Think like this: if we have a charged capacitor, and we physically pull the plates farther and farther apart, then the charges on the plates end up with more and more energy. (That's actually how Wimshurst and VDG machines work.) And, if we let the plates fall all the way together and touch, then the opposite charges cancel out, and the energy becomes zero. So, the energy in an electron (and in a proton) doesn't stick with the particles themselves. Instead, the energy depends on how far we've pulled the opposite charges away from each other.
Here's another example: if we have two uncharged capacitor plates, and we pull an electron from one plate and drop it onto the other one, then both plates now have opposite charges. And something weird: the entire surface of both plates becomes energized! Even with just one electron involved, the entire metal surfaces now have small excess charge. Also, the added energy was shared between every particle on the plate surface. (It's like pouring a bucket of water into a pond. The entire water level rises everywhere. The hydro-energy didn't stick with the added bucket-water.)
Or, drop one electron onto a metal ball, and the electron stays in place but the "excess charge" as well as the stored energy spreads almost instantly across the entire ball surface. It happens because the electrons that were already there in the metal, they must jostle around and slightly spread out to maintain a uniform distribution. The "electricity water-level" rose a bit over the entire metal surface, even when adding just one electron to the ball.
So, electrical energy doesn't stick to individual electrons and protons, any more than hydro energy sticks to a cup of water. When a dam pestock drains a lake to run a turbine, the entire lake's water level falls simultaneously, and energy is "sucked" nearly instantly from the entire lake, even though the water itself moves sideways quite slowly. And, if we progressively discharge a capacitor, the charges move across the metal plates quite slowly, yet the energy in the entire capacitor is "sucked" almost instantly across the plates and to the terminals.
"Voltage is the amount of energy per electrical particle"
This isn't right. It also appears to be an extremely widespread misconception.
Where's the error? Well, the statement is like insisting that "Gravity is the amount of energy per lifted kilogram." No, wrong, because gravity is still there, even when there's no boulder being lifted up to store some energy.
The same is true of voltage: the voltage is a way of measuring an e-field, and isn't a measure of particle energy. E-fields and b-fields can exist in empty space, with no need to be lifting any charges or magnet-poles while calculating energy. Look at the top of your 9V battery. There is voltage-flux in the space between the terminals. Half way between, there's 4.5V, hanging in empty space. Voltage is like magnetism and gravity: it's a field.
Here's a much better version of that statement:
"ELECTRICAL ENERGY IS THE ENERGY STORED WHEN A CHARGED PARTICLE IS TRANSPORTED ACROSS A POTENTIAL-DIFFERENCE OR VOLTAGE."
Simple? It reverses the wrong statement by stating that energy is determined by charge and voltage. (Then we just have to explain "charge" and "voltage." Heh.)
In similar fashion, it makes sense to say that gravitational energy is stored when work is done to transport a kilogram upwards against gravity. We don't turn this inside out, and insist that gravity itself is nothing but the energy per kilogram being moved!
I think this misconception about voltage has a definite origin.
Michael Faraday proposed the existence of "fields," of magnetic and electrostatic fields. Unfortunately the physics community of the time hated this, and completely rejected it. They stuck to their older concept called "instantaneous action at a distance," where forces and energy exist, but fields (and voltage) do not. Faraday died, still being ridiculed for his fields concept. Then JC Maxwell published his famous work, totally vindicated Faraday's "fields," and made them the basis of all EM science, at the same time discovering EM waves and the electrical nature behind the speed of light.
Yet some textbooks today still are sticking with the anti-Faraday viewpoint, and teaching the "distant-action" philosophy which insists that only forces and charges exist, but "fields" do not. Supposedly "fields" are nothing but an abstract mathematical gimmick: the energy per coulomb. (Heh, JC Maxwell says that magnetism, voltage, and radio waves flying through space aren't mathematical gimmicks, they're the stuff of pure EM fields!)
Yet we're left with deeper questions: We know what electrical energy is, given charge and voltage-difference it's just 0.5*Q*V^2. But what is the Q, the Electric Charge? What is the V, the Voltage? These are extremely important questions, but we don't even ask them if we've been taught that voltage doesn't really exist, and is nothing but the energy per unit charge.
What is voltage itself? Hmm. I can tell you what voltage looks like. Imagine that a charged particle is surrounded by a radial "puff" of flux lines of the e-field, like a dandilion-puff or a sea-urchin. In that case the "electrical potential" is a bunch of concentric spheres centered on the same particle, and are always perpendicular to the flux-lines of the electric field. If the lines of e-flux are like a bunch of hair, then the voltage is like a stack of paper, where every sheet of paper has flux-hairs poking through it at 90deg.
If e-field flux is an invisible star-shape with a charged particle in the center, then voltage is an "invisible onion" with a charged particle at the center. Both flux-lines and voltage (the "equipotential planes" or "shells") are descriptions of the e-field found in the space around electric.
So whenever two wires have a potential difference, this "voltage-stuff" actually extends away from the metal surfaces, and fills the space between wires, as if the wires were a pair of capacitor plates.