Recent content by albertrichardf

Thanks for answering. I mean, are there any analytical methods to solve, or approximate a solution to Poisson's equation in these cases? Or at least show mathematically, that the charges tend to concentrate at the tip of a pointed surface?

Hi all, I know qualitatively that charges tend to concentrate on sharp edges of conducting surfaces. I have tried searching online for a mathematical treatment of such a phenomenon, but I cannot find anything that's quite rigorous. I'd appreciate it if someone could guide me towards such...

Hi, consider the following curve: f(\theta) = \frac {I_0sin^2(n\theta/2)}{sin^2(\theta/2)} When the area over a cycle from ##0## to ##2π## is evaluated it gives ##(2πnI_0)##. This is exactly ##\frac {I_{max} + I_{min}}{2}## , since ##I_{min}## is ##0##. Is this a coincidence, or is...

I see, thank you for answering. If they are imprecise, then I suppose that the small angle approximation of ##sin 2\theta = 2 sin \theta## would also work, even if it was not mentioned. That would explain how he obtained the end result, provided that ##\theta## is the angle between ##PR## and...

I also got the same result, although I did not assume that D is small. From geometry, $$s - P'S = D sin \theta $$ $$ P'R - s = D sin \theta $$ And then the sum of the two equations gives ##P'R - P'S = 2 D sin \theta ## Somehow he gets rid of the factor of 2.

Thank you for replying. He refers to the angle ##\theta## as the "opening angle of the lens", which seems to mean that ##\theta## is actually the full angle of the lens. However, he states that ##D > \frac {\lambda}{n sin \theta}## is exactly equivalent to ##t_2 - t_1 > \frac 1 \nu## and he...

Hi, I read the Feynman Lectures Volume 1, Chapter 27, section 27-7, which can be here. In the lecture he describes the fundamental limits of resolution and provides a criterion. Here is the diagram I am referring to, figure 27.-9: There are two light sources, ##P## and ##P'## There is an...

Then again, none of them involve the geometric approach of the video either.

So, there'd be absolutely no way to solve this? I think that the commenter actually tried to curve the number line, so that part of it would form the end caps of a cylinder. The comment is kind of cryptic.

Hi, so I came across this video: which shows an interesting way to solve the Basel problem using lighthouses. Imagine a lighthouse that has absolute brightness 1. The apparent brightness then follows an inverse-square law. Now imagine an infinite number line with positive integers only (and...

Thanks for answering. Ultimately I decided to choose the US. I preferred the program there. We (Mauritians) do in fact, have to take the TOEFL in general. However, most of the universities I applied to gave a waiver based on standardised test scores, the fact that English is my native...

Oh sorry, I've been in this college selection for so long, the terms have stuck like glue. CCS is a college of UCalifornia, Santa Barbara: College of Creative Studies. Both its L&S (College of Letters and Science) and its CCS offer physics as a major, and the CCS one tends to be more...

Sure looks like it. Guess US it is then. Thanks for answering.

Hi, I'm going to do my undergraduate degree in physics this year, and I'm considering two main choices: Université Pierre et Marie Curie and UCSB (L&S physics, but I'm awaiting my decision regarding CCS). I'm definitely doing my phd in US, though. I have a few questions about UPMC, however...

You're right: physically, we cannot freeze time. Reversible processes exist only in our theories. However, through methods such as compressing gasses slowly, we can approximate reversible processes physically. Therefore, we can imagine freezing time and compressing the gas theoretically, which...