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.
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.
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:
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:
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.
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
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.
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