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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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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 ...
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Resistors equivalent using symmetry and equipotential line

I propose the following statement: In a circuit, while determining equivalent resistance across two points, if the circuit is symmetric wrt the line joining the two points , we may fold the circuit ...
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Is magnetic potential vector due to the magnetic field or energy stored in magnetic field?

My doubt is whether the magnetic vector potential is due to the potential energy stored in magnetic field or due to the magnetic field. Also I have another doubt. Since in electrostatics potential ...
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Laplace equation outside sphere

When solving the Laplace equation on sphere coordinates you get: $$ u(r,\theta) = \sum_{n=0}^{\infty}\left( A_n\,r^n + \frac{B_n}{r^{n+1}} \right) P_n(\cos\theta) $$ And it is clear that if you have ...
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Electric potential in circuits

From what I understand from my notes, an e.m.f or electromotive force provided by a battery is the electrical energy per unit charge converted from other forms of energy required to drive a unit ...
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Electric Potential in the Center of a Electric Dipole

I thought the electric potential at point B would be positive because placing a positive charge at point B would cause it to move releasing energy while doing so. The answer key states that the ...
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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 ...
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Finding the expected value of the momentum of a classical Particle in a Potential Well [closed]

Consider the classical equivalent of a particle in a potential well. This can be imagined as a particle bouncing between two perfectly elastic walls with uniform velocity. Find $\langle p \rangle$ by ...
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Electric potential due to a current source - Basic equations

In my book I found the folowing formula of the electric potential generated by a current source: $$ \Phi = \frac{I}{4 \pi \sigma} \frac{1}{r} $$ where I is the current, $\sigma$ the electrical ...
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Fixing the potential for a quantum particle

I have started studying quantum mechanics and have realised that we can solve the Schrodinger equation for a particle's wave function if we know it's potential energy function. But the potential field ...
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Ideal/Non ideal Voltmeter across a battery with no current flowing

If I consider a voltmeter and connect it across a battery , which is in such a circuit , that no current is flowing in that branch (Before Voltmeter is connected), will the voltmeter, show the EMF of ...
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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 $a>0$...
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Equipotentiality of the conductor surface with extra charges sprinkled and Poisson's equation

The electrostatic potential $\phi(x,y,z)$ everywhere on the surface of a conductor/metal is the same. For a quick reference see this post. Hence, any derivative of $\phi(x,y,z)$ must be zero on the ...
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Clarification on electric potential energy

From what I understand from my notes (correct me if I'm wrong), electric potential energy is the work done in bringing the charge from infinity to a certain point from the source charge. Let this ...
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How to take the derivative of potential?

The electric potential $\psi$ at a point inside the volume charge distribution is: $$\displaystyle \psi = \lim\limits_{\delta \to 0} \int_{V'-\delta} \rho'\ \dfrac{1}{|\mathbf{r}-\mathbf{r'}|} dV'.$$ ...
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Taking into consideration the non-0 value of an equipotential in a method of images problem

If the infinite conducting plane in the diagram above is grounded, then $V=0$ on the plane and the image problem is easy to solve - just put the dotted $-q$ charge there and the $V=0$ equipotential ...
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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 ...
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Why electric potential requires absence of acceleration?

As of 28/05/2019, Electric Potential is defined in Wikipedia in the article with the same name as: The amount of work needed to move a unit of positive charge from a reference point to a specific ...
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Is electric potential just the sum or measure of Electric Potential Energy for a given unit of matter with electric change?

I understand Electric Potential as follows (I "synthesized" the definition from different definitions I found online): The sum of Electric Potential Energy for a matter particle with an electric ...
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Showing $ \nabla \cdot \mathbf A = 0$ using integral formula

In Coulomb gauge the vector potential is chosen so that $ \nabla \cdot \mathbf A = 0$ and we find $$ \nabla^2 \mathbf{A}=-\mu_0 \mathbf j $$ The solution to which is $$ \mathbf A(r) = \frac{\mu_0}{4\...
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Even and odd solutions to time independent Schrodinger equation on symmetric potential

I have to solve the following problem: Consider the potential well: $$ V(x)=-V_0, \hspace{10px} |x|<a/2 $$ and $0$ everywhere else. $a$ is also a positive constant and so is $V_0$. Find the ...
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Connecting one lead of capacitor to a certain charged object (to get a potential difference)

Setup-A charged sphere , connected to one plate of capacitor , other lead of capacitor is free. Question-Will the capacitor plates go through a charge redistribution ? Arguments/Counterarguments-I ...
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Is a complete circuit required for capacitors to redistribute charges?

Suppose I have two capacitors of different capacitance $C_1$, $C_2$and they have been charged prior connecting by voltage of $V_1$ and $V_2$ respectively the positive plate of one capacitor is ...
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Work done in moving a charge in circuit?

Why is the work done in moving a charge from one point to another in a circuit through any path the same even though heat and other losses are there?
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How do you measure voltage from first principles? [closed]

I've always wondered if you were thrown back in time with just my cell phone, how could I charge it... I know how to make electricity, but how do I check the voltage if all I have access to is, shall ...
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Work done by battery?

Why the work done by a battery is Q*V where V is emf of battery and Q is charge that is made to flow in circuit?please explain detail? explain and write the formulas
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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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Why do terms in a field theory Lagrangian that are polynomial in the fields collectively called the “potential”?

Field theory Lagrangians are often of the form of a kinetic term plus a source term minus a potential term. How do we know that the potential term is a polynomial in the fields? On a related note why ...
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Why is choosing a suitable thermodynamic potential important?

Say we are undergoing an isothermal process that eventually settles at equilibrium. $F$ will minimize at equilibrium, and if the entropy of the system is not held constant $U$ will not. Why do we care ...
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Proving thermodynamic potentials minimize at equilibrium

Is there a way to prove, for instance, $F$ minimizes at equilibrium for isothermal processes by looking at the equation $F = U - TS$ or must it be derived by using a thermal reservoir and analyzing ...
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What are 'external parameters' in Thermodynamics?

According to a Wikipedia article on Thermodynamic potential: When the entropy $S $and "external parameters" (e.g. volume) of a closed system are held constant, the internal energy $U$ decreases ...
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Energy density in electrostatics - definition [closed]

Background: It can be shown that the potential energy of charge distribution can be calculated by $U = \frac{1}{2}\int_V \rho(r')\Phi(r') d^3r' $ by means of integration by parts and the poisson ...
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Please clarify a doubt in the article: Reflections in Maxwell's treatise

While going through an article titled "Reflections in Maxwell's treatise" a misunderstanding popped out at page 227 and 228. Consider the following equations $(23\ a)$ and $(23\ c)$ in the article (...
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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(...
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Different definitions of the EMF of a device - None of them applies to devices in a circuit

Wikipedia gives two formal definitions of the electromotive force: One in case of a closed loop, in which case the the EMF is supposed to be the path integral of the electric field (and all other ...
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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 ...
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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 ...
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Why do we assume the potential is independent of time in the Schrödinger equation?

In just about every text I read (online or in paper), when they handle the time-dependent Schrödinger Equation, I see something along the lines of "we always assume the potential is independent of ...
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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 $...
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For degenerate perturbation theory, how do we interpret the eigenvectors and eigenvalues of $\hat V$?

For the eigenvectors that are unmixed by the matrix $\hat V$, the eigenvalues are the energy corrections of this eigenbasis. However, the eigenbasis tends to always be (as far as I'm aware) a linear ...
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Why is it possible to write the electrical potential as a sum of $\int dV \,\rho/R$ and $\int da \,\sigma/R$?

I'm trying to understand why one can write the electrical potential as follows \begin{equation} 4\pi\varepsilon_0\phi(\mathbf r) =\int d^3 r\,\dfrac{\rho(\mathbf r')}{\|\mathbf r - \mathbf r' \|} + \...
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Why wavefunction becomes exponentially smaller during quantum tunneling?

I am interested in quantum tunneling and I am wondering why the wavefunction of a particle would becomes smaller so that there is a slight possibility of finding it at the other side of a big energy ...
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When to use Poisson's equation in electrostatics

When does when elect to use Laplace's equation when dealing with charge distributions. For example, if I had a metallic sphere of radius $R$ and charge $Q$, then $$\mathbf E = \begin{cases} 0, & ...
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Potential of a polarized hollow spherical shell due to uniform electric field

A hollow spherical shell has inner radius $a$, outer radius $b$ and is made with a material with dielectric constant $\epsilon_r = \epsilon / \epsilon_0$. It is placed in a uniform electric field $\...
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Why does a voltaic cell induce an electric force proportional to voltage?

I'm trying to understand the intuition behind Ohm's law (that current is proportional to voltage). I understand the basics of the Drude model: if the electrons frequently collide and on average reset ...
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Why can't Gauss surface be a cube?

For calculating field outside a charged plane conductor, a gaussian surface of Cylinder is considered. I have been said that we consider cylinder because the circle in its upper end is in equal ...
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Will a led, connected to a long conducting rod, shine when the rod is falling through the magnetic field of the Earth?

Visualize a long conducting rod of length $l$ falling towards the Earth (after being released from a hight of say $5(km)$) perpendicularly to the Earth's magnetic field. Near the earth's equator, ...
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Why is force 0 either side of an inflexion point in neutral equilibrium?

In Tipler & Mosca 5th edition p173 it defines neutral equilibrium as a point in a U-x curve where $\frac{dU}{dx}=0$ and also $\frac{dU}{dx}=0$ for a small displacement either side of the point. ...
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Differing definitions of Gibbs free energy and Helmholtz free energy

I am trying to understand, to me, the difficult concepts of thermodynamic potentials, and I find their definitions numerous and hard to connect between each other. For instance, here are two ...
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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 ...