Does charge have potential energy at each point in a circuit?

[speeding electron]

When we connect two points at different potentials in a cell with a conductor, we will have a circuit and charge will flow between the two points. Will each unit charge, just as if it were experiencing an electromagnetic force in free space, have a potential energy by virtue of its position from the point at lower potential it is attracted towards?

Each unit of charge will lose more of its potential energy (all of which it inevitably must lose if it is to reach the end of the circuit) in the loads with higher resistances. But this means that the charge can have different potentials at the same distance from the point at lower energy, depending on how much of the total resistance of the circuit it has gone through. Is there something I'm missing here? Does the force act somehow 'around the circuit', rather than straight?

Help is appreciated.

 

[turin]

Originally posted by speeding electron
Will each unit charge, just as if it were experiencing an electromagnetic force in free space, have a potential energy by virtue of its position from the point at lower potential it is attracted towards?

No, not just like in free space. It will not be in free space, but in a material that conducts, which is a very different situation. The cell has two poles. Why are you disregarding the other one?

Originally posted by speeding electron
Each unit of charge will lose more of its potential energy ... in the loads with higher resistances. But this means that the charge can have different potentials at the same distance from the point at lower energy, ...

That is because the potential field does not necessarily have the same symmetries in this case, as it would in free space. The presense of media (i.e. conductors) distorts the potential field.

 

[speeding electron]

OK, thanks for clearing that up.