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Does anybody can help me or suggest any textbook or paper for references to solve this problem of PDEs?

this question is a modified version of my previous question:https:[//physics.stackexchange.com/q/875717/589276] Consider the coordinate system S'. In the S' frame, there is a uniform magnetic field of magnitude B' in the x'y'-plane. The magnetic field lines are perpendicular to the x'y'-plane and point outward from the plane. There is also a uniform electric field E' in the x'y'-plane, directed d…

Is the generation of magnetic fields mainly due to certain spins of particles and the movement of electric charges? I mean fundamentally what are the sources. I recognize in aggregate, whatever generates magnetic fields will then result in bar magnets, planetary magnetic fields, etc. I'm asking about the fundamental physical origins of it. Not just "what in general can make magnetic fields?" Also…

I just recently watched a video where they were explaining the double slit experiment. I understand that the interference pattern would be observed if you send photons or electrons one after the other. The conclusion that the author seems to make is that it is as though the particle/packet of energy travels through both the slits after somehow splitting into two. Has anyone done an experiment whe…

In Landau's Mechanics volume at section 32 solved problem no. 5, the instantaneous axis is chosen as the one which coincides with the line where the cylinder touches the plane. This is possible only if there is rolling without slipping. My question is, had it been rolling with forward slipping, the instantaneous axis should be somewhere placed outside the cylinder. Am I right? PROBLEM 5. Find th…

I'm trying to construct the transfer matrix for an arbitrary system with 1 input and 2 outputs, like a splitter (shown below) or 1x2 multi-mode interferometer. (Image borrowed from http://www.fiberstore.com/images/ckfinder/images/tutorial/1x2_Splitter.jpg ) Currently, I have the entire scattering matrix for my device: $$ \begin{pmatrix} A_\text{in}^{(-)}\\ A_\text{out1}^{(+)}\\ A_\text{out2}^{(+…

In quantum mechanics, the state of a single particle in one dimension is a square-integrable function $\psi \in \mathbb{L}^{2}(\mathbb{R})$ , assume that a particle is in the following state: \begin{equation} \psi(x) = \sqrt{\frac{e^{-x^{2}}}{\sqrt{\pi}}} \end{equation} Suppose that i change my coordinate labels to $y(x) = tan(\frac{1}{2}erf(x))$ , where: $erf(x) = \frac{2}{\sqrt{\pi}}\int_{0}^{x…

So i got this question from another question posted on this website , in which the asker was asking if for a circle there will be infinite null points I have a few different question Firstly, i watched a video which shows why, in a system of 3 point masses placed at vertices of an equilateral triangle, there should exist 4 null points - in one the argument was made that on 2 different sides of a …

It has been asked before about the upper limit of surface charge density, at which the electric field starts to drain the charges off the metal surface. The medium between the metal surface is assumed to be vacuum (otherwise the medium might become conductive before the electrons are drained off). Yet there is another effect which would also puts an upper limit on the surface charge density, name…

Newton's laws function less as a single claim than as a schema for analyzing motion. The second law supplies the form: causes enter as forces, and force equals mass times the second derivative of position. But the choice of second derivative is not neccesarily forced. Suppose we replaced it with $$ F= m \frac{d^nx}{dt^n}$$ holding the other laws fixed and keeping force as the same independently m…

I'm supposed to derive a relationship in which the change in gravity $\delta g$ is linked to the change in length of the spring $\delta s$ . When the beam is tilted due to increased weight or gravity, the extra weight will tilt, and this will enhance the rotation. I understand this so far, but I can't figure out how to connect these two system. Without the extra mass one could easily used the Hoo…

The question in my textbook was "Conduction current is equal to displacement current when the source is:" and the most popular answers on internet are AC only. But I don't understand why not in DC too? In the case of a parallel plate capacitor with DC source, while charging the conduction current is equal to displacement current. And even when it is fully charged, both the currents= 0 i.e. still …

Weinberg says (Chapter 10, section 10.4) that we have to assume that the bare charge, $q_{Bl}$ that appears in the Lagrangian is equal and opposite for the electron and for the particles (two $u$ -quarks and one $d$ quarks) that make up proton. I don't quite understand the statement. I understand that the charge renormalization is a consequence of field $A_\mu$ renormalization. i.e. $q_{Bl}A_{B\m…

In a situation like this, I understood that the focal length is half of that of the original lens. However, I don't know whether its image is inverted or not. In this situation, will the image be inverted?

This is perhaps a bit of an odd question, but here goes. When physicists started investigating atomic nuclei, it turned out that protons and neutrons were composite, and the force binding them into nuclei was a complicated result of the strong interactions among their component quarks and gluons. Could it have turned out differently, without affecting the phenomena of everyday life? Could a unive…

In this document "a transparent derivation of rocket equation" , the author writes (on the last page): These are the classical and relativistic rocket equations. For the relativistic case, there is a maximum exhaust velocity for the reaction mass that is given by: $$ w=c\sqrt{e(2-e)} $$ where $e$ is the fuel mass fraction converted into kinetic energy of the reaction mass. I am not even sur…

This is perhaps a bit of an odd question, but here goes. When physicists stared investigating atomic nuclei, it turned out that protons and neutrons were composite, and the force binding them into nuclei was a complicated result of the strong interactions among their component quarks and gluons. Could it have turned out differently, without affecting the phenomena of everyday life? Could a univer…

Alexander Vilenkin writes that perhaps the laws of physics could have existed even before the universe emerged from nothing. How could the laws of physics exist without the existence of the universe that they describe? What does "from nothing" mean?

Recently, I have learn't about the Gamows factor, and I have plotted it. Then I realized that the probability of Deuterium and tritium fusing at a temperature of 150 million kelvin when they collide, was about 0.00048. But, I know that the nuclear cross section for fusion is extremely small (about 1-1000 barns). But why is this so? I f the probability of fusion is 0.00048 when they collide, then …

Gravity is one of the biggest mysteries. It is the weakest of the 4 fundamental forces but we have no clue how it works. Einstein never was able to figure it out in his lifetime. There is evidence that gravity affects time, another very poorly understood phenomenon. Now the universe was once in a tiny singularity point before the Big Bang and then rapidly expanded. Something held the universe tog…