1. ### Electric potential inside a hollow sphere with non-uniform charge

I tried to find the charge distribution using the given potential but couldn't produce the correct result. Also, Gauss's Law doesn't help, as the electric flux is 0 but we don't have any symmetry. Can someone please shine a light on this? Thanks in advance..
2. ### I Sign of potential term in Lagrangian mechanics

I have heard many times that it does not matter where you put the zero to calculate the potential energy and then ##L=T-V##. But mostly what we are doing is taking potential energy negative like in an atom for electron or a mass in gravitational field and then effectively adding it to kinetic...
3. ### I Matrix Notation for potential in Schrodinger Equation

I'm working on the time-dependent Schrodinger equation, and come across something I don't understand regarding notation, which is not specific to TDSE but the Schrodinger formalism in general. Let's say we have a non-trivial potential. There is a stage in the development of the TDSE where we...
4. ### Calculating gravitational potential due to a uniform ring tilted at an angle

I tried finding the potential due to a small element dM of the ring lets say dV, the summation of dV for all the dM's of the ring will give the potential at the point P, but since every element dM of the ring is at a different distance from the point P I am unable to come up with a differential...
5. ### I How do you normalize this wave function?

I have a basic question in elementary quantum mechanics: Consider the Hamiltonian $$H = -\frac{\hbar^2}{2m}\partial^2_x - V_0 \delta(x),$$ where ##\delta(x)## is the Dirac function. The eigen wave functions can have an odd or even parity under inversion. Amongst the even-parity wave functions...
6. ### Power of a particle on a wave

I've marked the right answers. They mainly indicate at power carried by the particles being zero, and here is my doubt- why should it be zero? Shouldn't it have some definite value? I do understand that the kinetic energy is max at the y=0 and potential energy is max at y=A, but I don't know...
7. ### Origin of potentials

I think the right choice is c. I'll pass on my reasoning to you: We can think that if the formula of the potential is V(r)=\dfrac{kq}{r} If r tends to infinity, then V(r)=0. But the correct answer is d).
8. ### Potential at a point

I thought the right choice was d). But when it comes to the solutions, it is b) and I don't understand why. My reasoning would be: the potential at a point is the work that the electric field does to transport a charge from infinity to that point, so if the field is zero, it does no work and...
9. ### Electric field and electric potential exercise

a) \vec{F}=\vec{E}\cdot q \phi =\oint \vec{E}d\vec{S}=\oint \vec{E}d\vec{S}=\underbrace{\oint \vec{E}d\vec{S}}_{\textrm{FACES } \perp}+\underbrace{\oint \vec{E}d\vec{S}}_{\textrm{FACES } \parallel}=0+\oint EdS\cdot \underbrace{\cos 0}_1= E2S \dfrac{Q_{enc}}{\varepsilon_0}=\phi \left...
10. ### Interaction energy of two interpenetrating spheres of uniform

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...
11. ### A Trapping stiffness of optical tweezers

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)...
12. ### S-wave phase shift for quantum mechanical scattering

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...
13. ### Finding the potential across capacitors in capacitor-only circuits

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?
14. ### B Chemical Potential μ in Solids

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?
15. ### Electric Potential

I found the potential at A, however I tried doing it with B but it says I have the wrong answer.
16. ### Determine the Electrical potential at a given point

A rod with a circular center in the middle (which causes the rod to change direction by 90 °) has an evenly distributed linear charge density 𝜆 of electrons along the entire rod. Determine the electrical potential of the red dot in the figure below which is at the center of the circular round...
17. ### I Electrical potential of a thin wire in an E field

Assume that an infinite metallic plate A lies in the xy-plane, and another infinite metallic plate B is parallel to A and at height z = h. The potential of plate A is 0, and the potential of plate B is constant and equal to V. So, there is a uniform electrostatic field E between plates A and B...
18. ### I Electrostatics: sign of the potential

The final result will only differ in its sign, but this is crucial. Having a positively, radially oriented electric field ##\textbf{E}##, I understand that the sign of the integral should be positive (## - (- A) = A##), but it is not! How and why is this the case? A line integral where the...
19. ### A The Laplacian of the potential q*exp(-r)/r

Hello, I have a problem where I'm supposed to calculate the charge distribution ρ. I need to calculate it by applying the Laplacian operator to the potential Θ. The potential is the function: q*exp(-αr)/r I found on the internet that for this type of potentials I cannot just apply the...
20. ### Python Visual Python Pendulum

Hello and thanks in advance for your help. For about a week now, I've been trying to write what should be a simple python program. The idea is first to write a program for a simple harmonic pendulum, then adapt it to a spring pendulum. However, in order to do this, I have to write the simple...
21. ### B Retarded and advanced potentials

"of the two types of solutions which the Maxwell equations yield for the wave equation, the retarded and advanced potentials, only the retarded field seems to have a physical meaning," let's start please with basic (and detailed as possible for the knowledgable layman! p.s-which equation is...
22. ### What happens when one of two cocentric spherical shells is grounded?

Hi! I need help with this problem. When the outer shell is grouded, its potential goes to zero, ##V_2=0## and so does it charge, right? ##-Q=0##. So the field would be the one produced by the inner shell ##E=\frac{Q}{4\pi\epsilon_0 R_1^2}##. When the inner shell is grounded, I think that...
23. ### I Morse Potenials Energy eigenvalues

I know the eigen value of energy in a Morse potential is Evib= ħωo(v+ 1/2) - ħωoxe(v+ 1/2)2 but is this the same for every Morse potential, given that the masses μ of the diatomic molecules are the same? The two potentials are these:
24. ### How to find the period of small oscillations given the potential?

I first found the equilibrium points taking the derivative of the potential. ##U'(x)=U_0 a\sin(ax)##, and the equilibrum is when the derivative is 0, so ##U_0 a\sin(ax)=0## so ##x=0## or ##x=\pi/a##. Taking the second derivative ##U''(x)=U_0a^2 \cos(ax)## I find that ##x=0## is a minimum point...
25. ### Why a DC power supply doesn't have a voltage with respect to ground?

I see that DC power supply have voltage between it's + & - and its 24V. However, there is no voltage with ground. I don't understand - if device's "point" has some potential, why doesn't it give some voltage with ground (which has ~0 potential) I tried this with phoenix contact...
26. ### Electric potential at the edge of a thin charged circular plate

My question might sound stupid to you but please clear my confusions. I'm taking an circular arc like element on the plate. That arc has a radius of 'r' (AB) and the radius is inclined at an angle 'θ' with OA (∠OAB). The area between arc of radius r and r+dr is dA. dA = 2θr.dr The charge on...
27. ### A position of stable equilibrium, and the period of small oscillations

I tried by taking the derivative of the potential to find the critic points and the I took the second derivative to find which of those points are minimum points. I found that the point is ##x=- a##. I don't understand how to calculate the period, since I haven't seen anything about the harmonic...
28. ### The potential between a cone and a plate

Homework Statement [/B] There is a conducting cone with angle α placed so that its vertex is normal to an electrically grounded plate, but electrically insulated from the plate and kept at a constant potential V. Find the potential V and the electric field in the region between the cone and the...
29. ### System of charges

Homework Statement Two charges, ##-q_1## and ##q_2## are fixed in the vacuum and separated by a distance ##a##. What should be the velocity ##v## of a particle with mass ##m## and charge ##q##, travelling from an infinitely far point along the line which unites ##q_1## and ##q_2## in order to...
30. ### Potential at center of sphere of radius R and charge -Q

Homework Statement What is the potential at the center of the sphere relative to infinity? The sphere is dielectric with uniform - charge on the surface of the sphere. Homework Equations ##k=\frac {1}{4\pi\epsilon_0}## ##V=\frac {KQ}{r}## The Attempt at a Solution If the distance r=0 it would...