What is the connection between electric field and a battery?

Question

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:

1. 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?

2. 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.

EDIT

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?

Answer 1

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?

The reference point is arbitrarily chosen, yes. But it doesn't have to be sea level (not least since sea level is only constant locally and not when you consider the globe) and it doesn't have to be Earth's centre (you can pick a lower shelf as the zero-reference so that a pot on a higher shelf is associated with gravitational potential energy).

In astrophysics in general, you would not base your zero-reference on the Earth. Rather, you define zero potential energy as at a point infinitely far away. The potential energy associated with an object on Earth is with this choice of reference negative. And increasing (becoming less negative) with distance above the ground. But again, the value is not important - only the difference is.

In electrics, the zero-reference would often be chosen as either a pole of the battery/voltage source or simply as ground (the Earth). But also here the choice is arbitrary and only the difference between points matters, as you also mention.

Note that gravitational and electric potential energy is very comparable, even in their reverse proportionalities to distance:

$$U_g=G\frac{mM}{r}\qquad\qquad U_e=k\frac{qQ}{r}.$$

What is the source of the electric field?

The source of any electric field is an accumulation of charges. When dealing with a battery, typically internal chemical actions move charges towards one terminal and accumulate it there until the built-up electric field cancels out the chemical forces.

The chemical process might happen via a charge separation where electrons are separated from molecules - those molecules are then in turn able to move through the electrolyte liquid as ions, whereas the electrons can't. Instead, the electrons will have to move through the external circuit. At the other terminal, when both ion and electron have arrived, they can recombine.

The reason for the existence of an electric field which you are asking to is both due to the electrons accumluated at the terminal causing large electric repulsion forces to push electrons into the external circuit as well as due to the lack of electrons (relative positive charge) at the other terminal cause a large attractive force.

If you do not attach any external circuit, then the electrons can't move and will have to stay at the initial terminal.

Answer 2

If we want to keep the analogy to gravity, the battery can be compared to a water system in a building, where the water from the supplier company is pumped to a water box at the roof.

The water there has potential energy, (and the higher floors can have issues with low pressure because the difference of potential is small there).

Once the water are being used by the apartments, the pump automatically turns on, keeping the water box level constant. That is the key part: in the battery, a chemical reaction keeps the voltage constant while the current is circulating through the circuit.

Answer 3

The choice of a zero point in the electric potential is arbitrary, just like in the gravitational potential. A practical example of this is ground. When you design a circuit you calculate all the voltages relative to the ground (be that the mains earth or some other ground), but there's no reason why you couldn't make the positive side of your resistor (or wherever) the zero point. It just shifts everything by some offset and, as you mention, the only thing that matters is the potential difference between two points. So the choice of the zero point doesn't matter (although you generally make the choice so that your calculations are easier).

Not sure how much you know about redox chemistry but basically if we consider just a single cell, one half of the cell spontaneously liberates electrons and the other absorbs electrons. This excess of free electrons/demand for free electrons creates a potential difference between the two, and when you connect a copper wire electrons will flow from one electrode to the other. To answer your question, the excess electrons are the source of the electric field.