30th Mar, 2022

Thales Group, UK

Question

Asked 18th Mar, 2022

A thin, circular disc of radius R is made up of a conducting material. A charge Q is given to it, which spreads on the two surfaces.

Will the surface charge density be uniform? If not, where will it be minimum?

Thank you Joerg Fricke, those are excellent resources.

**Get help with your research**

Join ResearchGate to ask questions, get input, and advance your work.

Hi Mohit Rattanpal ,

Certainly the surface charge density is not uniform. The surface charge density is highest at the margins and lowest at the center of the disk.

Best regards

Of course, what I said was assuming that the material of the disk is homogeneous and isotropic and the surface of the disk is smooth and polished.

A homework problem, that's stated in ambiguous terms, which leads to endless discussions. This is material that's part of a course, not part of research.

What is, hopefully, taught is what is needed to make unambiguous statements, not statements that don't mean anything.

Elias Sadeghi Malvajerdi Shouldn't the charge density at all patches on the flat surface be uniform as the curvature is same there??

Stam Nicolis Actually I have encountered this problem while I have been studying Electrodynamics from a textbook where the answer to this problem is not given. The author has himself asked to discuss such conceptual questions with friends. So i posted on Research Gate.

Dear Mohit Rattanpal ,

The electric charge accumulates at the edges and sharp points. Therefore, the electric charge should have a maximum value at the edges of the disk, and the farther we go from the edges to the center, the lower the electric charge should be.

I'd be interested in the answer this as well. It's not homework for me, I'm recently retired and this is just a pet project. My aim is to calculate the path of a charged particle fired at an acute angle towards any point on charged disc. What I've found so far are these discussions on the field and the potential which may be helpful:

Hi Mohit Rattanpal ,

when I don't "see" the answer to a problem immediately, I find it sometimes worthwhile to play around with the help of a math program. For example, with integrals such program replaces a heavy book like Gradshteyn, Ryzhik: "Table of Integrals, Series, and Products", and if an integral cannot be solved symbolically, it can be solved at least numerically for a few cases.

Assuming a unit disk, and using polar coordinates (r, φ), for a charge at a certain point (p, 0) on the surface one can split the surface into an inner disk with radius = p - ϵ and an outer ring with inner radius = p + ϵ, for a small ϵ (and outer radius 1, of course). Then one can write an equation for the r component of the force (the φ component is zero due to symmetry) which takes into account the 1/d^2 dependence of the force (d being the distance between p and an arbitrary point on the disk) as well as the angle of the force. 2D integration over the inner disk and over the outer ring results in the forces exerted by both, and addition gives the total force. Please see the attached figure 1. Since this procedure involves no term expressing a dependence of charge density on location, it covers evenly distributed charge, and figure 1 refutes this idea: Except at the center, the total force isn't zero, so the charge density would change (here, positive values stand for centrifugal forces and vice versa).

If the term to be integrated is expanded by a factor modeling a charge density dependent on r, then the results change accordingly. The correct term, 1/sqrt(1 - r^2) in the case of a unit disk, results in figure 2. In this case, the total force is zero everywhere, except at the edge of the disk.

These notes by Ted Bunn might be of interest because they explain how to arrive at the correct term:

1 Recommendation

Thank you Joerg Fricke, those are excellent resources.

Extracting the transmission amplitude for the photoemission using a quantum mechanical model?

Question

4 answers

- Asked 10th Sep, 2022

- Victoria Madeleine Bjelland

I am following the model explained in this paper:

which could give a good estimate of the QE regardless of wavelength.

However when it comes to this equation 6, I don't see how they get the transmission amplitude (Tn) out since it is inside a summation.

I am also having difficulties seeing the restriction for the fourier components l.

On the left side of the equation is dirac-delta(l), what kind of restrictions does this lead to the value of l?

About Riemann's Hypothesis and Quantics

Discussion

11 replies

- Asked 12th Aug, 2022

- Akram Louiz

Famous mathematicians are failing each day to prove the Riemann's Hypothesis even if Clay Mathematics Institute proposes a prize of One Million Dollars for the proof.

The proof of Riemann's Hypothesis would allow us to understand better the distribution of prime numbers between all numbers and would also allow its official application in Quantics. However, many famous scientists still refuse the use of Riemann's Hypothesis in Quantics as I read in an article of Quanta Magazine.

Why is this Hypothesis so difficult to prove? And is the Zeta extension really useful for Physics and especially for Quantics ? Are Quantics scientists using the wrong mathematical tools when applying Riemann's Hypothesis ? Is Riemann's Hypothesis announcing "the schism" between abstract mathematics and Physics ? Can anyone propose a disproof of Riemann's Hypothesis based on Physics facts?

Here is the link to the article of Natalie Wolchover:

The zeros of the Riemann zeta function can also be caused by the use of rearrangements when trying to find an image by the extension since the Lévy–Steinitz theorem can happen when fixing a and b.

Suppositions or axioms should be made before trying to use the extension depending on the scientific field where it is demanded, and we should be sure if all the possible methods (rearrangements of series terms) can give the same image for a known s=a+ib.

You should also know that the Lévy–Steinitz theorem was formulated in 1905 and 1913, whereas, the Riemann's Hypothesis was formulated in 1859. This means that Riemann who died in 1866 and even the famous Euler never knew the Lévy–Steinitz theorem.

Article

Full-text available

Mecanografiado Tesis (Magister Scientiae en Física Fundamental)-- Universidad de Los Andes, Facultad de Ciencias, Postgrado en Física Fundamental, Area de Electrodinámica Clásica, Mérida, 2002 Incluye bibliografía

Chapter

- Jan 2013

In this chapter we present a brief overview of classical electrodynamics in attenuating media. The formulas presented here are useful to understand the origin, behavior, and value of the attenuation coefficients that are used for the design, modeling, and simulation of optical and radio frequency (RF) underwater communication systems.

Article

- Dec 2003

This book is a manual for the course of electrodynamics and theory of relativity. It is recommended primarily for students of mathematical departments. This defines its style: I use elements of vectorial and tensorial analysis, differential geometry, and theory of distributions in it. Russian version of this book was published in 1997 under the app...

Get high-quality answers from experts.