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This is a sort of a generalized question and not just referring to the flow of current. This includes fluids and many other such entities.

But why does this flow occur. For example if I consider current, then the definition of potential at any point is the work done by external agent in bringing a unit positive charge from infinity to that point. How can we deduce from this definition that the current will flow from higher to lower potential. In fluids, the fluid flows from higher point to lower point. Why so (referring, again to potential)?

Please avoid any analogies in answering the question.

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    $\begingroup$ Can you give us a hint as to what you think the alternative might be? Are you thinking current may flow from low to high? Or are you thinking current might flow in a direction unrelated to potential? Knowing what you are thinking can help us craft answers. $\endgroup$
    – Cort Ammon
    Commented May 19, 2020 at 6:35
  • $\begingroup$ @CortAmmon Okay I'll try editing the question. Thank you for your suggestion. $\endgroup$
    – Arnav Mahajan
    Commented May 19, 2020 at 6:41

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To answer in terms of electric circuits, we know that electric field $\bf E$ is related to the electrical potential $V$ by

$${\bf E}=-{\bf \nabla} V$$

That means that a positively charged particle in a region with varying potential will experience a force pointing towards regions of lower potential (and a negatively charged particle will experience a force towards higher potentials). In either case we'd describe the result as a current from higher potential to lower potential.

But, it's not correct to say current always flows from high potential to low potential. Every circuit must include some current flowing from high potential to low potential, and some current flowing from low potential to high potential, in order to form a complete circuit. The circuit elements through which current flows from high to low potential consume electrical energy, converting it to some other form (or storing it temporarily). And the circuit elements through which current flows from low to high potential deliver electrical energy to the rest of the circuit, either converting it from some other form (as in a generator or battery) or releasing energy previously stored (as in a capacitor or inductor discharging).

In other systems, there are analogous processes of flow in both directions. For example, water only flows downhill (from higher to lower gravitational potential) because it previously was evaporated by solar energy and was transported to the higher potential region as water vapor and rain.

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  • $\begingroup$ I am in High School and I do not know the inverse delta operator. Can you pls elaborate it. $\endgroup$
    – Arnav Mahajan
    Commented May 19, 2020 at 5:53
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    $\begingroup$ @ArnavMahajan, it's the gradient operator and it basically gives you the slope of the function in 3 dimensions. The main point is that, from one point of view, the potential is only a kind of summary of the effects of the fields. And the fields tell you which direction a force will be applied to a particle in the field. So the relation between higher and lower potentials and which direction of force a particle will experience is very fundamental. $\endgroup$
    – The Photon
    Commented May 20, 2020 at 16:36

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