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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Point with zero electric potential inside triangle [closed]

If we have three equal point charges placed on a two dimensional plane at $(a_x, a_y)$, $(b_x, b_y)$ and $(c_x, c_y)$, what would then be the coordinates of the point at which the electric ...
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Potential difference of conductor with induced load

If a metallic sphere is grounded and close to a positive charge q, it will be charged with -q. Let's say that the electrons will arrive through the grounding. This charge will cover the surface of the ...
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Metastable $E=0$ s-wave bound state in a spherical potential well

I am currently dealing with scattering theory. I looked up the scattering on a spherical well potential. $$V(r) = \begin{cases} -V_0 & , r \leq R\\ 0 & ,r > R \end{cases} $$ where ...
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Potential of an infinitely long cylinder

Suppose I have an infinitely long cylinder with radius $R$, charged with longitudinal density $\lambda$. I want to calculate the potential outside the cylinder. The field induced by the cylinder is ...
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Why is the ground state energy of a 2DEG higher compared to the 3DEG?

I am reading something about a 2DEG (2-dimensional electrongas model) and can not understand it. My book says the ground state of the 2DEG is higher compared to a 3DEG because the confinement to 2D ...
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Can Ampere's Circuital law be used on an infinite number of alternating Helmholtz coils?

I have the following surface current density $$ \bar{\sigma}_s = \hat{\phi} \sin(kz) |\bar{\sigma}_s| $$ to approximate an infinite number of alternating Helmholtz coils stacked along the z-axis with ...
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Why does the potential difference between two charged plates increase as they move further apart?

Suppose a uniform electric field $E$ exists between to oppositely charged metal plates (one is positively charged and one is negatively charged). If the plates move apart, and the charges on each ...
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Why does the sphere with the smaller radius (r1) have the greater charge density?

Suppose two charged conducting spheres of different radii $r_1$ and $r_2 > r_1$ are very far apart but connected by a conducting wire. Why does the sphere with the smaller radius $(r_1)$ have the ...
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Dipoles and Potential Energy

I was pondering about electrostatics, particularly dipoles. How would one go about calculating the difference in potential energy of a dipole an arbitrary distance away from an arrangement of another ...
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Calculating the potential of 2 spherical perfect conductors with the image method

I am searching for a way to calculate the potential on the surface of two perfect conductors that are spheres. I am not sure my method is correct. Here is a diagram of what I am studying : They ...
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Kinetic energy and Potential of a photon

How does the potential and kinetic energy of a photon relate? Do they mean the same thing? Also how does De broglie wavelength and Potential relate?
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Electric potential at midpoint?

I understand that if you assume the field is uniform between R and S then you can use E=V/d to get E=(30-20)/(0.5)=20Vm^(-1), so the answer is C (which is correct according to the mark scheme). But ...
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Calculation & derivation of de-Broglie wavelength [duplicate]

How to calculate the de Broglie wavelength of an $\alpha$ particle that is accelerated through a potential difference of $V$ from rest.
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Need help on electric potential definition

I'm having trouble understanding electric potential. In my book it says "an electric force acts on a charge situated in an electric field." I understand this part. Then it goes on to say "If a charge ...
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Why is the zero of electric potential taken to be $r = \infty$, rather than $r = 0?$

Wouldn't it make more sense if it was taken to be zero at $r = 0$? This seems to imply that with a negative test charge at $r = 0$ from a positive point charge, $V = -\infty$, which I have trouble ...
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A Method of Images Problem from Electrodynamics (Cylindrical Surfaces)

This problem is from Introduction to Electrodynamics 4th Edition , Griffiths, problem 3.12 Two long, straight copper pipes, each of radius $R$, are held a distance $2d$ apart. One is at potential ...
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How to determine if a potential admits bound states?

According to Griffith's Quantum Mechanics, "$E$ must exceed the minimum value of $V(x)$, for every normalizable solution to the time independent Schroedinger equation" As an example, there is no ...
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At what distance is lightning dangerous for someone lying down?

My 8 yo child told me that they learned at school that they should lay down flat on the ground in case of lightning. I told him that the more correct position is crouching down with feet together, but ...
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How do the electrons know the route? [duplicate]

I've learnt in classroom that the requirements for electrical current to flow in a circuit are as follows: there must be a closed conducting path between negative and positive terminals there must ...
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What state does the particle in a box occupy?

My textbook derives the equations for the different energy states $E_n$ of the particle in a box. But my professor in class said this example was a good one because it spoke about the "superposition ...
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Why do we not require higher derivatives to match at boundary when solving the Schrödinger equation in a given potential?

When solving the time independent Schrödinger equation for a given potential in 1D, the main part of the solving involves matching boundary conditions. Usually, we require the value and the first ...
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How can I physically demonstrate potential difference in a circuit to a 14 year old?

Children of this age have a fair idea about current, resistance, and batteries. Potential difference is a thing that cannot be felt or physically visualized. A teenager asked me if he can touch ...
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Use of termination in solving quantum harmonic oscillator, hydrogen atom etc

I can't seem to understand the use of termination to make the series solutions physically acceptable (when solving the linear harmonic oscillator etc.). So what if the series does not terminate, it's ...
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Calculating the electric charge of two spheres knowing their potential

I have a system of two spheres, the first one is at a potential of $ V_1 = 1 V $ and the second one is at a potential of $ V_2 = 0 V $ The distance between them is $d$ and the radius are respectively ...
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Infinite Energies of a particle in a rectangular box

For a particle trapped inside a rectangular box of side lengths $l_x$ $l_y$ and $l_z$, the energies are ...
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Potential of a sphere induced by a charged sphere

I am trying to solve what seems like a simple problem but something is bothering me: Imagine we have a sphere (1) with a charge $Q_1$ and at a distance $d$ we have another sphere (2) which is a ...
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Why the electrons flow from higher potential to lower potential?

We know that every thing moves from a higher potential to lower potential. In fact we also studied in our textbooks that a charge travels from higher potential ie. Positive side to lower potential ie. ...
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Aharonov-Bohm experiment: A possible way to understand potentials?

I'm posting this question as a function of an another question I found here: What is potential energy truly? The answer of WetSavannaAnimal aka Rod Vance. As I understand the hole point is to see ...
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Probability of finding particle in infinite square well, displaced walls

Initially a quantum particle moves in a one-dimensional well ($x$-axis) from $-a$ to $ a$, $ V = \infty $ outside and $ V = 0 $ inside the well. So initially, the wave-function $$ \psi_0 = ...
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Importance of bound states

While solving a potential well problem we get scattering states and bound states (if exist). Number of the bound states we get depends on the potential profile. What I want to ask is, what is the ...
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From Liénard-Wiechert to Feynman potential expression

When studying the potential of an uniformly moving charge in vacuum, Feynman proposes to apply a Lorentz transformation on the Coulomb potential, which reads in the rest frame $ \phi'(\mathbf r',t') ...
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At what densities the many-body approaches are valid?

Suppose we have a n-particle interacting system with a potential $V=a/(r1-r2)$, it is a pseudo-coulomb potential: you can choose it fermion or boson. Then, at what densities the many-body approaches ...
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What is the difference between the potential $V$ and the effective potential $V_{eff}$?

What is the difference between the potential $V$ and the effective potential $V_{eff}$? Some times when solving problems, an effective potential $V_{eff}$ is defined and its usually equal to the ...
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Electric potential inside a conductor

I just began studying electrostatics in university, and I didn't understand completely why the electric potential due to a conducting sphere is $$ V(\vec{r})=\begin{cases} ...
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Physical interpretation of single layer potential in the plane

Let $\Omega\subset\mathbb{R}^2$ be a bounded domain with smooth boundary $\partial\Omega$. The single layer potential with charge density $f$ sitting on $\partial\Omega$ is defined by ...
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Potential and kinetic energy

If a ball stays on the ground, it has no height and no velocity. So what energy does it have kinetic or potential?
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Potential of a uniformly charged hollow sphere [closed]

If I use Gauss' theorem I find that, for $r\geq R$ $$V(r) = \frac{\sigma R^2}{\epsilon_0 r} = \frac{Q_{sphere}}{4\pi\epsilon_0r}$$ where $\sigma$ is the surface charge density and $R$ the radius of ...
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Particle in a one dimensional box conditions

Why does the wave function have to be $C^1(\mathbb{R})$ for a finite square well but not for an infinite square well? For an infinite square well with boundaries at $x=0$ and $x=L$, we have ...
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Finding finite square well width and depth from transmission resonance

For an electron incident a one-dimensional finite square well the transmission probability is $\approx$1 for electron energies $E_1=0.6 \textbf{ eV}$, $E_2=1.9 \textbf{ eV}$ and $E_3=3.4 \textbf{ ...
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Why can't electric potential be negative?

As a general concept, potential energy of a configuration is equal to the work done by an external force against an existing conservative force. It is this work done that gets stored in the body as ...
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Potential in uniform fields

First in a book I found that the electric field strength $\mathrm{E}$ of a uniform electric field from a charged plate is equal to $\frac{q}{2\times \epsilon_0 \times S}$ where $q$ is the charge of ...
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Potential Difference between 2 points in a curcuit

3 Cells and 3 capacitors are connected as shown in the diagram. What is the potential difference between points A and B ? What are the final charges on each of the plates of the Capacitor ? Does the ...
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Induced potential difference paradox

So,i was studying from some lecture notes from MIT's open course program,and i stumbled across this example The example says:The solenoid is so long that its external magnetic field is negligible. ...
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Induced emf problem

This is not homework question,just a thought experiment about a general question i have about induction. Let's suppose that we have a closed circuit with only two resistors in series.We also have a ...
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Can we have negative Electrostatic potential

What does it mean to have a negative electric potential? not talking about potential difference or voltage.
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What's my $dM$? Gravitational Potential inside a circle of mass

I'm trying to find the gravitational potential for an arbitrary point within a ring of uniform mass density. The point is constrained to be in the same plane as the ring. So we start with: ...
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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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Deriving the Force on an ion in the Classical Harmonic Crystal

I was following Solid State Physics by Ashcroft and Memrmin and their introduction to the Classical Theory of the Harmonic Crystal. (Chapter 22) If there are a large number of ions in a straight ...
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Does the electric field inside a circuit cause a potential drop with distance?

We know that when the system reaches steady-state(current does not change with time),the electric filed inside the circuit is constant. In many textbooks and lectures,professors make a graph like this ...
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Why do resistors always cause a voltage drop equal to the voltage of the battery

Consider a wire connected to a battery. Now,potential is analogous to the energy of the particles.And potential in a resistor drops because of the friction inside the resistor(considering there is no ...