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 of Point Charge (sign problem)

This question has been asked before, but the answers didn't clarify the problem for me, so I thought I might ask again. It's really a simple question. Let's say we're calculating the electric ...
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Calculation of electric potential in Geiger-Müller tube [closed]

We are given a cylindrical rod with linear charge density $λ$, and a coaxial cylinder with linear charge density $-λ$, as shown in the picture. We are to show that the potential difference between ...
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Normalization of a wave function in quantum mechanics

A more simple question, so I am watching a quantum mechanics lecture on potentials of free particles and am doing the general solution of schrodinger's stationary equation for a free particle when I ...
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Equipotential surface paradox

Consider a point charge +q as shown below. Now consider a equipotential surface and two points in it A and B. now the potential at A is equal to potential at B. If we now integrate (E.ds) from A to ...
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Perturbation theory for a particle in a weak potential

I have a basic question about quantum mechanics, maybe it has a basic answer. Take a free particle in a quartic potential, $L=\frac{1}{2}\dot{x}^2-\lambda x^4$ This is massless $\phi^4$ theory in ...
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How do integral representations of $\mathbf A$ and $\Phi$ satisfy Lorenz condition?

The following are the integral solutions of the potentials, obtained from the retarded potentials (by a Fourier transform): $$\mathbf A (\mathbf r) = \frac{\mu_0}{4\pi}\int_V \frac{\mathbf J (\mathbf ...
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A question relating to the Higgs boson scalar field

Just wondering. The potential for the Higgs boson is given by: $$ V(\varphi)=\lambda(\varphi^{2}-v^{2})^{2} $$ where $v≃$ 246 GeV is the vacuum expectation value required to explain mass in the ...
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Why doesn't $σ_xσ_p$ change with the width of the well in the infinite square well problem (intuition)?

I calculated that the product of the uncertainty in position $\sigma_x$ for the ground state of an infinite square well of width $L$ with the uncertainty in the momentum $\sigma_p$ for the same state, ...
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Doesn't any massive conductor look like “ground” to an AC supply?

I've been puzzling over this excellent answer to the perennial "Why don't I get shocked by a hot wire if I'm not grounded?" question. The orders of magnitude just don't seem right for two reasons: ...
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Method of image charges (semisphere on a metal)

I'm currently trying to study ahead for the upcoming semester since I'm on break and I'm stuck on the method of image charges. I've tried watching some youtube videos on that topic and I thought I ...
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Phase shift calculation in quantum scattering for potential $V=a/r^2 $. Neumann function missing

I'm tasked of finding the phase shifts for scattering from a potential of the form $V=a/r^2$. My thinking is as follows. For this specific potential I can bring the differential equation to the form: ...
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80 views

Does the kinetic energy change depending on the direction of the velocity? [closed]

The kinetic energy is calculated with the following formula: $$E_k = \frac 12 mv^2$$ Does $v$ represent the value of the velocity? I mean, if you have a specific direction of the velocity is the ...
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Relation between gravitational field and gravitational potential

gravitational field is the negative differential of gravitational potential . now gravitational potential due to a particle at a distance r is -Gm/r where m is the mass of the particle . If i take the ...
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2answers
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Electric Potential from separating charges [closed]

Say there are 2 charges, one of charge C, and the other with a charge of -2C. C=1.5*10^-6 C. Initially, they are right next to each other. I pull them apart to a distance of 15 cm. So I can use the ...
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External and internal multipole expansion for axisymmetric potential - the region of convergence

Say, we have a system of electrodes exhibiting symmetry around a certain axis. We know the explicit expression for the potential on the axis $\phi (z)$. We want to find the potential for any point in ...
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1answer
77 views

Gravitational potential energy lost by an object falling on the earth [closed]

I am stuck on this simple question: g is the strength of the gravitational field at the surface of the Earth; R is the radius of the Earth. Show an equation describing the potential energy ...
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1answer
36 views

Static pressure inside a planet made of a fluid

How can we find the static pressure at a distance r from center of the the planet made of liquid of constant density d. My attempt: First I tried to find the total gravitation force due to a sphere ...
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Does the material of a charged sphere affect electric potential?

Suppose we have two solid spheres, both with an equal total charge $+Q$ and equal radius, and the potential being zero infinitely far away. We know that a uniformly charged sphere can be treated as a ...
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The time evolution in Dirac delta potential [closed]

We know that the dirac delta potential has exactly one bound state. If the potential strength suddenly changes a value, the bound state should evolve to the new bound state, how to describe the time ...
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What exactly is potential difference? What are the factors that effect it?

I am asking this question because at first I thought that this concept was pretty clear to me, but it is not. So, my first question: Is potential difference only a property of an electric field? If ...
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1answer
44 views

$P=V^2/R$ confusion

I am confused on how to apply the formula $P=\frac{V^2}{R}$ If I am given a bulb say with power 60W and it is connected to a supply of 120V. Then the resistance of the bulb is 240$\Omega$ but if ...
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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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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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126 views

Electric Potential due to Sphere when cavity is at arbitrary position [closed]

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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1answer
65 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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1answer
45 views

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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136 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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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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1answer
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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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1answer
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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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1answer
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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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1answer
52 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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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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1answer
84 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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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 ...