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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Can't get correct sign of electric potential of dipole

We have a dipole and I need to find $V(x)$ for $x<-d$ First I calculate the potential at some point $A=(x,0)$ relative to $P = (-\infty, 0) $ of the $-Q$ charge as follows $$\int_A^P\vec {E} \...
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Different electric fields

What is the difference between an $electrostatic$ and a $non-electrostatic$ electric field?
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50 views

Why net EMF in series connection of cell is sum of individual EMF? [closed]

Suppose we have two resistor and let A,B,C be points across resistors.Va-Vc=Va-Vb+Vb-Vc.Thus pd across the resistor combination can be obtained by simply adding the individual pds across each resistor....
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Solving Laplace equation in Cylindrical coordinates with azimuthal symmetry?

I am having some trouble solving what the potential field looks like for a finite cylinder along the $z$ direction. Physical Scenario Consider a cylindrical electrode with radius $R_0$ that extends ...
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Trying to define the electrostatic potential of a point charge

I've been trying to define the electrostatic potential (V) for a while now, it's something that I've covered last year and now need to know what exactly it does mean, I came up with this and all I ...
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Potential drop in a resistor

What causes a potential drop in a resistor or load? Why a does wire with neglible resistance have the same potential across it?
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Electric potential and its signs

When we are calculating the potential due to the sphere, why do we integrate from $r$ to $\infty$ instead of from $\infty$ to $r$? Or do we integrate from $r$ to $\infty$? Regardless of who does the ...
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Potential of hydrogen atom solution of the Laplacian: Missing boundary condition to fix integration constant $c_1$

I have following problem, I want to calculate the classical potential $\phi(r)$ of the hydrogen atom in its ground state. The charge density is known: $$\rho(r)=\frac{-e_{0}}{\pi a^3}e^{-\frac{...
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Why are induced field lines circular?

Whenever we have a changing magnetic flux through a conductor an induced electric field is generated. It is often said that these induced electric field lines are circular in shape.But why is this so?...
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37 views

Why can two nodes at the same potential be collapsed into one node?

I have a problem where I have a cube with resistance $R$ along each edge. I am asked to find the potential between various nodes (corners) using symmetry and the fact that two nodes at the same ...
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Misunderstanding the calculation of the potential for a system of 2 concentric shells

Let's say we have 2 concentric shells. The little one has a charge $Q_1$ and a radius $R_1$ and the greater one has a charge $Q_2$ and a radius $R_2$ with $R_2$ > $R_1$. We want to calculate the ...
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Point with 0 electric field and non-zero potential

I'm quite new to physics and I don't totally understand the concepts of potential energy and work. I've been watching MIT courses and I got pretty confused, considering the following situation: We ...
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Electric potential due to two spheres

The setup is as below: The two conducting spheres, of radii $r_1$ and $r_2$ have charges $Q_1$ and $Q_2$. The distance between their centers is AB. BC is perpendicular to AB. The problem asks to ...
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The potential at a point

According to my book, 'The potential at a point is said to be 1 volt when 1 joule of work is done in bringing 1 coulomb charge from infinity to that point.' But I wonder how it is possible. As the ...
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Difference of potential between 2 disks of radius $R$ where $d << R$

Well, We have 2 disks of radius R where the distance between these 2 disks : $d << R$. These disks are uniformly charged. I have calculated the electric field near one disk, I have: $$E(z) = \...
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Finding the potential off axis of a uniformly charged disk

This is problem 3.22 from Griffiths We know the potential at any point on the axis perpendicular to the center of the disk, I'm asked to find the potential at any point $(r,\theta)$ assuming $r<R$ ...
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Potential functions for separation and isochronic gauges

Most potentials in physics are expressed as a radius or another geometric norm/gauge. I am looking to understand the significance of the choice of potential functions for force/pressure separation in ...
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Magnetic Vector Potential - a measure of Momentum

I am trying to understand the magnetic vector potential as momentum per unit charge, that is, somehow, the "total" momentum should be $p = mv +qA$. Here's a part of the paper I was reading - I am ...
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Is there an accepted way to plot a wave function and the potential?

When using the time-independent Schrodinger equation and finding a wave function $\psi(x)$ for a given potential $V(x)$ is there a consistent way to plot these two objects on the same image that takes ...
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Central Potential + Coupled Angular Momenta

I am considering a two-state system with a Hamiltonian of the form $$ H = \frac{p_1^2}{2m_1} + \frac{p_2^2}{2m_2} + V_a(|r|) + \bigg(\frac{1}{4}-\frac{S_1\cdot S_2}{\hbar^2}\bigg)V_b(|r|), $$ where ...
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How to perform integration for all of space?

Two conducting spheres of radii $a$ and $b$ have charges $Q_1$ and $Q_2$. Distance between their centres is $R$. If ${\vec E_1}$ and ${\vec E_2}$ are electric field vectors due to the two spheres at ...
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Confusion about this simple electrostatics line integral

Suppose we want to find the electrostatic potential $\phi_{0}$, with reference to infinity, at $r_{0}$ resulting from a positive charge $q$ located at the origin. For simplicity, let us assume we are ...
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Boundary conditions for an infinite line charge and grounded conducing plane

I'm not asking for a solution to the problem, I'm confused about what I should set the boundary conditions to, it's obvious that $V=0$ at $z=0$ because of the grounded $xy$ plane, but I don't know ...
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How current flows in an ideal wire when there is no potential difference? [duplicate]

Such as in this case: Even though potential difference between points A and B is zero, a current of 9A will flow between these two points. Why it is so? I understand potential difference must exist ...
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Has anyone solved the inverse hydrogen atom problem?

This question was motivated by a question asked yesterday (How to find the electrostatic potential of a hydrogen-like charge density?). This got me wondering about what would result from solving the ...
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What would be the potential due to a charge $Q$ at $Q$ itself?

We know that the potential due to a point charge $Q$ at any distance is given by $V=\frac{kQ}{r}$, but what would the potential be at the charge itself?
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Poisson's equation and electric field interpretation

My question is this: Are all solutions to Poisson's equation for a certain charge density such that the negative gradient of them will give me the electric field? In deriving the equation, we say ...
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1answer
42 views

How the earth keeps the electric potential?

I have the following DC circuit. A cell and a resistor (lightbulb) is serially connected and both ends are grounded. I see the lightbulb is on and hence the current flows. It is because the electric ...
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Double well potential and choosing coefficients

During lecture on single potential well, my professor had the following wavefunctions for the three regions: $\psi(x) = e^{\kappa x}\ for \ x<-L$ $\psi(x) = B\cos(ikx)$ for $-L<x<L$ $\...
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For the potential difference, how is it that $V=W/Q$=$U/Q$ when $U$ and $W$ are negatives of each other?

I'm currently studying electric potential and am somewhat overwhelmed by all of the different equations and their iterations. For instance, the first definition I learned was that: $$\Delta{V}=V_b-V_a=...
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Visualization of electromagnetic waves with potentials?

I wonder if there is out there any visualization of the propagation of electromagnetic waves, not only with the electric and magnetic fields components but an actual visualization of the underlying ...
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Gravity as part of the metric but not of a 4-vector potential

In class, I've been told that the scalar potential $V(x)$ (except the one associated to gravity) has to be introduced in the Lagrangian as the time-component of a 4-vector potential $A_\mu$, so what ...
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Why is the spin-orbit interaction for a nucleus so much more important than the spin-orbit interaction in atomic physics?

In atomic physics, the spin-orbit is a small correction between 1/1000 and 10ppm, so fairly small. In contrast, in nuclear physics the inclusion of the spin-orbit interaction is necessary to reproduce ...
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Reconstructing Charge Distribution from Multipole Expansion

Let $\rho$ be a static, discrete or continuous charge distribution, and $\phi(\mathbf{r})$ the corresponding electric potential. We may expand $\phi$ in a multipole series, $$ \phi(\mathbf{r}) = \frac{...
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What exactly do the zero-modes of the instanton mean?

I am studying instantons in quantum mechanics. My question is regarding the the zero mode of the fluctuation determinant that we get because the solution for the instanton breaks time translation ...
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Is the vector potential component $A_\phi$ for a dipole necessarily 0 due to symmetry about the $z$-axis?

Consider an electric dipole (+$q(t)$, -$q(t)$) [where say $q(t)=q_0\cos\omega t$] is placed along the $\hat z$ axis. In the spherical polar coordinates, its vector potential $$\vec{A} = A_r \hat r + ...
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Potential Difference between A and B is negative the potential difference between B and A?

Is the potential difference between a point A and a point B equal to negative the potential difference between point B and point A? Or, are they the same?
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Is electric potential always continuous?

In electromagnetism, we say that any conservative electric field $\vec{E}(\vec{r})$ is associated to a scalar potential $V(\vec{r})$ such that $\vec{E}(\vec{r}) = -\nabla V(\vec{r})$. If the electric ...
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Do we need to specify additional conditions in order to find the unique potential satisfying Laplace's equation?

Let us say we have a simple boundary value problem (BVP) in spherical coordinates : $$\Delta \phi = 0$$ along with $\phi=1$ at $\,r=1$, and $\,\phi =0\,$ at $\,\infty$. A surface sphere with radius ...
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Is potential difference in electricity discovered by decrementing two average potentials?

Is potential difference the difference (by mean of mathematical decrement; Y-X) by decremeting one measured average Joule of a charge (in point B in space) from ...
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What is the physics interpretation of work done of zero when moving a charged particle on an equipotential surface?

Assume I have a test charge of + 1 coulomb. If I move the test charge from a point with potential of +9 volt to another point with potential of -1 volt then the work done by me is -10 joule. This ...
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Incorporating matter effects on active-sterile neutrino oscillation with mathematica

I recently wanted to study the effect of a constant matter potential on a simple 2-flavor active-sterile neutrino oscillation system using Wolfram Mathematica, but I encountered a big problem in the ...
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Potentiometer analysis

As I was studying about potentiometer I came across how to use it to compare emf of two cells. It was written my text book that if current I flows through potentiometer wire then $$\mathcal{E}= v\...
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Intuitive explanation why electrons move from low to high electric potential

I know almost nothing about physics but am about to learn some electronics. I have trouble understanding why electrons move from low to high electric potential based on the definition given on the ...
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Relation between electric potential and Electric field

I'm unable to understand why the integration of $\mathbf E$ is done in two different ways for constant $\mathbf E$ and varying $\mathbf E$, as in case of parallel plate capacitor and spherical ...
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Connection between Schrödinger equations for a finite triangular well and a finite square well

Suppose we solve the Schrödinger equation, \begin{equation} -\psi''(x) + V(x) \psi(x) = -|E| \psi(x), \end{equation} where two cases are considered, $V(x) = -V_0$ (square well) and $V(x) = -V_0 (1 - |...
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Ambiguity between electric potential and voltage?

I understand that electric potential is a location based measure of electric potential energy per unit charge in an electric field, and that voltage is then the difference between two electric ...
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Charged conductor in an external electric field

If we put a conductor in a place where there is a uniform electric field, then the field will change. Take for example the case of a conducting cylinder, then the field lines would curve to return ...
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What is the quantum mechanical turning point of the $n^{th}$ energy eigenstate of an oscillator? [closed]

I am looking for an analytical expression for the most likely position for a quantum harmonic oscillator (which I refer to as the quantum mechanical "turning points"), in terms of $n$. For the quantum ...
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On proving that charge is linearly proportional to potential for a conductor

In Mr. Purcell's Electricity and Magnetism, page 103, it is stated, An isolated conductor carrying a charge $Q$ has a certain potential $\phi _{0}$, with zero potential at infinity. $Q$ is ...