# Potential Energy - Single Particles/Systems

If we have two charged particles in an electric field, then there is a potential energy in the system.

I am aware that it is meaningless to talk about the potential energy of a single particle alone. However,what about the phrase 'potential energy of charge $q_1$ due to $q_2$', for example, does that make sense?

I just need a bit of elucidation on the phrasing we use when we talk about potential energy (and some explanation of why would be appreciated).

• Just to clarify, so you have two charges plus an external electric field? And you want to give different names to different parts of the potential energy: potential energy of $q_1$ in the external field, potential energy of $q_2$ in the external field plus a term which depends on both $q_1,q_2$ May 10, 2017 at 12:35
• It is the electric potential energy of the system of two charges. May 10, 2017 at 12:40
• @user1583209 The electric field is created by the charges themselves. Is it wrong to speak about the potential energy of q_1 due to q_2 May 10, 2017 at 12:59
• I see (might want to edit your first sentence in the question which reads as if there is an external electric field). Personally, I'd describe this situation by saying that one charge (e.g. $q_1$) creates an electric field and the other charge ($q_2$) has a potential energy in this field. I would be fine with your short version (potential energy of $q_1$ due to $q_2$ as well. Also, saying just "potential energy of the system of two charges" (suggested by Farcher) is fine and avoids making the distinction between field-creating charge and "test"-charge. May 10, 2017 at 14:03

This is the physical meaning of the potential energy of $q_1$ due to $q_2$, or rather, the potential (energy) of any system of charges.