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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Where is the zero electric potential energy point?

Doe the point of the electric potential energy of zero is defined by human or dominated by the indefinite integral of the electric force?
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33 views

Why is the energy shift due to a 'sagging' potential negative and independent of box size?

Consider a box of width $L$ and the composed of the following potential $$V(x)=\frac{V_0x(x-L)}{L^2}, x\in[0,L]$$ and $V(x)=\infty$ elsewhere. Using perturbation theory - with a square box as the ...
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Charge Magnitude Based on Isoline Spacing

Suppose we have two positive charges of unknown magnitudes. We are given the isoline map (the equipotential lines) for the two-charge system. One has isolines more "squashed together" (more closely ...
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Electric potential inside a solid sphere [on hold]

We have charged solid sphere and have to find electric potential inside it. I tried it by two methods, By integrating $\int \vec{E}\cdot\text{d}\vec{r}$ for both outside and inside the sphere ( ...
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860 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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What is the charge density for line and surface charges?

In electrostatics it is common to see line, surface and volumetric charges being described differently. A line distribution is a function defined on the line, a surface charge distribution is a ...
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245 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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170 views

What is a Hulten potential?

What is the Hulten potential? (also spelled Hulthén, Hulthen, and Hultén.) When is it used? How is it derived? I vaguely heard about in the context of neutron synthesis / quantum mechanics.
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What is the answer to the numerical given below? [on hold]

An electron revolves along a circular path of radius 20cm with constant angular velocity 120 rad/s about an axis passing through the centre and perpendicular to the plane of the circle. if the ...
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30 views

How to calculate the vector potential $A$ inside an infinite cylinder using Poisson's equation? [on hold]

Poisson's equation is : $$ \Delta \boldsymbol A = - \mu_0 \boldsymbol J$$ we want to calculate $\boldsymbol A$ inside an infinite cylinder with radius $a$ and the current density is $\boldsymbol ...
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29 views

What is the relationship between potential energy and electrical potential?

I actually always thought this was trivial, now I am not so sure. For a potential $\phi$ the potential energy is $V=q\phi$ where q is a test charge. Now I am thinking this may work differently in two ...
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118 views

If systems minimize their potential energy, why do people climb mountains?

A person climbs a mountain. They convert the stored chemical energy of food in their body and back pack into heat energy on the mountain, and gravitational potential energy as they move towards the ...
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35 views

What happens to the electric field at the boundary of a dielectric?

The question in the title is a broader one, but for now, I want to confine myself to the following problem. I have the task to find the potential difference between points A and B shown in the ...
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1answer
33 views

Understanding electric potential in the context of gravitational potential?

I'm trying to understand the concept of electric potential and the significance of an electric field being related to the gradient/derivative of an electric potential. I found this question that ...
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1answer
133 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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35 views

What is the difference between length and velocity gauge when it comes to a dipole approximation?

Lets say we have plane wave with $\vec E$ perpendicular to $\vec k$. The dipole term will come from $\vec A\cdot \vec p$. Is the electric field longitudinal in the length gauge for the dipole ...
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I don't get the idea of potential in a capacitor [closed]

First off, what is meant by the potential of the conductors? Also potential difference between the two conductors is a function of distance from either right? Then why does it have an exact value. For ...
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4answers
548 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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Potential difference between point on surface and point on axis of uniformly charged cylinder

Question: Charge is uniformly distributed with charge density $ρ$ inside a very long cylinder of radius $R$. Find the potential difference between the surface and the axis of the cylinder. Express ...
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1answer
44 views

What is the difference between the potential difference and potential energy of an electron?

What is the difference between the potential difference and potential energy of an electron? Let's take an example the potential difference (PD) across a resistor. if there's a current flowing, the ...
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1answer
279 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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Motion of an electric charge within an electric field with two electric charges

Assume that air resistance and gravity are negligible and the only significant force acting in the scenario is the electric force. There are two electric charges, both with an equal and positive ...
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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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Particle in a Spherically Symmetric Box [closed]

Problem The spherically symmetric potential energy of a particle with mass $m$ is given by $V(r)=0 $ if $ a<r<b$ $V(r)=\infty$ elsewhere where $r^2 = x^2+y^2+z^2$. (a) ...
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336 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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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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If the potential drops across a resistor (=$V_d$) then shouldn't the potential difference be the $\epsilon-V_d$?

Consider the following circuit: Suppose a current $I$ travels in both the branches, then as the current $I$ passes through the $60$ ohm resistor, there will be a drop in the potential of $60I$. ...
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459 views

Potential Difference of a wire?

Imagine a circuit with only a 12 Volts battery and a wire connecting the ends of the battery. Point A and point B lies on the wire. What is then the potential difference between point A and B if the ...
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1answer
39 views

Can an electromagnetic potential be in two gauges at once?

I have a plane wave vector potential found using the free field form of Maxwell's equations and the Lorentz gauge: $\vec{A}(\vec{r},t) = \vec{A}_0 e^{i(\vec{k}\cdot\vec{r}-\omega t)}$ If I take the ...
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Relationship Gravitational Potential and the Tangential Velocity of a Satellite

So gravitational potential is given by $V(r)={\frac{GM}{r}}$ and the tangential velocity of a satellite is the square root of $V$, i.e. $\sqrt V$. So how do these two relate, if at all?
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2answers
30 views

Electric potential inside a shell

Inside a shell, electric field is zero. Then does it have a constant electric potential inside the shell? If $V=\dfrac Ed$, then since field is zero, potential should also have been zero. Please ...
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6answers
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What is the origin of the Dirac delta term in the dipole electric field?

I am a bit lost how one has deduced the formula for electric field with electric dipole because of some inconsistency between different sources. The Wikipedia article contains a delta function in the ...
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3answers
65 views

What does earthing do in electrostatics?

What does earthing actually do in electrostatics? As far as i know, it simply sets the potential of the object that is earthed to zero. To explain my question further with an example, consider this ...
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71 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
27 views

Relation between potential difference and electric field

I was reading an article about resistivity when I faced this equation: $$V_P-V_O=\int_P^O E.dr$$ The equation is in one dimension and $P$ and $O$ are points on the $x$ axis. The Electric field is ...
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Potential Energy of Point Charges in a Square [closed]

So, an AP Prep book for the Physics 2 test has the following problem: My reasoning is as follows: The total potential energy = the sum of the PE of each of the 4 charges Which will equal 4x the PE ...
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How is the curl of the electric field possible?

Taking the curl of the electric field must be possible, because Faraday's law involves it: $$\nabla \times \mathbf{E} = - \partial \mathbf{B} / \partial t$$ But I've just looked on Wikipedia, where it ...
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3answers
650 views

How to derive the expression for the electric field in terms of the potential?

How can I derive that $$\vec{E}=-\vec{\nabla}\phi-\frac{\partial \vec{A}}{\partial t}$$ where $\phi$ is the scalar potential and $\vec{A}$ the vector potential?
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Since a dipole has some potential energy,it should be able to do some work !? What is it?

We say a dipole has potential energy.What work can a dipole do ?.For eg : A ball on a shelf has a PE because it has the potential to fall down and do some work on the ground if shelf wasnt there.What ...
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Potential energy of a dipole in a uniform electric field convention?

When finding the potential energy of a dipole in a uniform electric field, I was told by my lecturer that the convention is that the potential energy is 0 when the dipole moment and electric field ...
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1answer
456 views

Dirac Delta Potential and bound/scattered states

Why does the attractive Dirac Delta distribution (function) potential $V = \alpha\delta$(x) (for negative $\alpha$) yield both bound AND scattered states? Is this due to the definition of the Dirac ...
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43 views

How to find the minimum value of potential in QM?

In MIT problem sets I followed a solution of an exercise which focuses on odd-parity energy eigenstates in finite square well. The point of problem is how to know or find the minimal value of ...
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1answer
45 views

What role does the center of mass play in this situation? (electric potential)

Four masses $10\ \mathrm{g}$ each are tied together by $10\ \mathrm{cm}$ strings to make a square as shown. Two of the masses carry a charge of $2\ \mathrm{\mu C}$. The string between the two ...
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84 views

Relation between Electric field and potential

I am unable to understand from this - sign comes. Which step I have done wrong?
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117 views

Scalar and Vector Potential

I am a physics undergraduate student currently studying electromagnetics. I have previously studied electrostatics and magnetostatics yet the concept of scalar potential, $V$ and the vector potential, ...
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38 views

How can current remain same when potential difference decreases?

According to Ohm's law, $$\text{potential difference} = \text{resistance}\times\text{current}$$ Also, current remains the same everywhere. Now when current passes through a bulb, the electric ...
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180 views

Explain confinement energy for a particle in a box

What is a "particle in a box"? How does confinement energy equal kinetic energy? How does confinement energy relate to the spectrum energy (the absortion/emission between energy)?
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Potential energy of a shell & point system

Consider the system of a point particle with charge $q$ and a spherical shell with uniform charge $Q$ and radius $R$ whose center is a distance $r > R$ away from the point particle. I'm trying to ...