Eli5: What is the difference between Electrical potential vs. potential energy?
In: Physics
They’re very similar concepts, in the same way that the electric force and the electric field are related: the electric potential is related to the electric field in the same way that the electric potential energy is related to the electric force.
If you just have point charges, that is, particles that don’t have a size (or at least, we approximate them that way), then they’re *really* similar. The difference (in simple terms) in this case is that the electric potential is the “electric effect” of each charge separately, but if you have a configuration of charges, then the electric energy of the configuration has to account for the electric potential of all of the charges by summing in a convenient way. The electric potential of the configuration is simpler, it’s just the sum of the electric potentials of all charges (we say that it’s “linear”).
When you have a source of the electric field that is not a point charge, but a continuous distribution, then instead of “summing” contributions you “integrate” them. They are essentially the same thing conceptually, but with a different mathematical formulation.
In the simplest of terms: electric potential is an effect that is accounted for a single charge or a single charge distribution, while the electric potential energy accounts for the contributions of the different members of the distribution.
EDIT: This is surprisingly hard to ELI5.
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