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.
Potential energy can be in the form of ANY energy source; a spring, hydraulic pressure, gravity, pneumatic pressure, etc.
Electrical potential is essentially voltage. A 12v battery has an electric potential of 12 volts.
Lets use another example: gravitational potential and gravitational potential energy. Gravitational potential is just how high up you are, gravitational potential energy is your height multiplied by your weight. Two objects of different weights but at the same height would be at the same potential, but have different amounts of GPE.
Electric potential and electric potential energy are the same as this. Two objects with different charge but at the same voltage would have the same electric potential but different electric potential energy.
You move something between two points and it gains or loses electrical potential energy (or keeps the same).
How much the change in potential energy is depends on where you are moving it from and to, and it depends on the thing (specifically its electric charge).
Electrical potential measures the same thing, but *factors out the thing’s charge* (by dividing by it). So rather than telling you how much potential energy changes when you move a specific thing between two specific points, it tells you how much potential energy would change when you move *any* thing between the two specific points (once you’ve factored back in the charge). It is a generalised version of potential energy.
If you want a definition, the electric potential between two points tells you the potential energy change in moving a thing *of unit charge* between the two points.
And you can do this with gravity as well; you can define a gravitational potential, where it tells you the change in gravitational potential energy for a thing of unit mass – it factors out the mass.
Mathematically, you can do this with all sorts of “field-related” forces. Any time you have a situation where the energy change *doesn’t depend on the path taken* you can define a “potential” function which will tell you about how the particular system will work. This ends up being neat as to do calculations you can ignore anything to do with the path taken, just looking at the start and end points.
And just as the (negative) gradient of the potential energy tells you the force (i.e. the force on an object will be in the direction of the steepest change in potential energy) the (negative) gradient of the potential tells you the local field strength.
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