Recent content by Vincf

I received a warning message about "Unacceptable references or topics." I'm new to this site. Does this mean I have to delete the reference I provided, or all the posts? It's a very traditional French journal aimed at French physics professors. I'm currently retired, and my goal is absolutely...

I prefer to pose the question this way: I have a finite charged plane and a point ##M## above the charged plane at a height ##z## much smaller than the distance to the edge. Does an "infinite plane" model allow me to predict the field at ##M## without worrying about the details of the plane's...

We agree. The transition to the infinite limit is not "physical" for the horizontal component of the field. That is to say, with regard to the horizontal component, the "infinite plane" does not correctly model a finite distribution with dimensions much larger than the height. (More precisely...

We've already discussed this, and I don't share the view that it's a boundary value problem. Here, we're dealing with a simple summation problem: I'm given the imposed charges, and I'm looking for the field they create. For a finite charge distribution, the answer is given by the Coulomb...

The Coulomb integral giving the horizontal field does not converge (its value depends on how far the surface is extended to infinity). This is why the application of Gauss's theorem is problematic: it says nothing about the horizontal field. Generally, when using this method, we say that "by...

Yes, it works in that direction. What I found more difficult was proving that it's the only possibility regardless of the Lagrangian that depends only on the square of the velocity.

Yes, but since he reasons in general terms, his conclusion should be true without exception? As I told you, Landau's reasoning is sometimes extremely rapid. And he was known to be quite exceptional himself in physics. So much so that, when we don't understand something, we always wonder if it's...

Landau's goal is to recover the Lagrangian form of a free particle using only translational invariance, spatial isotropy, and the principle of Galilean relativity. Mass appears as a multiplicative constant such that the ratio of masses remains invariant under a change of unit. It is this level...

Perhaps I'm missing something, but Landau's aim is to show that the Lagrangian is of this form for a free particle. He does this in the following paragraph 1.4. In paragraph 1.3, he uses very general arguments to show that the Lagrangian can only depend on the square of the velocity. Nothing more.

Upon further reflection, I think that my previous answer is correct except in some particular case. Let us consider the case where : $$ L(v^2) = \sqrt{v^2} = \sqrt{v_x^2 + v_y^2 + v_z^2}. $$ Then $$ \frac{d L}{d v^2} = \frac{1}{2\sqrt{v^2}}. $$ Therefore, $$ \frac{\partial L}{\partial...

I am not sure you have correctly understood the notation used by Landau. There is a footnote explaining that $$ \frac{\partial L}{\partial \mathbf{v}} $$ is a vector whose components are $$ \frac{\partial L}{\partial \mathbf{v}} = \begin{pmatrix} \frac{\partial L}{\partial v_x} \\...

The first law of thermodynamics, written in the form ##U_2 - U_1 = W + Q## , only applies to a closed system. That's why we isolate a closed system at a given instant and track it over time. In the explanation provided, the closed system contains the porous zone that maintains the pressure...

Hello, Indeed, for series that are not absolutely convergent, the problem is well known. And when I was a student, in France, the math professor didn't joke about it! The physics professor was much less strict. But as physicists, we have to be careful from time to time. There's the wonderful...

For the case of a finite plane, which is the most interesting, we could extend the use of Gauss's theorem with a slight modification. We take the traditional Gaussian surface, for example, a vertical cylinder extending from ##z## to ##-z## but with a small radius ##r##. The flux of the field...

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...