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Physics
Classical Physics
Electromagnetism
Clarifications about electric potential and potential difference
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[QUOTE="etotheipi, post: 6404996"] 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: [URL]http://teacher.pas.rochester.edu/PHY217/LectureNotes/Chapter3/LectureNotesChapter3.pdf[/URL] [/QUOTE]
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Clarifications about electric potential and potential difference
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