Questions tagged [potential]

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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Scalar potential vector

I am trying to find the scalar potential, $\phi(\vec r)$, of a conservative vector field $\vec a(\vec r)$. I am integrating along a straight line from $\vec r_0$ to $\vec r$ which is parametrised by $\...
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What is gravitaional field $\Phi$ vs gravitational potential $U$

I am confused about my teachers notation. I have a set of problems about "gravitational potential $\Phi$." But is $\Phi$ normally written as $U$ is a lot of caseses? Is there a difference? Rant or ...
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Electric force and potential difference

When an electron moves from lower potential to higher potential and the work done by electric force is positive. Therefore we will conclude that whenever a negative charge moves from a lower ...
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Electrostatic potential due to a point charge

$$V=\frac{W}{q}=\frac{q}{4π\epsilon_0r}$$ however the above equation shows that equal distances from a point charge $q$ "the value of potential is same what is the meaning of the above sentence"
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About potentials with infinitely many bound states

Let's say I have two quantum systems. The first is described by the Hamiltonian $H_{1}=-\Delta+V_{1}$ and the second by $H_{2}=-\Delta+V_{2}$. If $H_{1}$ has an infinite number of bound states and $V_{...
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Hamiltonian for a system of 3 interacting particles and the meaning of potential

I'd like to discuss some physics basic. assume we have 3 particles $\{\vec{q_i},\vec{p_i}\}, \quad i=1,2,3$ whereas $\vec{q_i}$ is the position and $\vec{p_i}$ is the momentum. We also have a "pair-...
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The Schrodinger equation with strange potential

The particle of mass $m$ moves in potential $$V(x) = \dfrac{\alpha \left( \left( 2 \alpha +1 \right)x^2-a^2 \right)}{m \left( a^2 + x^2\right)^2},$$ and $\alpha > 1/4$. Find the energy and the ...
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Can we speak of an absolute voltage without a convention?

In most practical cases I have seen, voltage was regarded as a difference in electric potential, save the odd change of magnetic flux over time which, as a form of change, also conveys the notion of a ...
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Terminal potential difference of cell [closed]

I was given two cell X and Y of emfs 6V and 4V and internal resistance 2ohm and 8 ohm respectively connected in series with an external resistor of resistance 10 ohm and asked to find terminal ...
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4answers
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Potential inside a hollow sphere (spherical shell) given potential at surface

Suppose that we have a hollow sphere (spherical shell) whose surface is held at some constant potential V0. What is the potential inside the sphere? I had an argument with my physics professor over ...
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Energy spectrum for a step potential

Most of the books tend to give this explanation that for a bound physical system, the energy and momentum eigen values have discrete spectrum and otherwise, they have a continuous spectrum, which I ...
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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 ...
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Physics 2 electricity and magnetism [closed]

A total charge $+Q$ is uniformly distributed over thee volume of an insulating sphere ($\text{radius}=R$). On the other hand, a spherical conducting shell of radius $2R$ and thickness $t$ encloses the ...
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Quantum filter, potential barrier

I have been trying to teach myself quantum mechanics for quite a time now and I need help with a probably simple problem. We are looking at the Schrödinger equation of particles of mass $m$ in one ...
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Does a Static $E$-field Increase the Gauge Invariant Vector Potential Without Bound?

The gauge invariant formulation of Maxwell's Laws (7.13): Indicates that the transverse electric field is the time derivative of the transverse vector potential. This gauge invariant vector ...
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How can I find the volume charge distribution? [closed]

The electric potential in a certain region of space depends only on the $x-$coordinate as $V=-ax^3 + b$ ,where $a$ and $b$ are constants. The volume charge distribution of space is? I tried equating ...
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Laplace equation outside finite cylinder

I am trying to find a solution to Laplace's equation outside a finite cylinder of radius $a$ and height $h$ with the boundary condition that $u=\frac{c}{\rho}$. where $c$ is a constant and $\rho$ is ...
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Lagrangian of a moving charge distribution under action of a eletromagnetic field

We all know that for a single charged particle, we can derive the Lagrangian starting from Lorentz law of force: $$ \mathbf{F}=q(\mathbf{E}+\mathbf{v}\times\mathbf{B}) $$ and by using the ...
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Applications of the quartic potential [closed]

What are the applications and experimental purpose of quartic potential in Physics, Chemistry, or Biology? Please include the references.
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Is electric potential difference a state function? [closed]

Is electric potential difference a state or a path function? I came across a question which says "find the potential along this path".
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176 views

Why the electric field on the surface of charged spherical shell of radius $R$ and charge $q$ is $\frac{kq}{R^2}$?

As we know the electric field at a point due to charge $q$ is equal to $\frac{kq}{r^2}$ where $k$ is the constant of proportionality and $r$ is the distance between the charge and the point (where we ...
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What exactly is a bound state and why does it have negative energy?

Could you give me an idea of what bound states mean and what is their importance in quantum-mechanics problems with a potential (e.g. a potential described by a delta function)? Why, when a stable ...
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Solve the 1D poisson equation by integrate twice the charge density

Let's say I have a set of data ((1-D)array) called charge density along the z direction (obtained from DFT calculation)and I want to integrate it twice with respect to z coordinates points (i.e., if $\...
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Energy of EM Fields in terms of Potentials

In reading the paper On the nature of the Hamiltonian for the interaction of radiation with atoms and molecules: (e/mc)p⋅A,−μ⋅E, and all that by E. A. Power, and T. Thirunamachandran (AJP, 1978), I ...
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Why is entropy maximal under $(U,V)$ constraint? Construction of maximal entropy at equilibrium from thermodynamic potential

Let us consider a system exchanging work via pressure force only. It is assumed to be at mechanical equilibrium with the environment. We can write down the differential of the thermodynamic potential ...
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160 views

Approximation to the dipole of 2 infinite line charges

This is the question: 2 infinite line charges are located at distance $l$ and charged with linear charge density $\lambda $ and $-\lambda$. Find the electric field and the electric potential away ...
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Electron degeneracy in white dwarfs

Consider a plasma in a star. Now in a plasma electrons are so excited that they can no longer be held by the electromagnetic field of the nucleus. But then when we are talking about cores or red ...
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Can a Gaussian surface have infinitesimally small thickness?

This question originated while solving the charge density with the variation of electric field potential known. The potential in space varies as $\phi=-ax^3+b$, where $a$ and $b$ are constants. To ...
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1answer
40 views

Qualitative thought model for retarded potentials

I attempted to grasp the retarded potentials by staring at them and wanted to know if my thoughts seem to work out. Equation taken from wikipedia (replaced $t_r$ with its definition): $$ \mathrm\...
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1D Finite potential well: solutions with $\sinh$ and $\cosh$?

So I am studying the (one dimensional) quantum mechanical finite potential well defined by: $$ V(x) = \cases{0, &|x|>a\cr -V_0, &|x|<a} $$ where $V_0>0$ is a real number. I know ...
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Why is the electric potential at infinity zero?

As per net results, the potential at infinity is considered to be zero. Apart from considering this as a physics law, is there any proper reason why we consider potential at infinity to be zero?
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If the potential shifts by $a$ in x axis, would the Wave function shift by $a$ as well?

While solving problems in QM I had the following question in mind. If the solution is found to be $\psi(x)$ for the original potential $V(x)$ in the time independent Scrödinger equation, would it be ...
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Constant current through a conductor is a problem of electrostatics or electrodynamics?

When you connect a constant voltage source across a resistor, there will be a constant current through the wires. Is this a problem of electrostatics or electrodynamics? If it is a problem of ...
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Why is $\nabla U(r) = \frac{dU(r)}{dr} \nabla r$?

Does anyone have a proof for the equation: $$\nabla U(r) = \frac{dU(r)}{dr} \nabla r$$ Where $r=|{\bf r}|$ is the distance and $U(r)$ is a potential for a central force. This is from page 13 of "...
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What would the graph look like if the electrodes were non-equidistant from the dipole?

Hypothetically speaking using the diagram above. If the negative electrode was very far away from this excitable tissue and the positive electrode was right next to it. What would the voltage graph ...
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886 views

Vector potential of a solenoid in the Coulomb gauge

I understand the usual argument for calculating the vector potential outside of a solenoid of radius $R$ with $n$ turns per unit length carrying current $I_0$ using $$ \oint \mathbf{A} \cdot d \mathbf{...
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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 ...
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Chloride equilibrium potential is negative shouldn't it be positive?

Chloride flows down its concentration gradient into the cell. At a certain point a minute amount of net positive charge develops on the outside, enough to electrostatically attract chloride ions back ...
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1answer
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Deriving Euler-Lagrange equations for generalized coordinates without “virtual work”?

I have been reading "Classical mechanics" by Goldstein, Poole, and Safko. In particular, the section on "D'alembert's principle and lagrange's equations", in which the principle of virtual work is ...
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Identify Electric Field [duplicate]

I have electromagnetics homework to do , and it is asked to find de volumetric density and potential of this electric field. But I am having a hard time understanding what this expression represents. ...
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141 views

Non-local potential

I read that the Schrodinger equation for a non-local potential is given by $$-\frac{\hbar^2}{2m}\nabla^2\psi(x)+\int V(x,x')\psi(x')dx'=E\psi(x).$$ In case of a local potential, $$ V(x,x')=V(x)\delta(...
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Non-symmetric double-well energy levels

While going through Konishi's and Paffuti's book Quantum Mechanics: A New Introduction, I came upon an example that I see in many books on QM - the double well potential. The problem is then posed as ...
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Meaning of the differential form of Gauss's theorem and Poisson's equation

The differential form of Gauss's theorem is that the divergence of the electric field is proportional to the charge density of the region being considered (crudely speaking). My question is, how is ...
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Electric potentials and superposition

I had a question regarding the addition of electric potentials. Consider two positively charged particles $q_1$ and $q_2$ at distance $R$ apart. Let the charges have magnitudes $q_1$ and $q_2$. For a ...
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Why is $\varepsilon=\frac{W_{chemical}}{q}=\Delta V_{-\to+} $ the emf of a battery?

In my book, the electromotive force (emf) of a battery is defined as follows $\varepsilon: = \frac{W_{chemical}}{q}$. The book then states that for an ideal battery, $\varepsilon = \Delta V_{-\to+}$, ...
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What is the difference between positive negative potential and positive, negative work done?

if work is done along the direction of force,then the work is regarded as positive work and if work is done in a direction opposite to the direction of force then it's regarded as negative work....
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Lagrangian of a particle in a gravitational potential and conservation of angular momentum

I'm trying to prove via Noether's Theorem that the angular momentum of a massive particle in a gravitational field is conserved. The attempt follows: OBS: I'm working in the euclidean space so I'll ...
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Potentiometer comparison of two resistance [closed]

How is the current in both cases in secondary circuit same because we have changed the resistance first it is R then X so current should change.
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1answer
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Finding the charge distribution on a charged sphere - image method

Considering the case where we have a grounded sphere (so the potential on the surface is 0) and the following charge system: Now, I'm trying to solve the case for when, instead of a grounded sphere, ...

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