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As I understood, the analogy of a charge moving through a circuit is similar to water flowing from a high altitude to a low altitude (like waterfalls).

But in waterfalls there are two requirements if we wanted to keep that same water repeating the cycle: we need a gravitational field (which is caused by the earth),and an energy supplier that will do work on water to move it from the low altitude (low gravitational potential) to high altitude (high gravitational potential).

In circuits, I do understand that the battery does the part of moving a positive charge from a low potential energy point (the negative terminal) to the high one (the positive terminal) so it can -again- move to the negative terminal naturally.

But for that movement to occur (moving in the external circuit) we need an electric field (in analogy of the waterfall we need earth to establish its gravitational field), so the battery should establish an electric field, and give energy to charges in the wires to "re-climb" to higher potential energy points relative to that field?

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    $\begingroup$ It's unclear what your question is. Please clarify. $\endgroup$ Commented Jan 26, 2021 at 12:37
  • $\begingroup$ @ThePointer in order for electrons to flow the battery does both the jobs of getting charge to high potential energy (after the electron reaches the positive terminal , it need to rejoin the negative one so it has the potential energy to re-travel the circuit ) and creating that potential difference . My question is: how does it manage to do it ? $\endgroup$
    – Jalaleddin
    Commented Jan 26, 2021 at 12:40
  • $\begingroup$ Maybe you are basically asking what the electric field inside and outside a simple circuit looks like. See the electric field and the equipotential lines in fig 7 and 9 in this article by Muller: web.archive.org/web/20150922060250/https://… . That electric field is generated by the battery. $\endgroup$
    – jkien
    Commented Jan 26, 2021 at 17:13

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When battery moves a positive charge, battery also moves the electric field that exists around the positive charge. All the electric fields around all the positive charges that the battery moved to the positive terminal form an electric field around the positive terminal.

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The hydraulic analogy is, in my opinion, not a good analogy. The main problem with the analogy is that hydraulic flow is substantially more complicated than a circuit. I want analogies to be simpler than the thing they are representing, not more complicated.

You have identified one such complication. Indeed, this is a difference between the hydraulic analogy and a circuit. In a circuit the “height of the waterway” depends on whether the battery is connected or not.

My recommendation is, since the analogy is confusing you, abandon it. Learn circuits on their own terms using their own equations, which are far simpler that the equations of fluid flow. You do not need the hydraulic analogy to understand circuits. They can be understood directly. There is no benefit in patching up an analogy when the time spent fixing the analogy and then using it to understand circuits could instead be used to directly understand circuits.

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  • $\begingroup$ I see your approach , but I nonetheless find it so much useful in many cases , so my question becomes : does the battery do both the jobs of giving the energy to charges so that they get from low to high potential energy AND maintain an E field ? $\endgroup$
    – Jalaleddin
    Commented Jan 26, 2021 at 13:43
  • $\begingroup$ Yes ........... $\endgroup$
    – Dale
    Commented Jan 26, 2021 at 13:44
  • $\begingroup$ Thank you, if any documentation is available on this specific question and can be shared , it would help me so much , Im willing to spend the time to fully understand it $\endgroup$
    – Jalaleddin
    Commented Jan 26, 2021 at 13:46
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    $\begingroup$ I doubt such documentation exists. You are the first person that I have met with this specific question. And I would not produce such documentation, but just use it as one more example of the many failures of the analogy. It is pointless to waste time to fully understand a failed analogy. Spend that time learning circuits directly instead. $\endgroup$
    – Dale
    Commented Jan 26, 2021 at 13:54
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    $\begingroup$ Yes. And if an analogy doesn't immediately work for you then the analogy is not worth pursuing further. The only value of an analogy is if it immediately clarifies and simplifies a complicated concept. If the analogy itself is unclear then it has failed. $\endgroup$
    – Dale
    Commented Jan 26, 2021 at 14:19

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