Is this a correct way of thinking about voltage?

Question

I don't know why but voltage makes me super confused. I've been stuck for three days trying to understand it. I see voltage as a position in space, in which if you put a charge, if the charge is big it would move and do a lot of work, if the charge is small it would move and do a little work. Just like if I put a pen high above the floor it wouldn't do a lot of work, and if I put a book in the same position it would make a lot of work (being heavier). I don't know if it's good to think about voltage in this way. I got this analogy from by textbook:

And I guess it helped me a little.
With this analogy, measuring a potential difference (voltage) is like measuring from a point to another. I can start measuring at the positively charged plate in the picture above and say that $V_a$ is at "$5V$ above $V_b$ ($V_b$ would be at $0V$).
Is this a correct and useful way of thinking about voltage?

oliver · Accepted Answer

It is a very good analogy. You only have to take care that you do not identify electric potential with height/position itself. It is not the height/position that respresents potential energy, but rather the gravitational/electric field that is defined for each position. In mathematical language, it is not position $x$ that defines potential energy, it is the function
$$x to Phi(x)$$
that exists independent of space: the field. Then voltage is $Phi(x_1)-Phi(x_2)$.
If there was no gravitational field, there would be no potential energy with height (think about the outer space).
The other difference between the electric and the gravitational field is that all gravitational charges (i.e. masses) experience attraction, but for the electric field, some charges get attracted, and some get repelled.

user291777 · Answer

I think of voltage as pressure on a gas being pushed through a pipe that is packed with stones that have gaps between them The stones offer resistance. to the flow of gas.
I need a pump to keep gas flowing and the pump burns fuel. Similarly negative and positive charges must be pumped onto  capacitor plates to keep the voltage (attraction of  positive and negative charges for each other) constant and to allow a steady curre by to flow through wires attached to the plates.
A battery can be the pump.

ziv · Answer

As a starting I would recommend you to read about potential energy. The definition of electric potential is the potential electric energy divided by the particle charge. The units of this physicals size are measured in voltage (just like distance is measured with meters).
Answering your question, it is correct and useful to think about voltage (as any other potential energy) in this way . This analogy is correct because both the rock and the particle in the electric field are example to object that has potential energy.

Is this a correct way of thinking about voltage?

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