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Currently I have three different pictures to describe/understand conservative forces. For the moment I just want to get an electron from point A to point B. In the near surrounding is another electron and thus it gets complicated, they repel.

  1. The first is like my "standard" imagination of forces. You make things move and as you move them, you might feel some sort of resistance, which pushes in the other direction. That means you have to apply constantly a force and constantly submit energy to keep the whole process alive. Well, it is a conservative force, so you are allowed to choose an arbitrary path as long as A and B stay.

However this confused me... because you could take paths that go through A several times before one reaches B, or you also just encircle B... In the end I have to imagine imaginary or negative energy to justify it. That seems wrong.

  1. I imagine the path like given mountain railway or a slide, the path for the electron is already predetermined and just push the electron and then it moves. And because there isn't really a different path, it is forced to move on that railway or whatever. Then I would imagine the force as an one time event, it also has the same flaw as the standard picture I have. I don't see how the given path cancel itself out. I might have to revise my imagination/picture.. but then, what is a force?

  2. My 3th imagination is just like a description of F(B) - F(A). Then I can explain it well, without problem. However then I don't understand for example the concept of force and force with the opposite direction..

Has someone an idea, how to help me with my problem? Maybe I just need more time.. I will check later this day for replies and maybe add to my thoughts, if needed.

Tea is life
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Imago
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    A force is that which causes an acceleration of a mass in an inertial system. A "conservative force" is a force field, where the potential energy of a test particle subjected to the local forces of that field depends only on the current position of the particle, but not on its past positions. Absolutely nothing is left to your imagination. :-) – CuriousOne Sep 20 '14 at 09:58

2 Answers2

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A conservative force is such that the work needed to go from A to B is path-independent (see for example https://physics.stackexchange.com/questions/118410/on-conservative-forces).

  1. If you choose a complicated path which for example goes from A to B several times, you will do positive work in certain traits (meaning that the point you are considering "uses" its energy) and negative work in other traits (meaning that the point will acquire energy from its surrounding, e.g. from the other charge).
  2. What do you mean by saying that the path is predetermined? The path the electron will take is dependent for example by its initial velocity. Specifying the initial and final position is not enough to characterize the trajectory.

Another related question is Conservative Forces & Conservation of Energy?.

Community
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glS
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A conservative force is one where

$$ \nabla \times F = 0$$

Aron
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    This is not a very helpful answer. You could improve it by exploring the consequences of the equation you cite. – John Rennie Jun 10 '15 at 06:52