Scalar and vector potentials in electromagnetism. The scalar potential is potential energy per unit charge. For potential energy, use the potential-energy tag.

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Potential energy of a shell & point system

Consider the system of a point particle with charge $q$ and a spherical shell with uniform charge $Q$ and radius $R$ whose center is a distance $r > R$ away from the point particle. I'm trying to ...
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If Electric field is constant in a region, does it imply potential is also constant?

I am a bit confused about these concepts- when is electric field or electric potential constant so i would appreciate if anyone could brief me about these things as well. Here i am referring to ...
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How can current remain same when potential difference decreases?

According to Ohm's law, $$\text{potential difference} = \text{resistance}\times\text{current}$$ Also, current remains the same everywhere. Now when current passes through a bulb, the electric ...
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Spherical Conducting Shells, Potential

When we have a spherical conducting shell and charge on outer surface of the shell then the potential inside remains constant i.e, kQ/R (R=radius). But say the inner surface of the shell is charged ...
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grounding spherical shells

a Q1 charged spherical shell A with radius of a is inside a Q2 charged spherical shell B with radius b. now A is grounded. since no force is acting on Q1 all of them should be neutralized. and at the ...
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Charged conducting wire ring and Greens function

ρ(r) = q 2πa2 δ(r − a)δ(cos θ). If this is my charge distribution on a conducting wire ring. radius=a. I am attempting to show my electrostatic potential as an integral along the z-axis I started by ...
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Movement of charges in presence of electric potential difference

This might appear to be a bad question to some but i can't figure out the answer. While reading about an electric circuit, i found this on the web: Over the course of time, one could think of ...
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Method of image charges — Why is a *grounded* plate needed?

In the classic image charge problem of a charge $q$ above an infinite grounded plane, it is well known that the field lines essentially behave as though there were a negative charge behind it, and the ...
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Calculating potential differences: why integrate E- and not D-field?

So here's my problem. I was thinking about the following. Let's say we have a parallel plate capacitor, filled completely with a dielectric medium. If we want to find the potential difference between ...
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Reflectionless potentials in quantum mechanics

Scattering on potential $$V(x) = -\frac{(\hbar a)^2}{m}\text{sech}^2(ax)$$ with 1D equation of Schrodinger is famous problem. It is dealt with in Problem 2.48 of Griffiths book or online here. It is ...
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Is the electric field strength along an equipotential surface constant?

I'm trying to determine whether or not the electric field strength $|\vec{\mathcal{E}}|$ is constant everywhere on an equipotential surface. I know an equipotential surface is defined as $$ S = ...
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Maxwell's equations from differential forms

I found the following in some lecture notes I took some time ago: $$ \mathbf{E}=-\text{grad}\Phi-\partial_t\mathbf{A}\\ \mathbf{B}=\mathrm{rot}\mathbf{A} $$ These are the electromagnetic fields ...
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Representing an ISW wavefunction graphically [closed]

I'm trying to decode this diagram given to us for an assignment. The description of the diagram is 'Consider a particle of mass m confined to a 1-dimensional square well, given graphically by the ...
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1answer
57 views

How can we tell the potential from the orbit?

The orbit is $$r(θ) = a(1+\cos θ).$$ The orbit of the particle is in polar coordinates. How can we tell the potential $U(r)$ from this? $U(r)$ goes to zero at infinity.
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Potential of a long cylinder from infinity

I have a question about a long, effectively infinite, cylinder. The cylinder has a radius of $R_{1}$ and charge density $\rho.$ For $r>R_{1}$, the potential difference is $\Delta V_{ab} = ...
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1answer
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Particle in infinite square well with $\langle E \rangle = (1/4) E_1 + (3/4) E_4$

Suppose we have a particle in an infinite square well with $\langle E \rangle = (1/4) E_1 + (3/4) E_4$. I know that I can calculate the uncertainty in the particle's position by $\sqrt{\langle E^2 ...
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How to find the graph of electric field when the potential is given [closed]

Suppose the electric potential due to an electric field is given as $x^2-y^2$, then what will be the graph of the electric field? My attempt: Differentiating the potential partially with $x$ ...
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How should I think of a liquid in terms of interatomic potential and molecular speed?

A rather simple question for liquids specialists I guess but I have hard time finding information about this. Here is my problem. I understand the ideal gas theory and the Maxwell's speed ...
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How to estimate the ground state of a potential well when a confinement dimension is added

I have a finite harmonic potential where I trap an electron. The confinement length changes in size. Now, I'm interested in the ground state energy, so I have this 1D Poisson solver which gives me the ...
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1answer
50 views

Question about electric vector potential [closed]

n_0}\frac{Q\vec{e_r}}{r^2}=\frac{Q}{4\pi\epsilon_0}\frac{\vec{e_\theta}\times\vec{e_\phi}}{r^2}=\frac{Q\sin{\theta}}{4\pi\epsilon_0}[\frac{\vec{e_\theta}}{r}\times\frac{\vec{e_\phi}}{r\sin{\theta}}]$$ ...
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1answer
34 views

Why potential at infinity is 0? (sphere of constant electrostatic potential)

Suppose I have a sphere of radius $R$ with potential $V_o$. Since the volume inside the sphere is bounded, then the lack of curvature of the potential (i.e. $\nabla^2\phi = 0$) gives a potential ...
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Electric Potential of Point Charge (sign problem)

This question has been asked before, but the answers didn't clarify the problem for me, so I thought I might ask again. It's really a simple question. Let's say we're calculating the electric ...
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2answers
35 views

Calculation of electric potential in Geiger-Müller tube [closed]

We are given a cylindrical rod with linear charge density $λ$, and a coaxial cylinder with linear charge density $-λ$, as shown in the picture. We are to show that the potential difference between ...
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2answers
89 views

Normalization of a wave function in quantum mechanics

A more simple question, so I am watching a quantum mechanics lecture on potentials of free particles and am doing the general solution of schrodinger's stationary equation for a free particle when I ...
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2answers
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Equipotential surface paradox

Consider a point charge +q as shown below. Now consider a equipotential surface and two points in it A and B. now the potential at A is equal to potential at B. If we now integrate (E.ds) from A to ...
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Perturbation theory for a particle in a weak potential

I have a basic question about quantum mechanics, maybe it has a basic answer. Take a free particle in a quartic potential, $L=\frac{1}{2}\dot{x}^2-\lambda x^4$ This is massless $\phi^4$ theory in ...
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70 views

How do integral representations of $\mathbf A$ and $\Phi$ satisfy Lorenz condition?

The following are the integral solutions of the potentials, obtained from the retarded potentials (by a Fourier transform): $$\mathbf A (\mathbf r) = \frac{\mu_0}{4\pi}\int_V \frac{\mathbf J (\mathbf ...
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A question relating to the Higgs boson scalar field

Just wondering. The potential for the Higgs boson is given by: $$ V(\varphi)=\lambda(\varphi^{2}-v^{2})^{2} $$ where $v≃$ 246 GeV is the vacuum expectation value required to explain mass in the ...
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1answer
106 views

Why doesn't $σ_xσ_p$ change with the width of the well in the infinite square well problem (intuition)?

I calculated that the product of the uncertainty in position $\sigma_x$ for the ground state of an infinite square well of width $L$ with the uncertainty in the momentum $\sigma_p$ for the same state, ...
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3answers
76 views

Doesn't any massive conductor look like “ground” to an AC supply?

I've been puzzling over this excellent answer to the perennial "Why don't I get shocked by a hot wire if I'm not grounded?" question. The orders of magnitude just don't seem right for two reasons: ...
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1answer
96 views

Method of image charges (semisphere on a metal)

I'm currently trying to study ahead for the upcoming semester since I'm on break and I'm stuck on the method of image charges. I've tried watching some youtube videos on that topic and I thought I ...
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Phase shift calculation in quantum scattering for potential $V=a/r^2 $. Neumann function missing

I'm tasked of finding the phase shifts for scattering from a potential of the form $V=a/r^2$. My thinking is as follows. For this specific potential I can bring the differential equation to the form: ...
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91 views

Does the kinetic energy change depending on the direction of the velocity? [closed]

The kinetic energy is calculated with the following formula: $$E_k = \frac 12 mv^2$$ Does $v$ represent the value of the velocity? I mean, if you have a specific direction of the velocity is the ...
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24 views

Relation between gravitational field and gravitational potential

gravitational field is the negative differential of gravitational potential . now gravitational potential due to a particle at a distance r is -Gm/r where m is the mass of the particle . If i take the ...
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2answers
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Electric Potential from separating charges [closed]

Say there are 2 charges, one of charge C, and the other with a charge of -2C. C=1.5*10^-6 C. Initially, they are right next to each other. I pull them apart to a distance of 15 cm. So I can use the ...
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External and internal multipole expansion for axisymmetric potential - the region of convergence

Say, we have a system of electrodes exhibiting symmetry around a certain axis. We know the explicit expression for the potential on the axis $\phi (z)$. We want to find the potential for any point in ...
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1answer
79 views

Gravitational potential energy lost by an object falling on the earth [closed]

I am stuck on this simple question: g is the strength of the gravitational field at the surface of the Earth; R is the radius of the Earth. Show an equation describing the potential energy ...
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1answer
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Static pressure inside a planet made of a fluid

How can we find the static pressure at a distance r from center of the the planet made of liquid of constant density d. My attempt: First I tried to find the total gravitation force due to a sphere ...
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Does the material of a charged sphere affect electric potential?

Suppose we have two solid spheres, both with an equal total charge $+Q$ and equal radius, and the potential being zero infinitely far away. We know that a uniformly charged sphere can be treated as a ...
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The time evolution in Dirac delta potential [closed]

We know that the dirac delta potential has exactly one bound state. If the potential strength suddenly changes a value, the bound state should evolve to the new bound state, how to describe the time ...
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What exactly is potential difference? What are the factors that effect it?

I am asking this question because at first I thought that this concept was pretty clear to me, but it is not. So, my first question: Is potential difference only a property of an electric field? If ...
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1answer
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$P=V^2/R$ confusion

I am confused on how to apply the formula $P=\frac{V^2}{R}$ If I am given a bulb say with power 60W and it is connected to a supply of 120V. Then the resistance of the bulb is 240$\Omega$ but if ...
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Quadrupole configuration

The general solution to the 2D Laplace equation, $\nabla^2 \psi = 0$ is \begin{align} \psi(r,\theta) = P_0 \ln r + \sum_{k = 1}^\infty \dfrac{Q_k \cos(k\theta)+R_k\sin(k\theta)}{r^k} \end{align} The ...
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electric potential and other potentials

We know that without potential difference no electric current can flow.If two conductors carrying positive and negative charge respectively then the first one will have positive and the rest one will ...
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How does commutation between the hamiltonian and angular momentum operator (squared) imply conservation of Angular momentum?

So we are looking at central potentials in QM; The lecturer poses the question, when is $\textbf{L}$ conserved? He then considers the commutator of $\hat{H}$ and $\hat{L^2}$. We have; ...
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Will there be a potential difference between two conductors if there is same charge between them but the magnitude of charge is different?

By same charge I mean that same nature of charge i.e " Both positive or Both negative " . To be more specific consider two plates both of the plates are held face to face close to each other much like ...
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Can charge flow to a neutral body?

If an electrically positive object is kept with a neutral object, in which direction will charge flow? Will charge flow from positive to neutral until both have equal charges, or will nothing happen ...
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161 views

Electric Potential due to Sphere when cavity is at arbitrary position [closed]

While doing practice question, I came across a question... A solid sphere of radius a has a cavity of radius b which has a uniformly charge distributed with density $-\rho$ and the remaining part ...
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1answer
68 views

Physical meaning of multipole moment

Is there a physical interpretation for multipole moments? For a quantity governed by the Laplace equation ($\nabla^2 \omega = 0$), I understand that the general solution is given by the multipole ...
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1answer
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Gravity well and constant total energy in circular orbit [closed]

According to this question, the total energy of an object in a circular orbit in a $1/r^2$ potential does not depend on the radius of the orbit. However, if you look at "circular orbits" in a gravity ...