Definition of potential energy

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Discussion Overview

The discussion revolves around the definition of potential energy, particularly the concept of potential energy difference in an electric field and the implications of moving a charge without acceleration. Participants explore the relationship between work done, potential energy, and kinetic energy, raising questions about the conditions under which these definitions hold true.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants assert that potential energy is defined as the work done by an external force in moving a charge without acceleration, questioning the necessity of this condition.
  • Others argue that if a charge is accelerated, its kinetic energy changes, complicating the relationship between work done and potential energy.
  • A participant explains two cases: one where the charge remains at rest after movement (no acceleration) and another where it is moving (with acceleration), highlighting the difference in kinetic energy.
  • Some participants propose that the work-energy theorem relates net work to changes in kinetic energy, while others challenge this by introducing the concept of conservative and non-conservative forces.
  • There is a discussion about whether the equations relating work done by conservative forces to changes in potential energy and kinetic energy are universally applicable, with some participants expressing uncertainty.
  • One participant emphasizes the importance of defining terms clearly when discussing these equations to avoid confusion.
  • Another participant notes that potential energy is attributed to conservative forces and that the work done by such forces does not depend on the path taken.
  • Some participants question the applicability of certain equations in scenarios involving only conservative forces, particularly in the context of movement without acceleration.

Areas of Agreement / Disagreement

Participants express differing views on the necessity of moving without acceleration in defining potential energy, the implications of the work-energy theorem, and the applicability of equations relating work, potential energy, and kinetic energy. The discussion remains unresolved with multiple competing perspectives presented.

Contextual Notes

Participants highlight the dependence of definitions on specific conditions, such as the presence of conservative versus non-conservative forces, and the implications of acceleration on kinetic energy. There are unresolved questions regarding the application of certain equations in various scenarios.

  • #61
gracy said:
Here we are not told whether this external force is conservative or non conservative.But I think I will suppose it to be non conservative because in our portion /syllabus there are only three types of conservative forces spring force,electric field force and gravitational force.

In the formula

Wnc = ΔPE + ΔKE

you account for the work done in one of two ways. Either as a Wnc or as a ΔPE. The work done by the external force in this question must be accounted for as a Wnc because even if it were a conservative force you have no way of accounting for it as a ΔPE.

If the force is conservative it has a potential energy function, if it isn't it doesn't. Here's another way to look at it.

Wnc = ΔPE + ΔKE
Wnc - ΔPE = ΔKE
Wnc + Wc = ΔKE
Wnet = ΔKE
 
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  • #62
Mister T said:
The work done by the electrostatic force is path independent. The work done by the other need not be. It could be, for example, that had a different path been taken the total work done might not be zero.

Agreed. That is a reasonable objection. If, for instance, we were to push the charge through the field with our hands, we would not normally describe the force from our hands as "conservative". However, the problem statement does not restrict the set of paths that could be taken. It does require slow movement on any path that actually is taken. So the force applied by our hands must indeed always be equal and opposite to the electrostatic force at every place (and time) where it is applied.

Perhaps I can rephrase as "if the external force is supplied by a force that can be described by a static field then that field must be conservative".
 
  • #63
jbriggs444 said:
So the force applied by our hands must indeed always be equal and opposite to the electrostatic force at every place (and time) where it is applied.

Good point. I hadn't thought about that. So in this case the work done by the force applied by the hand actually must be path independent. That, however, doesn't mean that the force is in general path independent. It might be the case, for example, that along some other paths that end in different locations the work done by this particular force might be path dependent. Thus it doesn't qualify as a force for which a potential energy function exists.

Interesting.
 

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