TITLE: A conservative force is the gradient of potential energy. But force on what?
QUESTION [1 upvotes]: A conservative force can be expressed as the negative gradient of a potential. But what troubles me is where this force acts. For example if we have a system of charges we can find the electrostatic potential energy and take its derivative. This should be the force. But is this the force on one charge, the system as a whole?

REPLY [1 votes]: The forces are on what are called test particles: hypothetical particles that allow one to probe the field without affecting it. For electric fields, a test charge has a non-zero charge so it can feel the force of the electric field in its vicinity, but not so large that it affects the field being measured. For gravity, a test particle has a small but non-zero mass so that it feels the local gravity without contributing to it.
In other words, the force of the field is what a new particle would feel if it was placed in the field.
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