# Does having an electric potential difference necessarily mean having current?

I'm fairly newbie to these concepts, so please try to give a simply answer.

Electric energy is often compared to gravitational energy. This analogy helps to understand the concept of voltage. With gravitation, there is a potential difference between two points (given that they're not in the same height), and this potential difference is the potential energy difference per unit of mass. With electricity, the potential difference is potential energy difference per one Coulomb of charge.

My question is: With gravitation, the mere arrangement of having 2 points with potential difference between them doesn't mean having a flow of mass between them. We need to bring some mass to the higher point in order to have potential energy. But with electricity, it seems that if you only have two points with potential difference between them, meaning that you already have potential energy, and all you have to do is to connect this two points with a conductive material.

Another question related to this: The difference in gravitational potential difference is rooted in the difference of the height between the points. What is the root cause of the electrical potential difference between two points?

Everything will work exactly as with gravity except the fact that charges have a sign.

Exactly like gravity, you need to put charges in points of high potential energy for them to move towards lower energies. Of course, this picture breaks down if there are other forces acting on the charges (same as with gravity, if you put something high up but there are other forces they won't fall: think of airplanes!). So charge tightly bound will also not move. If you have no free charges to move however, nothing will flow, exactly like with masses.

One difference with gravity is that some materials have some charge always available, so if you apply a voltage difference to them something will happen most of the times. If you connect two points with different potential energy with a wire, the wire will supply some electrons to move. However, unless you have a "charge source" [a battery] you won't have current forever as the charges will accumulate on the lower potential energy point and stay there (it is actually a bit more complex as charges also repel each other strongly, but I think you got the point: current stops).

Plus, same as with gravitational potential energy, which depends on the distance from some mass generating the "gravitational field" (in the simplified version of gravity on Earth, the mass is the plane and the distance is the height, of course), voltage arises from the distance to some charge which is generating the "electric field". So you can think of the "electrical height" as the "distance from a charge with opposite sign" (if there are multiple charges, you need to sum their "heights" though). But in both cases the source of potential energy is some charge (or mass) distribution in space which generates the field at each point (height) in space.

Does having an electric potential difference necessarily mean having current?

No. "Static" electricity what we call situations where there are potential differences with no current.

With gravitation, the mere arrangement of having 2 points with potential difference between them doesn't mean having a flow of mass between them.

Likewise with electric fields.

all you have to do is to connect this two points with a conductive material.

If you connect two points with different potentials with a conductive material, then current will flow (for as long as the two points continue to have different potentials).

The difference in gravitational potential difference is rooted in the difference of the height between the points.

Assuming that no magnetic fields are involved, electric fields are generated by charges. The electric force between two charges (again with no magnetic fields) follows the same inverse square law as the gravitational force between two masses. The law is known as Coulomb's Law. One significant difference between an electric field and a gravitational field, however, is that there are both positive and negative charges. In our little corner of the universe, here on earth, we don't see negative masses.

In electrics, adding a conducting path between two points at differential potentials corresponds to pushing the plant pot over the sill so it can fall.

In both cases you have influenced the system to overcome an initial so-called activation barrier. When this is overcome, the plant will continue falling and a charge continue moving all the way until it finds a stable equilibrium at a lower potential-energy level.

The difference in gravitational potential difference is rooted in the difference of the height between the points. What is the root cause of the electrical potential difference between two points?

It is also distance. For gravitational potential energy it is distance between the two attracting masses - for electric potential energy it is distance bewteen charges. The formulas are very similar:

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

• @JalfredP answered: "Exactly like gravity, you need to put charges in points of high potential energy for them to move towards lower energies". Do you disagree with that? Jun 6, 2021 at 12:49