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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How does an electrical circuit works? [closed]

I am not getting how Electrical circuit works? what do we mean when we say potential difference of battery across the terminal? Is it the work done by electrical field created by the two terminals of ...
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Laplace's equation in presence of a dipole

I know that in classical electrodynamics we're dealing with stuff macroscopically, so I can pretend that some volume of space is empty of charge when it's actually full of matter consisting of charged ...
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How to solve the Gauss' law?

Imagine we have the first Maxwell Equation: $$ \nabla \cdot \mathbf E = \frac{\rho}{\varepsilon_0} \\ \mathbf E = -\nabla \phi \\ \nabla \cdot (-\nabla\phi) = \frac{\rho}{\varepsilon_0} \\\nabla^2 \...
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What is the correct derivation of energy stored in parallel plates capacitor?

I am little confuse in deriving the energy stored in the capacitor. I read two different derivation in totally different way but yet getting the same value. Here they have calculated work done by ...
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Will the potential energy is same in both the cases?

Suppose there is a charge $Q$. Now bring in another charge $Q'$ from infinity to a position a distance $r$ from charge $Q$. Then the change in potential energy is equal to $kQQ'/r$. My question is: ...
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What is the meaning of potential of the capacitor?

I am little confuse about the potential of the capacitor. Suppose we have two parallel plates of capacitor and both have equal and opposite charges on it. Let say plate "A" has positive ...
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Equilibrium points in lagrangian mechanics with generalized potentials

I understand the way i calculate equilibrium points when i have a lagrangian without mixed terms (with coordinates and velocities multiplied), thinking of the coordinate dependent part of the ...
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Why not say a scalar potential as a function representing the matter itself? [duplicate]

[Question] Why not say a scalar potential as a function representing the matter itself? At first glance, this idea seems to make the duality, which is the biggest difficulty in understanding quantum ...
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Infinite conducting plane

Let $\pi$ be an infinite conducting plane laying in $z=0$. the plane is kept in potential of 8 volts, ($\phi(z=0)=8[V]$). Prove or disprove: the surface charge density - $\sigma$ is well defined.(...
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Relation between Electric Potential and Electric Field Intensity

Suppose we have been given a curve y = V(x) where V(x) represents the Electric Potential at x. Now if for a range the curve is a horizontal straight line, can we say that the Electric field intensity ...
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When should I need the constant of integration when I calculate electric potential?

For example, electric potential is given by the formula. $$V = -\int_\infty^a \vec{E} d\vec{l}$$ For some questions, I would just use this formula to get the potential and it would be the correct ...
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Why only the first derivative of the wave function must be continuous?

Let's say we have a piece-wise differentiable periodic potential. For example, like a zigzag. Let's assume that we know eigenvalues and eigenfunctions on each interval, $\Psi_{1, 2}$ on the left and $\...
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How can I find the potential form given the particle trajectory? [closed]

Given the angular momentum $L$. Find the potential form $U(r)$ such that the particle trajectory affected by this potential is given by $$r(\phi) = r_0\exp(\alpha\phi)$$ with $r_0$ and $\alpha$ ...
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How to find expansion of slightly modified Coulomb's potential?

From here I know that, ${{\frac {1}{|\mathbf {r}_1 -\mathbf {r}_2|}}=\sum _{\ell =0}^{\infty }{\frac {4\pi }{2\ell +1}}\sum _{m=-\ell }^{\ell }(-1)^{m}{\frac {r_1^{\ell }}{r_2^{\ell +1}}}Y_{\ell }^{-m}...
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Why most of the things in this universe wants to become Sphere? [duplicate]

in our solar system , every planets revolve in elliptical path and their shapes is almost oval or approaches to Sphere . Sun is also looks like Sphere . Question: Why everything trying to approaches ...
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Derivation of the Yukawa potential by integration

I'm trying to solve the Yukawa potential using standard integration methods, but can't seem to be getting the correct result. This derivation is a part of Bellan's "Fundamentals of Plasma Physics&...
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Find the number of bound states in a finite potential well [closed]

I know how to derive the concrete energy levels in a finite potential well with the typical graphical analysis. But I want to know if one can do it differently without any complicated math and a ...
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What is the difference between electrostatic and electric potential?

What is the difference between electrostatic and electric potential in a circuit?
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Metal/good conductor frame in a changing magnetic field

Imagine that we put a metal/good conductor frame into a changing magnetic field. Due to the fact that this is an electromagnetic induction phenomenon, an induced EMF can be measured between the two ...
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Why don't we know the electric potential at any point in a circuit, only the difference in the electric potential (voltage)?

Why in circuit analysis, don't we know the electric potential at any point in a circuit?
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Finite potential well as potential goes to infinity and width to zero

I am studying the solutions of the finite potential well and I came over the following question: "What happens if we put the potential to infinity, but at the same time make the well thinner and ...
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Relation of potential difference and charge in a capacitor

So, there is something regarding capacitors which is bothering me. It is said that in capacitors connected in parallel, the charge is divided between different capacitors, while potential difference ...
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What happens when one side of the capacitor is grounded?

Let's say one side of the capacitor is connected to a voltage $\frac{V}{2}$ and the other is connected to a voltage $-\frac{V}{2}$. So the charge on the capacitor will be $Q$ and $-Q$ respectively. ...
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Direct calculation of the gravitational potential inside a hollow sphere

I calculated the gravitational potential inside a massive sphere with constant density and got the result: $$\Phi = -2\pi G\rho R^2 + \frac{2}{3}\pi G\rho R_p^2$$ Where $R$ is the radius of the sphere ...
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Vector potential due to a spinning spherical shell with a non-uniform surface charge distribution

In Griffith's Introduction to Electrodynamics 4th edition example 5.11 the solution for the vector potential of a uniformly charged spinning spherical shell is given. Now let's assume that the ...
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Finding capacitance of this setup

Let's say there is a capacitor of the following setup: A parallel plate capacitor of area A, plate separation d and capacitance C is filled with three different dielectric materials having dielectric ...
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Electric potential generated by spherical symmetric charge density

I know this question is pretty basic but I found a supposedly wrong formula in my notes and I'm trying to understand where this is coming from. Suppose we have a spherically symmetric charge density $\...
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2 votes
1 answer
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Spherical cavity inside a uniformly magnetized material VS uniformly magnetized sphere

In Jackson 4.4, boundary value problems in dielectrics page 159, a simple relationship is shown between the electric potentials and hence between the electric fields of a spherical dielectric and ...
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1 answer
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Relation Between Gravitational Potential and Acceleration due to gravity

I have always had this question in mind. I know expression for gravitational potential is given as $$V=-\frac{GM}{r}$$ While acceleration due to gravity is given as $$g=\frac{GM}{r}$$ So i assume $$V=-...
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What is the point of the four different thermodynamic potentials?

Why are there four different thermodynamic potentials? What is the point? Nothing new is defined, just a reshuffling? Could someone help me in showing this? Does it relate to doing experiments? If I ...
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What causes the potential difference in a half-cell?

This question pertains to the subject of electrochemistry --specifically a half-cell and not a full galvanic cell. From what I understand, a half-cell has a potential of its own. This is voltage is ...
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How does the potential difference between two points in an electric field be the work done?

I was learning about electric potential and it was pointed out by my professor that the potential we calculate between two points is the potential difference and not the absolute potential; if ...
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Finite Potential well inside an infinite potential well

Let us consider the following potential $V(x)$ such that $$ V(x) = \begin{cases} 0&0<x<b \\ V_0&b<x<a \\ \infty&x>a \\ \end{cases}$$ And we have $V(x)=V(-x)$. We are ...
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The capacitance of an isolated spherical conductor

I just started my topic on capacitance today. In the above derivation of capacitance of an isolated conducting sphere,+q charge is distributed uniformly. After substituting the value of potential, we ...
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What does negative electrical energy signify?

When we derive the formula for potential energy caused by the torque of a dipole in uniform electrical field we get $U = -pE \cos \theta$. And my textbook tells me that the when the dipole is kept ...
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Calculating $\mathbf{B,E}$ for electric dipole field radiation [closed]

I tried to read posts regarding this question, but I only found ones with different notations which I didn't understand. I'm trying to calculate $$\mathbf{B(x,}t)=\nabla \times \mathbf{A(x},t)=\nabla \...
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"Forbidden nodes" of a quantum particle trapped in a harmonic oscillator potential

Let's consider a confinant potential $V(x) \in C^2(\mathbb{R}, \mathbb{R})$, of the form of a harmonic oscillator ($V(x) = x^2$ for example): Consider a classical particle which has a kinetic energy $...
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Find the surface charge that appears on a cavity

The problem is of a conducting medium in a uniform field $E_0$. A spherical cavity of radius $a$ is formed inside said medium. I already found the potential inside and outside the cavity $\Phi_{\text{...
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Contradiction in my understanding of wavefunction in finite potential well

Most things like to occupy regions of lower potential. So the probability amplitude should be higher in a region of lower potential. I denote the potential by V. However, we also know that the kinetic ...
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4 votes
2 answers
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Electric potential vs electromagnetic potential questions

We were all taught about the electric potential $V$, which is defined up to a constant, and can be measured with a voltmeter or an oscilloscope. On the other hand, in electromagnetism are defined the ...
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Contradiction from Poisson-Boltzmann equations -- Gouy-Chapman model

Recently I have been investigating the problem of a neutral solutions (with equal number of anions and cations) interacting with an infinite surface $z=0$ with electrostatic potential $\phi(z=0)=\...
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Plate with positive potential and Gouy-Chapman model

I am thinking about the following mental experiment. Imagine I have an infinite flat plate at $z=0$ with electrostatic potential $\phi_0$, i.e., $\phi(z=0)=\phi_0$. Now I embedded this plate within an ...
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How to calculate the field distribution due to a current radiating in one direction?

Given a surface current distribution, $\textbf{J}(r)$, we can calculate the magnetic potential in the Lorenz gauge using $$ \textbf{A}(\textbf{r})=-μ_{0} ∬g(\textbf{r},\textbf{r}')\textbf{J}(\textbf{r}...
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Working of a van de Graaff generator

Experiments show that when a charged conductor is placed in contact with the inside of a hollow conductor, all the charge on the charged conductor is transferred to the hollow conductor. In principal ...
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Current without potential difference, in the given circuit?

In the given circuit, the value of current comes out to be 0.5 A Now if I calculate potential difference between point A and B i.e. $$V_B + 3i-1.5=V_A$$ On putting value of $i=0.5A$ we get, $$V_A-V_B=...
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Why is current density in a conductor of uniform cross sectional area constant at all points?

According to what I was taught, if current was dispersed “uniformly,” current density would remain constant. So, in a conductor, the 'current density should be the same at all points.' But, given that ...
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Is electric potential inversely proportional to the voltage at a point?

Consider this simple diagram, where the thermistor's resistance = $500\Omega$. Let's suppose the temperature of the room increases. Then, Electric potential at point ...
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Deriving non-relativistic potentials from QFT

Some systems, like atoms, are described well by quantum mechanics, where one just gives the Hamiltonian in the form $H=T+V$ and computes the eigenvalues and eigenvectors of this operator to figure out ...
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Why charges does not move through the conductor here if potential at both ends of wire is same?

Two conducting solid spheres are kept apart, one with charge Q1 and radius R1 and the other with charge Q2 and radius R2. Q1=5Q2 and R1=5R2 When these spheres are connected by a conducting wire, the ...
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Conducting shell surronded by, dielectric shell, and an outside $q$ charge

I would like some help with my solution attempt. I have a conducting shell with radius $R1$, surronded by a dielectric shell with $\varepsilon_1$ and radius $R2$, and on the outside i have a $POINT$ $...
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