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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If the potential drops across a resistor (=$V_d$) then shouldn't the potential difference be the $\epsilon-V_d$?

Consider the following circuit: Suppose a current $I$ travels in both the branches, then as the current $I$ passes through the $60$ ohm resistor, there will be a drop in the potential of $60I$. ...
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I don't get the idea of potential in a capacitor [closed]

First off, what is meant by the potential of the conductors? Also potential difference between the two conductors is a function of distance from either right? Then why does it have an exact value. For ...
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1answer
40 views

Can an electromagnetic potential be in two gauges at once?

I have a plane wave vector potential found using the free field form of Maxwell's equations and the Lorentz gauge: $\vec{A}(\vec{r},t) = \vec{A}_0 e^{i(\vec{k}\cdot\vec{r}-\omega t)}$ If I take the ...
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Relationship Gravitational Potential and the Tangential Velocity of a Satellite

So gravitational potential is given by $V(r)={\frac{GM}{r}}$ and the tangential velocity of a satellite is the square root of $V$, i.e. $\sqrt V$. So how do these two relate, if at all?
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Electric potential inside a shell

Inside a shell, electric field is zero. Then does it have a constant electric potential inside the shell? If $V=\dfrac Ed$, then since field is zero, potential should also have been zero. Please ...
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1answer
32 views

Motion of an electric charge within an electric field with two electric charges

Assume that air resistance and gravity are negligible and the only significant force acting in the scenario is the electric force. There are two electric charges, both with an equal and positive ...
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1answer
35 views

Relation between potential difference and electric field

I was reading an article about resistivity when I faced this equation: $$V_P-V_O=\int_P^O E.dr$$ The equation is in one dimension and $P$ and $O$ are points on the $x$ axis. The Electric field is ...
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Potential Energy of Point Charges in a Square [closed]

So, an AP Prep book for the Physics 2 test has the following problem: My reasoning is as follows: The total potential energy = the sum of the PE of each of the 4 charges Which will equal 4x the PE ...
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21 views

Since a dipole has some potential energy,it should be able to do some work !? What is it?

We say a dipole has potential energy.What work can a dipole do ?.For eg : A ball on a shelf has a PE because it has the potential to fall down and do some work on the ground if shelf wasnt there.What ...
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How is the curl of the electric field possible?

Taking the curl of the electric field must be possible, because Faraday's law involves it: $$\nabla \times \mathbf{E} = - \partial \mathbf{B} / \partial t$$ But I've just looked on Wikipedia, where it ...
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What does earthing do in electrostatics?

What does earthing actually do in electrostatics? As far as i know, it simply sets the potential of the object that is earthed to zero. To explain my question further with an example, consider this ...
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How to find the minimum value of potential in QM?

In MIT problem sets I followed a solution of an exercise which focuses on odd-parity energy eigenstates in finite square well. The point of problem is how to know or find the minimal value of ...
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179 views

Relation between Electric field and potential

I am unable to understand from this - sign comes. Which step I have done wrong?
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1answer
48 views

What role does the center of mass play in this situation? (electric potential)

Four masses $10\ \mathrm{g}$ each are tied together by $10\ \mathrm{cm}$ strings to make a square as shown. Two of the masses carry a charge of $2\ \mathrm{\mu C}$. The string between the two charged ...
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182 views

Scalar and Vector Potential

I am a physics undergraduate student currently studying electromagnetics. I have previously studied electrostatics and magnetostatics yet the concept of scalar potential, $V$ and the vector potential, ...
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14 views

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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2answers
81 views

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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1answer
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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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44 views

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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2answers
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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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162 views

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
61 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} = \int_{a}^{...
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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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2answers
32 views

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 $x$ and ...
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1answer
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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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31 views

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]

$$\vec{E}=\frac{1}{4\pi\epsilon_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{\...
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1answer
38 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 $\phi(...
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2answers
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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
37 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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90 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
58 views

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 B ...
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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 0+...
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1answer
72 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
107 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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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
98 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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1answer
96 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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1answer
74 views

Relation between gravitational field and gravitational potential

The gravitational field is the negative differential of the gravitational potential. Now the gravitational potential due to a particle at a distance $r$ is $-Gm/r$ where $m$ is the mass of the ...
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2answers
61 views

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 ...