Ok I'll start my question with laying some background: (Correct me if I'm getting things wrong - but don't be picky).
- Put electro-magnetism aside for this discussion - an electric field is some space in which an electric charge will experience force.
- What generates an electric field is an electric charge. Electric charge is a property of matter, and it can be either positive or negative.
- When some charged material is put in an electric field, it will experience force rejecting or attracting it, depending on the direction of the field and the type of the charge.
Now, let's talk about Voltage - electric potential difference. Every video or article I watched or read about this explained the concept of electrical potential difference using the analogy to gravitational potential difference this way:
Gravitational potential energy (PEg) is the potential energy stored in an object, with respect to some other point lower than where it is currently placed. It is $m * g * h$ where h is the delta between the two points.
Gravitational potential (Pg) is a property of position: It is the PEg (in Joules) per kg of mass. So every kg you place at this point will hold this amount of Joules. Eventually, what we really care about when talking about the potential of a position is the potential difference between this position and some other position.
Now let's see how this translate to electricity:
In electricity, much like in gravity, we have a field exerting a force on objects. This time we talk about charges rather than mass. Electrical potential energy (PEe) is the amount of energy (Joules) that a certain amount of charge possesses when placed at a given position in the field. But again: that amount of energy is only relevant compared to some other position. I mean - the PEe is how much work is needed to bring this charge from some other position to this position, and therefore how much energy it stores when placed at that position. Same as with gravity - Potential (Pe) is a property of position in the field, and defines how much PEe one Coulomb of charge will hold at that position.
So far so good, but there are 2 basic things I don't quite understand in all this:
When we talk about gravity - we are talking about one system. It's true that the potential of a position is only relevant compared to another position. But eventually, all the positions in the world can be referred to one position - let is be the earth's center or sea level. How does this translate to electric fields?
I don't quite understand how this model is applied in a 9V battery for instance. All the videos I watched are showing this big floating somewhere in space, and then talk about the little q pushed towards the big Q
how does this model fit in a battery (or any other DC power supply)? What is the source of the electric field? And - as far as I understand - voltage is the mere difference in electric potential between two points. So if we take every two points in the field we can calculate the Voltage between them. But if we won't place any charges there, there won't be any current. But with batteries - we say that the mere presence of voltage meaning that there'll be current flowing if we close the circuit.
I'll try to make the question more clear: When we talk about gravitational potential energy, every point we'll choose has some height. We can always take 2 points (let's leave outer space out foe this discussion) and tell the difference between them. My question is: is it the same with electricity? Is there any reference point we can all agree upon and measure every two positions in the world and tell the difference between them?