equals the total work that some outside agent has to do, in order to bring both charges from infinity to their final locations.

Start with both A and B at infinity.

Bring charge A to its final location. This requires no work, because charge B is still infinitely far away.

Bring charge B to its final location, a distance rAB from A. This requires work kqAqB/rAB.

The total work and the potential energy are therefore 0 + kqAqB/rAB.
 
But doesn't the potential of A and B increase as A or B gets closer because both of the particles a simultaneously changing their positions in the elctric field of each other?
 
There's just one potential. The potential due to the configuration of A and B. There's no two separate potentials that you are thinking of. There isn't a potential of A and a potential of B, there is just potential of A and B.
 

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