Clarifications about electric potential and potential difference

In summary, potential energy is the energy of interaction between charges, and electric potential is the scalar field that corresponds to this energy. You need to be clear about the difference between potential, potential difference, potential energy, whatever. A potential ##\phi = \phi(\vec{r})## is a scalar field. Often (we're talking about statics, here) you'll start with ##\vec{E} = -\nabla \phi##, which when you take the divergence gives you$$\nabla \cdot \vec{E} = -\nabla \cdot \nabla \phi \implies \triangle \phi = -\frac{\rho}{\
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greg_rack
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Specifically, I haven't really got all the "methods" through which you could calculate or derive the electric potential and in some situations, I cannot understand how and when to apply this concept.
Is it something caused by any charge, or must there be an interaction between the two to properly talk about potential? How is a generator keeping the potential(almost, for short periods of time) constant to one end?
 
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greg_rack said:
Is it something caused by any charge, or must there be an interaction between the two to properly talk about potential?

I think you just need to be clear about the difference between potential, potential difference, potential energy, whatever. A potential ##\phi = \phi(\vec{r})## is a scalar field. Often (we're talking about statics, here) you'll start with ##\vec{E} = -\nabla \phi##, which when you take the divergence gives you$$\nabla \cdot \vec{E} = -\nabla \cdot \nabla \phi \implies \triangle \phi = -\frac{\rho}{\varepsilon_0}$$which is Poisson's equation. You need some boundary conditions. There are lots of ways to go about solving it in different problems, e.g. Green's functions. Sometimes you're lucky if ##\rho=0## in the region you're doing the integration, since you get Laplace's equation ##\triangle \phi = 0##. At this point it's really more of a calculus exercise 😜.

It is potential energies that are energies of interaction, i.e. you can't localise potential energy within a system. You should try and keep the ideas of electric potential ##\phi## and the electric potential energy ##U## of a configuration separate, although they're linked (e.g. a point charge in an external field, you say the system has potential energy ##U = q\phi##. In other cases, though, it's not so obvious how the potential energy/self energy of a system relates to ##\phi(\vec{r})##).

Some problems here:
http://teacher.pas.rochester.edu/PHY217/LectureNotes/Chapter3/LectureNotesChapter3.pdf
 
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Given any collection of charges, we divide them into those charges that cause the field and those that are interacting with the field. This division is arbitrary. It is not capricious (I could have been a lawyer...) but rather made to ease the burden of calculation. For two point charges this seems silly. But for a circuit plugged into the power grid it is obviously not.
The forces on charges are the physical observable, therefore the value of the field is what matters. The field is the gradient of the potential and so any constant can be added to the electric potential (but this must be consistently done if two potentials overlap!) . The conventional practice is to set the average potential of the universe (or the planet which is why we call it ground) ) to zero. If you always talk about potential difference it doesn't matter...any consistent choice will do.Note: Having written this already I will append it @etotheipi excellent comments above

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1. What is the difference between electric potential and potential difference?

Electric potential refers to the amount of electric potential energy per unit charge at a certain point in an electric field. It is a scalar quantity and is measured in volts (V). Potential difference, on the other hand, is the difference in electric potential between two points in an electric field. It is also measured in volts (V) and is a vector quantity.

2. How is electric potential related to electric field?

Electric potential is directly proportional to the electric field strength at a given point. This means that the higher the electric field strength, the higher the electric potential. Mathematically, electric potential (V) is equal to the electric field strength (E) multiplied by the distance (d) between two points: V = Ed.

3. Can electric potential be negative?

Yes, electric potential can be negative. This occurs when the electric potential energy at a certain point in an electric field is lower than the reference point. In other words, the electric potential is negative when the electric field is directed towards the reference point.

4. How is potential difference calculated?

Potential difference is calculated by subtracting the electric potential at one point from the electric potential at another point. Mathematically, potential difference (ΔV) is equal to the final electric potential (Vf) minus the initial electric potential (Vi): ΔV = Vf - Vi.

5. What is the unit of electric potential?

The unit of electric potential is volts (V). This unit is named after the Italian physicist Alessandro Volta, who invented the first electric battery.

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