All Questions

0
votes
0answers
18 views

Calculating vector potential inside a Cylindrical shell carrying surface current in z direction [on hold]

I am trying to calculate the vector potential inside a cylindrical shell that carries constant surface current in the z-direction. We know that the field inside the cylinder is zero so I can't use, $$...
0
votes
1answer
51 views

Finite potential well; finding the energy “in a limit”

I've come a across the following variant of the finite-potential-well-problem in quantum mechanics: The potential is given by $V(x)=0$ for $|x| \geq a/2$ and $V(x)=-V_0/a$ for $-a/2<x<a/2$ where ...
0
votes
0answers
22 views

What is the electric field between two coaxial conducting cylinders when a charged sphere is placed within the inner cylinder?

A long cylindrical capacitor of length $l$ consists of an outer conductor of radius $a$ and an inner conductor of radius $b$, where $l>>a$. The outer conductor is earthed, and the inner ...
2
votes
3answers
104 views

Understanding bound states in quantum mechanics

Suppose I have this potential: $$ \ V(x)= \left\{ \begin{array}{ll} +\infty & x < 0 \\ -V_0 & 0\leq x\leq a\\ 0 & x>a \\ \end{array} \right. \ $$ for $a>0$...
-1
votes
3answers
63 views

How can you use the potential to find the electric field? [closed]

Lets say we have the above system of point charges. We were asked to find the electric field at the centre. Superposition of electric fields gives the right answer, but how can we do it by ...
0
votes
0answers
32 views

Problems in calculating potential of uniformly charged infinite plane or wire

From $\int_Vd^3x \rho(\vec x)\mathrel{\mathop{=}\limits^!}Q_V$ and by use of Dirac's delta distribution one finds that the charge density for the uniformly charged infinite plane is $\sigma\cdot\delta(...
0
votes
2answers
42 views

Direction of gravitational field given equipotential lines

I've attached the question as an image below as it's a graphical question. It simply states: "The diagram shows equipotential lines near a group of asteroids. Which arrow shows the direction of the ...
0
votes
1answer
40 views

Electric potential and voltage

A capacitor is connected to a battery with constant voltage. If you approach one of the plate to the other, what happens to electric potential? I already have an answer to this question but it's ...
0
votes
1answer
51 views

Schrödinger equation in unknown potential well [closed]

Have a question from my class which I'm struggling with. We have a particle $m$ with wavefunction $φ=Ax \exp(-ax)$ when $x≥0$, and $φ=0$ otherwise. We are asked to show that the double derivative $...
1
vote
1answer
47 views

Calculating electric potential — denominator going to zero [closed]

Calculate the potential inside a uniformly charged solid sphere of radius $R$ and total charge $q$. My attempt: There are several ways to solve this problem but I'm curious as to whether this ...
-1
votes
1answer
56 views

Find its radius and location of its Centre [closed]

Two fixed charges $-2Q$ and $Q$ are located at the points with coordinates $(-3a,0)$ and $(+3a,0)$ respectively in the x-y plane. Show that all the points in the x-y plane where the electric potential ...
0
votes
2answers
52 views

How Do I Calculate the Potential of System?

I was doing my homework when I came across this question: Three equal point charges, each with charge $1.40 \, \rm\mu C$ , are placed at the vertices of an equilateral triangle whose sides are of ...
-2
votes
1answer
100 views

How do I solve this Laplace equation? [closed]

I'm stuck with the following problem: Suppose we have an infinitely long box whose cross-section has a rectangular shape of dimensions 2×3. Take the four last digits of your student ID number as a ...
1
vote
0answers
60 views

electric potential of electric dipole in 2D

I have the homework question as follows. What I did was first find that $$\phi = \frac{-\lambda}{2\pi\epsilon_0}(\ln(r_+)-\ln(r_-))=\frac{-\lambda}{2\pi\epsilon_0}\ln\left(\frac{r_+}{r_-}\right).$$ ...
1
vote
1answer
45 views

Problem based on Laplace and Poisson's Equations. How to find the charge from electric field and potential?

In the above problem, I have found out the potential and the electric field in the medium between the two conductors. From here, how can I calculate the approximate charge per plate?
3
votes
2answers
166 views

Energy measurement from position eigenstate

Given that the eigenstates of the position operator can be written as $\delta(x-x')$, and suppose we measure a particle in an infinite potential with walls at $x=0$ and $x=L$. I measure the particle ...
1
vote
0answers
80 views

1D Time independent Schrodinger eq. with limit

The one dimensional Schrodinger equation for an exponential potential $$-{\hbar^2\over 2m} \frac{d^2\psi}{dx^2}+-\alpha\frac{e^{-\vert x\vert\over\epsilon}}{2\epsilon}\psi=E\psi$$ I am interested ...
0
votes
1answer
40 views

Method of Images conundrum

My lecturer and I have found separately valid solutions to Poisson's equation in the region of interest for the following problem: Here is my interpretation of the boundary conditions: $$V(x,y,z \to ...
1
vote
2answers
38 views

Potential in open branch of a parallel circuit with grounding [closed]

If the switch is still open, what will the electric potential at Q be, i.e. negative, positive or zero? Is there a potential difference across the grounded point and point Q, or R3, even though the ...
2
votes
1answer
88 views

Particle in a box plus step (ground state)

I am trying to come up with a QM problem that: Can be solved analytically Contains a potential that is a sum of some analytically solvable potential and another contribution: $V'=V_0 + V$ Is then ...
6
votes
0answers
162 views

Sphere half-submerged on a dielectric

This is a classic problem in electrostatics with a twist, so I thought it could be useful for others here. I did have a problem with the integration at the end, but on general I think the idea can ...
2
votes
1answer
108 views

Energy formula for finite potential well [closed]

The energy formula for infinite potential well is $$E=\frac{n^2h^2}{8ma^2},$$where $m$ is the mass of the particle, $a$ is the width of the well but in the case of finite potential well, I actually ...
0
votes
2answers
53 views

Confusion about Change in Integration Variable [closed]

I'm working through example 3.2 of Zangwill's Modern Electrodynamics and have come across a change in integration variables that I just can't seem to get. The example has two different change ...
4
votes
0answers
173 views

Understanding conformal mapping in electrostatics

I'm trying to understand the use of conformal mapping to solve problems in electrostatics. To better understand the idea, I'm trying to learn how to solve this example (but you can propose any other ...
1
vote
2answers
103 views

Calculation of Gravitational Potential at the centre of the cube [closed]

I came across this problem in a test and have been able to come up with a solution however I am unsure if it is correct. I started by building a cube of twice the initial dimensions to bring point P ...
2
votes
3answers
94 views

Does gravity get stronger when you climb a mountain?

As stated in the question title, what happens to the strength of the gravitational field (or equivalently, your weight) as you climb a hill or mountain? Would a weighing scale show that you were ...
1
vote
0answers
46 views

Determining Electric Potential due to a line of nonuniform charge density [closed]

A rod of length $L$ lies along the x axis with its left end at the origin. It has a non uniform charge density $\lambda = \alpha x$ where $\alpha$ is a positive constant. Calculate the electric ...
1
vote
1answer
90 views

Can electric potential be discontinuous?

I am studying the following problem, which is 9.11 of "Modern Electrodynamics" by Zangwill. The idea is that you have a wire attached to a perfectly conducting sphere (radius $a$) buried into the ...
1
vote
3answers
194 views

How do we deduce the vector potential for a constant magnetic field?

How do we show that for a constant magnetic field $\vec B = const$, the vector potential is $\vec A = \frac12 \vec r \times \vec B$?
-2
votes
1answer
60 views

Given the parameters of the electrostatics problem, is this integral possible to evaluate analytically? [closed]

A cone with apex at the origin has a height $h$ and a top radius $h$, a uniform charge density with no charge on the top face. I need to find the potential $V$ at a position $z$ on the cone's axis ...
3
votes
1answer
79 views

Power series solution for a shifted spherical harmonic oscillator

I'm trying to solve the Schrodinger equation for a radial Harmonic oscillator whos equilibrium point has been shifted away from the origin, i.e. $V(r) = V_0(r-1)^2$. The standard approach is to make ...
1
vote
1answer
218 views

Fourier tranform of Coulomb-like potential $1/|r-r'|$

I've found that Fourier transform of Coulomb potential $V= q/r$ is $F[V]= 4\pi q/k^2$. Now I need to calculate fourier transform of function $1/|r-r'|$. And I exactly don't know how to operate with ...
2
votes
1answer
78 views

Electric potential - Batygin, Toptygin book

I found in Batygin and Toptygin problems in electrodynamics a particular problem: Density of charge is $$\rho = \rho_{0}\cos{\alpha x} \cos{\beta y} \cos{\gamma z}$$ in whole space. Find electric ...
0
votes
1answer
42 views

Introducing stream function with given velocity equation

Bit information about the problem We are dealing with the slide coating process - where basically a polymer is being put onto a slot, which is moving in the $x$-direction with velocity $v_0$. The ...
0
votes
1answer
197 views

Electric Potential of Non-Uniformly Charged Infinite Plane

A little background: I was tutoring an undergrad upperclassman when we came to a problem that he had been assigned which I couldn't make heads or tails of - at least in terms of what was being ...
0
votes
0answers
16 views

Finite potential well without using even/odd symmetry

This is a follow up question to this question. I tried using the hint in the accepted answer to get the tangent equations but when I divide the equations at $x=-a$, I get: $$\begin{align} \kappa &...
1
vote
1answer
429 views

Electric field from a quadrupole

In the following problem, I have already solved for the value of the potential, and I would like to tackle the extra exercise, which asks for the electric field of a point quadrupole: At every ...
0
votes
1answer
44 views

What is the ratio of the turns in the transformer when it is impedance-matching?

I study physics on my own. There is a question in my textbook: A transformer may be used to provide maximum power transfer between two AC circuits that have diffirent impedances $Z_{1}$ and $Z_{2}...
1
vote
2answers
262 views

Expression for electric potential around an electric dipole in Cartesian coordinates

I'm trying to find the equation of the electric potential of a electric dipole in Cartesian coordinates. The equation should take the form of something looks like this: $$z = x\exp(-x^2-y^2)$$ ...
1
vote
2answers
796 views

How to calculate the dipole potential in spherical coordinates

I want to calculate the dipole potential in spherical coordinates. I know that the potential can be calculated with $$ \phi = - \int \mathbf E \cdot\mathrm d\mathbf r,$$ but I don't know the electric ...
1
vote
2answers
363 views

Earthing the plates (one or both) of a parallel plate capacitor — How can one make use of the fact that the potential of the plate is zero? [closed]

Please take a look at this question : In the figure, plate $A$ has $100 \times 10^{-6}$ C charge, while plate $B$ has $60 \times 10^{-6}$ C charge. Find the values of $q_{1}, q_{2}, q_{3}, q_{...
0
votes
1answer
99 views

$\mathbf{g}(\mathbf{r})=-\boldsymbol{\nabla}\psi(\mathbf r)$: searching for a minus sign error

Consider the following figure where $R=\sqrt{(x-x')^2+(y-y')^2+(z-z')^2}=|\mathbf{r}-\mathbf{r}'|$ is the module of the $\mathbf{R}$ vector depends not only on the location of the $P$ point but also ...
1
vote
0answers
153 views

Ground state wavefunction of Double-well potential

How does the ground state wavefunction ($\psi_0$) will look like for a double-well potential if the barrier height is lower than the ground state energy? It looks like, if the barrier height is lower ...
2
votes
0answers
72 views

Multipole expansions: test on a function $\zeta=\zeta(t)$

Considering the potential $\psi(r)$ of a sphere of mass $M$ with density $\rho(\mathbf r')$, connected by a small volume positioned in the $P'$ point as shown in the figure: The $\psi(r)$ is: $$\...
1
vote
1answer
82 views

Parallel voltage source concept

I am having doubt understanding this: If two voltage sources V1 and V2 are connected in parallel with different voltages like 2v and 3v is it possible or the scenario is wrong. An example is this ...
0
votes
2answers
355 views

Electrostatic Potential of a Hollow sphere [closed]

When calculating the electric potential inside the hollow portion why are we adding all the electric potentials of the previous cases??? Instead when calculating for other cases i.e the cases before ...
-1
votes
1answer
44 views

Obtaining Components of the Vector Potential [closed]

I am given $\boldsymbol A(r,\phi) = \frac{i}{e}a(r)U(\phi)\nabla U^{\dagger}(\phi)$, where $U(\phi)=e^{in\phi}$. I want to obtain the magnetic field $\boldsymbol B$ from this vector potential, so ...
2
votes
0answers
90 views

Which test function (under variational method of approximation) should be used for a linear potential?

There is this problem, it is not for evaluation, I mean, it is not homework. There is a 3-dimension potential $V(r)=C . r$, where $r$ is the radial coordinate and $C$ is a real constant (I think it ...
1
vote
0answers
113 views

Energy values for particle in a box with strange potential

I am trying to analyze a particle in a box with a rather strange potential inside the box: $V(x) \propto x^{3/2}$ I've tried using the WKB approximation, but I get some strange results and I don't ...
1
vote
0answers
38 views

Question about general solution to Poisson's Equation [closed]

I've never taken a course on solving partial differential equations before, but I was wondering if my understanding on how to solve these types of questions is correct. Let's say I have an equation of ...