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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Quadrupole configuration

The general solution to the 2D Laplace equation, $\nabla^2 \psi = 0$ is \begin{align} \psi(r,\theta) = P_0 \ln r + \sum_{k = 1}^\infty \dfrac{Q_k \cos(k\theta)+R_k\sin(k\theta)}{r^k} \end{align} The ...
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electric potential and other potentials

We know that without potential difference no electric current can flow.If two conductors carrying positive and negative charge respectively then the first one will have positive and the rest one will ...
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Physical Nature of the electric field of the current in a circuit

As most of us know that the electric current in a conductor is due to free electrons moving in the conduction band of metallic conductors. What makes them move ? An electric field of course. ...
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How does commutation between the hamiltonian and angular momentum operator (squared) imply conservation of Angular momentum?

So we are looking at central potentials in QM; The lecturer poses the question, when is $\textbf{L}$ conserved? He then considers the commutator of $\hat{H}$ and $\hat{L^2}$. We have; ...
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Will there be a potential difference between two conductors if there is same charge between them but the magnitude of charge is different?

By same charge I mean that same nature of charge i.e " Both positive or Both negative " . To be more specific consider two plates both of the plates are held face to face close to each other much like ...
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Can charge flow to a neutral body?

If an electrically positive object is kept with a neutral object, in which direction will charge flow? Will charge flow from positive to neutral until both have equal charges, or will nothing happen ...
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Electric Potential due to Sphere when cavity is at arbitrary position [on hold]

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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Applications of almost periodic functions [closed]

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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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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Gravity well and constant total energy in circular orbit [closed]

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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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?
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How much energy does an electron have when it is situated right next to a negative point charge?

The formula for potential energy regarding point charges is $E=kQq/r$. If $r=0$, then will the energy be approaching infinity? But what about an electron in a parallel-plates situation where it is ...
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Finite two-dimensional potential square well [closed]

I'm trying to solve the Schrodinger equation $$ -\frac{\hbar^2}{2m}\nabla^2 \psi+V(x,y)\psi(x,y)=E\psi(x,y) \tag{1}$$ for the finite two dimensional potential square well, that is, where ...
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What is the gravitational potential at the centre of the earth?

Assuming the gravitational potential at infinity to be zero and ignoring the other celestial bodies, what is the gravitational potential at the centre of Earth? As no force acts at infinity the ...
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Non-dimensionalize Schroedinger's equation for this potential

I am having trouble non-dimensionalize this S.E. in order to solve numerically.. the potential is $$V(x)=-V_{0}/(1+x^2/L^2)$$ we know that $A = V_{0}/\hbar \omega$ is dimensionless, and $B = ...
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How do we find the number of bounded states in this potential?

for the potential $$V(x)=-\frac{1}{1+\frac{x^2}{m^2}}$$ we can approximate the wave function and bounded state accurately for $x << m$ as simple harmonic oscillator, so what are we gonna do if ...
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Guess the wave function in a given potential

Are there any techniques in guessing the ground state wave function in any given potential? For example, for a given potential like $$ \frac{1}{1-x^2}$$ or $$ \frac{1}{1-x^3}~?$$ I know wave ...
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Work done in moving a body out of Gravitational influence

By "out of Gravitational influence ", I suppose it's meant that Gravity of a planet has no effect whatsoever on the body. Am I correct? Could we do it by making the object reach Escape Velocity by ...
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Mass hanging from spring: potential energy [closed]

I have encountered a problem with a mass $m$ hanging from a spring. I want to find the maximum distance it will be stretched from the spring's equilibrium. At the maximum distance the spring is ...
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Is electric potential a field?

I'm just learning about electric potential in my second-semester physics class. My textbook is emphasizing the fact that electric potential is a property of the source charges and that I'll soon learn ...
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Retarded potentials and fields

Why can't we use retarded times to make an expression for retarded fields instead of potentials? As far as I know it doesn't work, since the solutions produced ("retarded fields") don't satisfy ...
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What is the potential difference between $a$ and $b$ in this basic circuit, when the switch is open? [closed]

My professor says the potential difference between $a$ and $b$ is the difference between the voltages on the top left capacitor and the bottom right capacitor. My friend and I however both think it's ...
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Is negative energy(work) less than positive energy(work)?

We cannot talk about magnitudes in case of work, but if someone did (-42 J of work) by stopping a moving object. And if someone did 42 J of work, by pushing something, who did more work? Does it ...
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Bound states of Dirac Delta function in infinite well

If there is a potential of $-\alpha\delta(x)$ for $-a<x<a$ and $\infty$ elsewhere, and the energy of the system is less than 0, then I'm trying to find the wave function. From the Schrodinger ...
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What is the criterion for a vector field (dim > 1) to be conservative?

We know that if the curl vanishes: $$ \nabla \times \vec{v} = 0$$ then the field is irrotational and is conservative, but what about in higher dimensions than 1? The cross product is not defined ...
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A false proof of drag force being conservative

Consider a particle moving along some trajectory in the $x$-$y$ plane, in a viscous medium. Then its equation of motion is given by: $$\mathbf{F}_d = - b \mathbf{v} .$$ it's well-known from the ...
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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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Is “applying a voltage” the same as “applying a potential” to an electrode?

From what I understand, voltage is the potential difference, but it seems like the terms are used interchangeably. This is confusing me because I am only just learning what these terms mean. I'm also ...