Recent content by Vincf

Solving the parallel-plate capacitor problem as a boundary value problem is actually very complicated. Take a look at the article I linked on the AJP website. Even the conducting disk problem isn't easy to solve. If I remember correctly, the exercise is posed in the third edition of Volume II of...

The parallel-plate capacitor is almost never treated as a boundary value problem. Aside from the rather limited conformal transformation, I only know of one article in the AJP that addresses it as such, and it's very complicated...

The supposedly applicable conditions (see the quote from Walter Lewin) are that the height must be small compared to the distance from the edge. These conditions are correct for an infinite wire. They are correct for an infinite plane with respect to the vertical component, which, in the example...

The capcitor problem is different because we have two charged planes with opposite charges. The horizontal components cancel each other out. But consider this question : I'm imagining a large, uniformly charged disk with σ = 1 C/m². The disk's radius is 1 km. Point M is 1 mm above the disk and...

By "error" I just meant that by using the model, we could predict the horizontal field to be zero, whereas in reality, it's of the same order of magnitude as the vertical field. To be more precise, we should look at a concrete example of using the infinite plane model to see what it yields...

When I was a student, I remember endless discussions about the difference between quasistatic and reversible processes. Different authors didn't agree on the definition. It's been a long time since I read Callen's book, but I recall sometimes feeling frustrated while reading it. Some important...

I think you have a misconception about Joule-Kelvin expansion, which is sometimes distorted by the diagrams used. It's not a small upstream reservoir with gas expanding into a small downstream reservoir via a porous wall (or expansion capillary). In true Joule-Kelvin expansion, there's a...

Yes, I agree with you, a limit process can be problematic. But in physics, we use these kinds of infinite limits to approximate real-world situations. Therefore, the limit is only useful if it's close to the finite situation. What I think is that this isn't the case for the infinite plane with...

Hello, I share your conclusion: There is a mathematical convergence problem for the horizontal component of the field. This is somewhat equivalent to saying that an integral that only converges in principal value converges in the usual sense. Indeed, we must consider the practical consequences...

For the usual infinite plane, we cannot impose the usual boundary conditions. The field does not tend towards 0 at infinity, and the potential diverges. This is, in fact, part of the problem: we extend the Coulomb integral to an infinite distribution without worrying about the convergence of the...

Hello, The sum you're showing is a Riemann sum. The Riemann sum is $$\sum_{n=0}^\infty f(x_{n})(x_{n+1}- x_{n}) $$ with the function $$f(x)=\frac {1} {1+x^2}$$ and ## x_{n}=na##. You do indeed arrive at the function ##arctan(\infty)=\pi /2 ## But you're only calculating the vertical component...

I don't believe it's necessary to introduce an external field. This is the field created by the distribution itself. We can look at the problem another way. Since the "infinite charged plane" is part of our students' curriculum, it must be useful for modeling something. Could we discuss an...

We agree: there are infinitely many solutions for the horizontal component of the field. But then, why talk about "the" uniformly charged infinite plane if there are infinitely many? And when I model a finite distribution with an infinite plane, which one should I choose? If I consider a finite...

Hello, I wrote another question to clarify things. Have you seen this other question? https://www.physicsforums.com/threads/infinite-scaling-limit-of-an-elliptic-charged-surface.1084226/ It concerns a planar distribution with an elliptic boundary that is scaled towards infinity.

It is indeed a uniform charge distribution with a constant charge density σ. However, its boundary is elliptical instead of rectangular as in the previous post. This is closer to a circular partition, with a single parameter, as many participants seemed to prefer.