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This is a bit of a vague question, but I was wondering if someone could explain.

As far as I know, potential energy is formally a property of a system (for instance, the GPE of two gravitationally attracting particles). In many physics problems it happens to be the case that one of the bodies in the system doesn't do anything, so all of the energy transfers take place in the other body - if a ball falls from 10 metres, the GPE of the ball-Earth system decreases by however many joules but we never really consider the kinetic energy of the Earth because we assume it to be stationary. Hence we can effectively neglect the other body and just consider the work done on one body.

This sort of reasoning is fine for me until we get to more complicated problems, such as those involving more than 2 bodies. If two planets A and B are sitting at rest at different points in space and we bring another planet C from infinity towards them, we have created two new systems AC and BC, and we can work out their potential energies as usual. However, pretty much every source I've read would just call the sum of these potential energies the PE of planet C.

And if we have a particle in a field, the notion of a source particle (or even charged plates and the like) seems to be neglected entirely. If an electrical force moves a charged particle from points A to B in an electric field, doing 5J of work, it is always quoted as the potential energy of the particle decreasing by 5J. Or for another example, if the potential of a point in space is 2J/C, we'd consider this the potential energy of a unit charge at that point and not really pay attention to the source of the field.

I suppose all of the things I've mentioned can be linked back to the idea of a system, but in a lot of cases it seems practical to just imagine the potential energy as a property of the particle.

My question is effectively, is it only valid to neglect the 'sources' and their contributions to/from PE only when they are stationary, or are there any other factors we need to worry about?

As far as I know, potential energy is formally a property of a system (for instance, the GPE of two gravitationally attracting particles). In many physics problems it happens to be the case that one of the bodies in the system doesn't do anything, so all of the energy transfers take place in the other body - if a ball falls from 10 metres, the GPE of the ball-Earth system decreases by however many joules but we never really consider the kinetic energy of the Earth because we assume it to be stationary. Hence we can effectively neglect the other body and just consider the work done on one body.

This sort of reasoning is fine for me until we get to more complicated problems, such as those involving more than 2 bodies. If two planets A and B are sitting at rest at different points in space and we bring another planet C from infinity towards them, we have created two new systems AC and BC, and we can work out their potential energies as usual. However, pretty much every source I've read would just call the sum of these potential energies the PE of planet C.

And if we have a particle in a field, the notion of a source particle (or even charged plates and the like) seems to be neglected entirely. If an electrical force moves a charged particle from points A to B in an electric field, doing 5J of work, it is always quoted as the potential energy of the particle decreasing by 5J. Or for another example, if the potential of a point in space is 2J/C, we'd consider this the potential energy of a unit charge at that point and not really pay attention to the source of the field.

I suppose all of the things I've mentioned can be linked back to the idea of a system, but in a lot of cases it seems practical to just imagine the potential energy as a property of the particle.

My question is effectively, is it only valid to neglect the 'sources' and their contributions to/from PE only when they are stationary, or are there any other factors we need to worry about?

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