Potential Definition and 1000 Threads

In this image of Introduction to Electrodynamics by Griffiths . we have calculated the vector potential as ##\mathbf A = \frac{\mu_0 ~n~I}{2}s \hat{\phi}##. I tried taking its curl but didn't get ##\mathbf B = \mu_0~n~I \hat{z}##. In this thread, I have calculated it like this ...

Goldstein, the oracle of classical mechanics, says: But Morin also reliably tells me that These two definitions contradict in their treatment of external conservative forces. Morin only counts the action of internal conservative forces in the definition of the potential energy of the...

Article being reviewed here: https://theconversation.com/we-found-and-tested-47-old-drugs-that-might-treat-the-coronavirus-results-show-promising-leads-and-a-whole-new-way-to-fight-covid-19-136789 Journal article: https://www.nature.com/articles/s41586-020-2286-9 This is not anything we can use...

I know how to solve this problem when the energy at ground state is zero but I don't know how to deal with 1st excited state energy as zero. According to me since the potential energy is zero therefore the kinetic energy must be 13.6eV according to conservation of energy. I also know that the...

Is emf the work done to move a positive charge from LOWER potential to HIGHER potential to maintain the potential difference or else the charges move from higher potential to lower potential and will reach a point where the potential is the same between the two points and the charge will stop...

When you ground something in electrostatics, the potential of that body becomes the potential of the Earth once equilibrium has been reached. In this context, it is usually taken that the Earth is at 0V. There are two possibilities for this. Either the constant of integration is chosen such that...

a. This solution is i can consider the charge Q as a point charge and the electric potential at a distance r is ## V = Q/(4πεοr)## b. This is where the confusion starts again when r2>r>r1, my answer ## V = ρ*4*π(r^3 - r_1^3)/(3*4πεοr) \\ V = ρ*(r^3-r_1^3)/3εοr; ## I know i am making some...

I was thinking, what would be the consequence if we wouldn't adopt the ro in the infinite, and i conclude that it would just irritate the accounts, with one constant more, am i right? Once what matter is the diference between the U, and no the U infact.

If we have a conservative vector field, then we can describe it as ##\textbf{F}=\nabla\phi## where ##\phi## is some potential. This here is the derivation of Newtons law of gravity: Where ##\nabla u## is the gravitational potential. If we were to ignore it as a gravitational field, why is it...

I have not clear how to solve this problem. Here it is my attempt at a solution: Let the charge at ##-a## be the number one and the one at ##+a## the number two. the potential energy of the punctual charge ##-Q## due to each charge +Q will be then ##E_{pi}=-k \frac{Q^2}{r_i}##, whit ##r_i## the...

This is just a representative diagram to visualize Surely a very tough one for me to solve. The number of nickel atoms are not mentioned. if the number of decays are ##3.78∗10^8## and with each decay depositing 100keV. The total energy deposited is ##100keV∗3.78∗10^8=6.048∗10^6## I have to...

https://www.mytutor.co.uk/answers/11559/A-Level/Physics/What-is-gravitational-potential-energy-Why-is-it-negative/ But a parallel plate capacitor is oppositely charged, so the plates attract. With the same logic don't they store negative energy and wouldn't you get the wrong answer from a...

Hello there. I want to understand the mathematical idea behind boundaries that we write for a potential well. Why we use equally greater and smaller than let's say x between -4a and -2a but we only write x is less than -4a ? How to approach this idea with convergence theorem or Hilbert space...

My attempt, pictorially it looks like I am confused with the questions (a). Does the positron emerge from the field at x =0? There is no potential at x=0, so the positron will continue with the same speed hence its motion is not reversed. For the (b). The maximum volt is 200V, if i apply the...

This is my attempt the system The 1 is the initial configuration where the 3 electron is at infinity. The 2 is the final configuration where the 3 electron is midway.U1 is the potential energy between e1 and e2 U1 = (q1*q2)/(4*π*ε0 * (0.02)^2); // q1, q2 charge of electrons K1 =...

I do not have the solutions to this problem so I'm wondering if my attempt is correct. My attempt at solution: We have two surfaces which we can calculate the area of. I think we can use gauss law to find the electric field and then integrate the E-field to find the electric potential. So for...

Why aren't the right handed Weyl spinors included?

I am trying to calculate the interaction energy of two interpenetrating spheres of uniform charge density. Here is my work: First I want to calculate the electric potential of one sphere as following; $$\Phi(\mathbf{r})=\frac{1}{4 \pi \epsilon_{0}} \int...

Hello, I have answered the question below but would like some advice on whether I can improve my answer or if anyone is able to check whether I have made any mistakes ? i. 1 V = 1eV in a 1:1 relationship, therefore; 6.5 TeV = 6.5 TV = 6.5 *10^12V ii. E=W W=V * Q Q=number of particles * charge...

I read in some articles that the force in optical tweezers can be written as: F=kx, with no minus because the force will increase as the distance increased and the particle moves to the source..., This I can understand, but what I can not understand if I make integral (it is conservative force)...

In Sommerfeld’s Lectures on Theoretical Physics, Vol II, Chapter 2, Section 6, Page 43 we derive an expression for the equilibrium of liquids as $$ grad ~p = \mathbf F$$ Where ##p## is the pressure and ##F## is the exertnal force. Then he writes, [ The equation above ]includes a very remarkable...

But yet again my text says that option 4 is correct.

a.) The potential is a delta function, so ##V \left( r \right) = \frac {\hbar^2} {2\mu} \gamma \delta \left(r-a \right)##, therefore ##V \left( r \right) = \frac {\hbar^2} {2\mu} \gamma ## at ##r=a##, and ##V \left( r \right) = 0## otherwise. I've tried a few different approaches: 1.) In...

Summary:: If the conductor is having a cavity and is provided with some charge, with the cavity too having some charge then how the potential will be affected on the outer surface of the conductor. The center of cavity and the center of hollow sphere does not coincide. As if their centers do...

In quantum mechanics in books authors discuss only cases ##E<V_0## and ##E>V_0##, where ##E## is energy of the particle and ##V_0## is height of the barrier. Why not ##E=V_0##? In that case for ##x<0## \psi_1(x)=Ae^{ikx}+Be^{-ikx} and for ##x\geq 0## \psi_2(x)=Cx+D and then from...

I tried to attempt it by applying KVL to both the loops. I tried to find a possible charge distribution for the capacitors. I guess this is right. On solving I get: from what I know potential difference between M and N is Q1/C2 but the solution is given as: Where am I wrong?

The book's procedure for the "shooting method" The point of this program is to compute a wave function and to try and home in on the ground eigenvalue energy, which i should expect pi^2 / 8 = 1.2337... This is my program (written in python) import matplotlib.pyplot as plt import numpy as...

I’m trying to learn about simple circuits but I have a few questions because I don’t fully understand what’s going on . 1. If the reason current flows when a wire is connected to the ends of a battery is due to a potential difference across a battery , why can’t the current just flow through...

The problem of my question is the b part below: I know that the potential energy is just the gravitational potential energy, which is mgh(𝜃) = mg[(R+b/2)cos𝜃 +R𝜃sin𝜃], derived from the geometry. The equilibrium point is at 𝜃=0 and the system is a stable equilibrium for R>b/2. However, I have no...

I've been trying this problem for a long time. By operating the lower part of the logarithm and clapping the real and imaginary part of the logarithm, I have come to the conclusion that the correct lines must be those in which it is true that: $ d \ frac {(x ^ 2 + y ^ 2-a ^ 2) ^ 2 + 4y ^ 2a ^...

U=-∫F*v*dt= -∫(m*g/3)*cos(ω*t) dt = -(m*g/3 )* (v/ω )* sin(ω*t) except that according to the official solution, I should be getting positive sign instead of negative. Am I doing something wrong?

In some other thread someone mentioned that a 3D cubic potential well always has a ground state that is a bound state, but a spherical well doesn't necessarily have if it's too shallow. I calculated some results for 3d cubes, spheres and surfaces of form ##x^{2n}+y^{2n}+z^{2n}=r^{2n}##, which...

How do we verify whether a condition on the magnetic vector potential A constitutes a possible gauge choice ? Specifically, could a relation in the form A x F(r,t) be a gauge , where F is an arbitrary vector field?

Hi everyone, I have abit of trouble with this question. Please help! Given charges +q, +2q, −5q and +2q are placed at the four corners ABCD of a square of side a, taken in cylic order from the bottom left corner. Find the electric field E and the potential V at the centre and verify that they...

Hi, I've been stuck for a long time with this exercise. I am not able to calculate the potential vector, since I do not know very well how to pose the itegral, or how to decompose the disk to facilitate the resolution of the problem. I know that because the potential vector must be parallel to...

There is the equation: μ= Eu +Eg/2 +3/4kβTln(mu/mc) Eg is the band gap, but I don't understand what Eu stands for and how we can calculate it? Could it be the valence band?

Generally potential energies are associated with a system of two bodies. If more than two bodies are involved the total can be determined by summing the contributions pairwise. It would appear as though in any system, the potential energies are all internal to the system. However in classical...

I was wondering if there is a way to deduce the solution of the potential of a charge outside a sphere given by the image method, though Green functions. Because of a Dirichlet condition (GD(R,r')=0), I know that a solution can be written as GD=Go+L, where ∇2L=0. But in order to approach this...

Hello folks, A bit stumped with the following question: Consider a potential well with an infinite wall at x=o and a finite wall at x=a. The height at x=a is such that U0=2E1' where E1' is the energy of the particle's n=1 state in this semi-infinite well. How can one show that E1' is lower...

Hello, I understand that the action potential represents a potential difference variation (depolarization) of the voltage across a cell membrane. This concept is generally presented in the context of nerve cells (neurons) as the change in potential across the axon membrane. What about the...

We have a retarded magnetic vector potential ##\mathbf{A}(\mathbf{r},t) = \dfrac{\mu_0}{4\pi} \int \dfrac{\mathbf{J}(\mathbf{r}',t_r)}{|\mathbf{r}-\mathbf{r}'|} \mathrm{d}^3 \mathbf{r}'## And its curl, ##\mathbf{B}(\mathbf{r}, t) = \frac{\mu_0}{4 \pi} \int \left[\frac{\mathbf{J}(\mathbf{r}'...

Hi, I am confused by a point which should be relatively simple. When we consider classical motion of a particle in a central field U(r), we write the total energy E = T + U, where T is the kinetic energy. The kinetic energy contains initially r, r' and φ' (where ' denotes the time derivative)...

I've seen this figure kicking around, and just wanted to check that I'm not going mad. ##r_{0}## is supposed to be the Bohr radius of the first electron. I don't think this is quite right, since at ##r_{0}## the potential energy is about ##-27eV## or something, so I think they've actually...

I'm considering the arrangement shown below. Let the positive charge be ##q##, and the negative be ##-q##. To derive the potential energy of this configuration, one usually adds the potential energies of both of the charges in the external field, taking the zero volts equipotential of the...

This is in python: #ELECTRIC POTENTIAL from mpl_toolkits.mplot3d import Axes3D from matplotlib import cm import numpy as np import matplotlib.pyplot as plt dx = 0.1 dy = 0.1 xrange=np.arange(-1,1,dx) yrange=np.arange(-1,1,dy) X,Y = np.meshgrid(xrange, yrange) max_dV = 10e-5 blockRadius = 3...

U(x) = - ∫Fdx = - (1/2)kx^2. T = (1/2)m(x')^2. E = (1/2)[m(x')^2 - kx^2]. We could write out the Lagrangian here, but the chapter this comes from (Taylor's Classical Mechanics 13.6) indicates we should probably write the Hamiltonian, H = T + U. As far as I can tell, this doesn't tell me a...

a) From X -Y. The work done on the positive charge is negative as the displacement is in the negative y-direction i.e. It is a positive charge moving in parallel to a negative E-field: W= F*(-s) = (+)(-) = - b) Y-Z. The work done is 0. The E-field in the x-direction is 0 as they cancel due to...

Summary:: Linear Quantum harmonic oscillator and expectation value of the potential energy (time dependent) Hello, I have attached a picture of the full question, but I am stuck on part b). I have found the expectation value of the <momentum> and the <total energy> However I am struggling with...

https://phys.org/news/2020-02-green-technology-electricity-thin-air.html I am not competent to judge this (what seems very edgy to me) article. Basically it says: a ten micron thick protein layer with Geobacter on the surface and protein nanowires arranged in a mesh, when exposed to...

First I calculated the electric fields outside of the sphere in terms of the total charge Q. total charge Q: Q = aπR^4 electric field outside: (r>R) E(r) = (1/4πε) Q/r^2 (ε is the vacuum permittivity) electric potential...