101The classic analogy here is balls rolling on hills. Whatever book you're using probably uses this analogy. If it doesn't it's a bad book. If you have some shape of hill, you can assign potential energy values to every point on that hill. You're energy is going to be something proportional to the height. (remember pot.E.=m g h). This energy is a scalar because it's energy. Now it's the same for E fields as gravity. Every point in space has an energy associated with it just like the balls did. Only with a few twists. Firstly, the energy that an object has at any one place is proportional to whatever the charge on that object is. This is just like the mass in mgh. Only it's not always useful to carry this around so we divide it out.
pot.E.
_____ = gh
m
This pot.E/m is the equivalent of the electric potential. Multiply any electric potential by a charge and you get the potential energy of an object with that charge at that point. Potential and voltage are used pretty interchangeably.
Potential difference is also a scalar. Here we're talking about the difference in potentials between two points. As in, "at (1,1,0) the potential is 5 J/C and at (1,2,0) the potential is 3 J/C so the potential difference between the two points is 2 J/C"
hope that helps. Remember energy is always a scalar.
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