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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Electric Potential due to Sphere when cavity is at arbitrary position

While doing practice question, I came across a question... A solid sphere of radius a has a cavity of radius b which has a uniformly charge distributed with density $-\rho$ and the remaining part ...
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26 views

Applications of almost periodic functions [on hold]

can anyone give me a reference for a resource about the applications of almost periodic functions in physics? Thanks in advance
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221 views
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36 views

Potential energy of a spherically symmetric charge density in a spherically symmetric electrostatic potential

I'm interested in calculating the potential energy of a spherically symmetric charge density in a spherically symmetric electrostatic potential. More specific, I'm currently trying to calculate the ...
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1answer
34 views

Gravity well and constant total energy in circular orbit [on hold]

According to this question, the total energy of an object in a circular orbit in a $1/r^2$ potential does not depend on the radius of the orbit. However, if you look at "circular orbits" in a gravity ...
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1answer
43 views

Physical meaning of multipole moment

Is there a physical interpretation for multipole moments? For a quantity governed by the Laplace equation ($\nabla^2 \omega = 0$), I understand that the general solution is given by the multipole ...
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What is the electrical potential at point A, 15.4 cm from the center of the charge? [on hold]

I am simply looking for a place to start or a correct formula to use. Physics isn't my strong suit so if I could just get a lead then hopefully that will help. I've tried the electric potential ...
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2answers
24 views

Potential across the plate of a capacitor

So I came across this question: Two capacitors are connected in series of given capacitance $5\ \mu\mathrm F$ and $10\ \mu\mathrm F$. The first plate of the $5\ \mu\mathrm F$ capacitor is given a ...
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25 views

Green function for cylinder [closed]

I cannot calculate what is the green function for exterior region? I mean, there is a cylinder of radius $R$ and height $2L $, the charge density $ρ=ρ'(z/L)$ and i try to find potential $z>L$. I ...
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4answers
355 views

Dipole in a spherical cavity in an infinite dielectric

In this example the assumption is made that inside a spherical cavity (with an infinite dielectric) with a dipole placed at its centre, the potential takes the following form: $$\phi_{in}= \frac{p ...
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2answers
535 views

Degeneracy in one dimension

I'm reading this wikipedia article and I'm trying to understand the proof under "Degeneracy in One Dimension". Here's what it says: Considering a one-dimensional quantum system in a potential ...
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0answers
34 views

Calculating potential energy per ion of an one dimensional ionic crystal

The problem states to calculate "the potential energy, per ion, for an infinite 1D ionic crystal with separation $a$"; the crystal is a 1D lattice of alternating charges, likes so: ...
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1answer
62 views

A question when using $E= - \nabla V$

This problem is from Problems and Solutions on Electromagnetism. A thin but very massive disc of insulator has surface charge density $\sigma$ and radius $R$. A point charge $+Q$ is on the axis of ...
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44 views

How can energy be negative in a finite square well?

Say if the potential $V(x) < 0$ in the well but the sides or the scattered states its zero potential, anyways How is that the energy in the well is less than zero? Is it because the potential ...
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2answers
303 views

How the electric potential of a charged body depends on the surface area of the body?

I have studied in the book that electric potential of a body depend on the surface area of the body, that is as the surface area increases potential decreases keeping the charge as constant and vice ...
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2answers
142 views

Electric Potential Energy

When work is done on a positive test charge by an external force to move it from one location to another, does the potential energy increases or decreases, and does the electric potential increases or ...
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24 views

Series expansion of potential due to a dipole displaced from the origin

I learn that we can expand the electric potential in an infinite series of $\rho$ and $\cos(n \phi)$ when solving the Laplace equation in polar coordinates. The problem I want to consider is the ...
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1answer
97 views

Why is the Taylor expansion of the gravitational potential cut off after first term?

In this answer to a question on this site, the gravitational potential of the Earth is expanded as $$U(r) \approx U(r_0) + \left.\frac {dU(r)}{dr}\right|_{r=r_0}(r-r_0),$$ keeping only the linear ...
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1answer
206 views

Finite potential well, parity of solutions

I'm working through some problems for a QM exam and I've realised I don't really understand the concept of parity of solutions. I'm looking at a simple finite potential well problem: $$V(x)=0, \quad ...
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1answer
66 views

What is $Δf=ρ$ in Physics?

I asked a while ago a question on mathoverflow. It was a mathematical question with physical implications. To cut the story short, one mathematician said that Classically, a potential satisfies ...
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1answer
125 views

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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2answers
261 views

Infinite square well that suddenly decreases in size

A well known exercise in basic quantum mechanics is the sudden (diabatic) increase of the length of an infinite square well. Now consider a particle in an eigenstate of an infinite well that is ...
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1answer
28 views

Basic PE question about moving a planet.

If you lifted enormous masses (eg. many gigantic rocks) at one point (A) of the planet's equator. Then after 180 degree planet rotation, released the potential energy by lowering the rocks (B). ...
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In potentiometer does resistance connected in parallel to emf affect the balance pont?

In this question they have taken current in the potentiometer wire to measure the resistant. According to me there is no way we can find X because connecting it in parallel should not have any affect ...
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20 views

Potential difference across a resistor

I would like to know if the potential difference between the two ends of the resistance is same as the potential difference between any tow points in the resistance whose length is smaller than the ...
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2answers
43 views

Kirchoff's rules and inductance

Can Kirchoff's loop rule be applied in a scenario involving an inductor? Kirchoff's loop rule states that the closed loop integral of E dot dl is equal to zero. But, in a situation with an inductor, a ...
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1answer
31 views

Is there an electric field within a superconducting inductor?

I have learned that the magnitude of the EMF (potential difference) between the terminals of an inductor is equal to L*di/dt. Does this imply that an electric field does indeed exist in an ideal ...
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1answer
157 views

Semi-infinite / Asymmetric potential well

I'm asked to come up with an ansatz and solve for the coefficients of a asymmetric infinite potential well, where: $$ V = \begin{cases} \infty \text{ for } x< 0 \\ V_0 \text{ for } 0 \leq x \leq L ...
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1answer
257 views

Dielectric sphere placed in another dielectric medium with uniform external field: is there a surface charge density?

Consider a dielectric sphere placed within a dielctric medium. There is a uniform electric field $E_0$ present throughout in the medium. Would there be surface charge on the sphere?
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1answer
22 views

Electron gun; potentials around charged plates

I know that an electron gun releases electrons by thermionic emission and accelerate the electron through charged plates, and that the electrons are not gaining any energy after they leave the gap ...
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1answer
111 views

potential inside a cylindrical shell in terms of the surface potential?

Given a potential distribution $V(\phi)$ at the surface of an infinite cylindrical shell, is there an easy way to derive the potential inside the cylinder. No charges or currents anywhere.
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1answer
63 views

Deriving the Lienard-Wiechert Potentials

Let $\mathbf{w}(t)$ be the trajectory of a moving charge. Let the observation event be $(\mathbf{r},t)$. The scalar potential is: $\phi = \frac{q}{4\pi\epsilon_0}\int \frac{\delta(\mathbf{r'} - ...
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1answer
38 views

Why is it true that Laplace's equation does not hold within the sphere in this case?

Find the average potential over a spherical surface of radius $R$ due to a point charge $q$ located inside. (In this case Laplace's equation does not hold within the sphere) This is a question ...
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1answer
371 views

Induced electric field due to a moving wire

An infinite wire carrying a constant current $I$ in the $\hat{z}$ direction is moving in the $$y$$ direction at a constant speed $v$. Find the electric field, in the quasistatic approximation, at the ...
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47 views

Gravitational potential of planets

How do you work out the gravitational potential of planets in the solar system? Do orbiting planets have gpe? And what would it be relative to? The equation I know for it is mgh. But what would the ...
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Why is the electric field perpendicular to every point on the surface of a conductor?

I am reading Berkeley Physics Course, Volume 2 (Electricity and Magnetism by Edward M. Purcell). I am in chapter $3$, page $92$, and the book discusses conductors. The following is from the book: ...
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Measure a current from a charged surface caused by charge separation

I have separated a charge in an electric field like here (http://elektroniktutor.oszkim.de/grundlagen/gr_pict/coulomb5.gif) and I put the metal out of the field. The charge density on the surface of ...
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Plane-wave wave function in 3D with vector potential

I was looking into a monopole scattering problem in 3D with magnetic potential. What would be the most general incident plane wave solution ? The way I see this is that I need to ensure that current ...
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738 views

Child-Langmuir space charge law for non-zero cathode potential (non-zero initial electron velocity)

I'm trying to reconcile some conflicting results that I've found in publications that address the idea of the current in a vacuum diode in the case where the cathode has a non-zero potential, in other ...
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1answer
53 views

Tricky particle in an infinite potential well question

For a particle in an infinite square-well potential in an energy eigenstate, the probability distribution relating to outcomes of position measurements vanishes outside the square well and takes a ...
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1answer
119 views

Minima & maxima of Laplace's equation

I don't get the following sentence from David J. Griffiths' Introduction to Electrodynamics (the ambiguous sentence is in bold) Laplace's equation tolerates no local maxima or minima; extreme ...
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1answer
100 views

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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772 views

Bound states for sech-squared potential

I'm working on an introductory qm project, hope somebody has the time to help me (despite the length of this post), it will be highly appreciated. My goal is to determine the bound states and their ...
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3answers
58 views

What would be the capacitance of an unequal charged capacitor?

I searched for this question but I cannot get satisfactory answer. Say if we have a parallel plate or cylindrical capacitor and if I supply unequal charge to it how could I find its Capacitance. We ...
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1answer
56 views

Superpotential for Gaussian potential well? [closed]

so I am looking for the super potential of a Gaussian well, namely $V= -e^{-x^2/2}$, and the super potential has to satisfy the Riccati equation,$ − W′ ( x ) + W ( x ) = V ( x ) − a$. Somehow I ...
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5answers
163 views

The potentiality of the electric field

Could you please explain using just words why electric the field is potentially? I know the proof using integral: $$A = \int_{12}q\vec{E}\cdot{d}\vec{r} = qQ\int_{12}\frac{\vec{r}\cdot{d}\vec{r}}{r^3} ...
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1answer
312 views

In a positively biased PN junction, where do the injection carriers come from?

I am not quite understand i-v character of PN-junction diode. Here is the model in textbook. The PN junction diode can be divided into three regions. They are One depletion region near the PN ...
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1answer
78 views

Change in acceleration due to gravity because of rotation of earth [duplicate]

The formula above is the equation for acceleration due to gravity when earth rotates. G is the original acceleration. Can someone explain how this formula came?
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Can we create ladder operators for any potential? [duplicate]

I understand the mechanism for the harmonic oscillator, so can we generalize the ladder operator in order to work for any 1-D symmetric potential such as Gaussian potential well?