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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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 there,...
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352 views

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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62 views

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 ...
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79 views

Finding the electric and magnetic fields from the vector potential $\vec A=\vec{E_0} e^{i(\vec k\cdot\vec r-\omega t)}$

I am trying to find the electric and magnetic fields from the vector potential $$\vec A=\vec{E_0} e^{i(\vec k\cdot\vec r-\omega t)},$$ I know $$\vec B=\vec \nabla\times \vec A$$ and $$\vec E=-\vec\...
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Is gravitational potential always defined for a system?

I have studied about Gravitational potential energy ($GPE$) and Gravitational potential ($GP$). ..while everywhere it is said that $GPE$ is always of a system as it depends on the configuration of the ...
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141 views

George Green's derivation of Poisson's equation

I was reading George Green's An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism, and I got confused on one step in his derivation of Poisson's Equation. ...
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40 views

Integration path with opposite direction from the unit vector

The task is to calculate the voltage between points $M$ and $N$ if the electric field vector is known to be $\vec{E}=\frac{V_0\cdot x^2}{a^3} \cdot \vec{i} + \frac{V_0 \cdot y}{a^2} \cdot \vec{j}$, ...
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Lorenz Gauge Dipole Potentials Formulation In SI Units? [closed]

After hunting in vain* for a documented closed form solution (ie: no integrals or differentiation in the formula) for $\phi$ in terms of A under the Lorenz condition, of an electrically short dipole (...
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93 views

Electric field and electric scalar potential of two perpendicular wires

So, I've been trying to come up with an idea that seems plausible to me for the last half week or so, but I'm stuck and I can't seem to get anywhere with this problem. The problem is as follows (...
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139 views

Defining gravitational potential

I recently came across the definition of gravitational potential where ..... Suppose a particle of mass $m$ is taken from a point $A$ to $B$. Let $U(A)$ and $U(B)$ denote the gravitational ...
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50 views

how to test whether a potential gives rise to a force field

A preamble to my problem. I have measured a discrete vector field, $\vec{F}(x,y) = (F_x(x,y), F_y(x,y))$ representing some forces i'm currently researching. $\vec{F}$ is the average of forces acting ...
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23 views

find cylindrical multipole coefficients

How does one find the coefficients to the cylindrical multipole expansion? I have the harmonic function $\omega = \dfrac{f(\theta)}{\sqrt{r}}$ where $f(\theta)$ is function with a period of $2\pi$ ...
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1answer
65 views

Zero Energy State of a Mechanical System? [closed]

Would a mechanical system in a particular frame (when I say mechanical I mean pulleys, elastic strings, etc.) that has no potential energy (loaded springs, pulled back elastic, hanging weights, etc.) ...
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1answer
52 views

What is the relation between ‘Electric Potential’ and ‘Electric Potential Energy’?

What is the relation between ‘Electric Potential’ and ‘Electric Potential Energy’?
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87 views

Potential vs Potential Difference for a line charge

How would I calculate potential for an infinite line of charge a distance 'r' away from it? What does the reference point for potential difference mean? I know delta v = Q/(2pi*epsilon0*L)*ln(r2/r1) ...
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91 views

Are the boundary conditions for a sphere in an electric field affected by its charge?

Find the potential outside a charged metal sphere (charge $Q$, radius $R$) placed in an otherwise uniform electric field $E$ I know this question can be solved by the method that so called ...
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1answer
80 views

Work done by Electric Field vs work done by outside force

I'm confused as to the signage of the equation: W=qv, W=-U, W=-qv? When is work positive? When is it negative? Why is this different for the work done by the electric field vs the work done by an ...
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Gauge Permitting c Magnetic Vector and Instant Electric Scalar Potentials?

The Lorenz gauge requires c propagation of both scalar and vector potentials. The Coulomb gauge requires instant "propagation" of these potentials but is stated in such a way as to permit c ...
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189 views

Multipole expansion in cylindrical coordinates

I am seeking the general solution for the Laplace equation in cylindrical coordinates or $$\nabla^2 \omega = 0. $$ In several texts, the general solution can be found via separation of variables ...
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1answer
92 views

Pauli's exclusion principle and square well potential [closed]

Consider an infinite square potential well with potential $$V(x)=\begin{cases} 0 & \text{if} -a<x<a\\ \infty & \text{otherwise.}\\ \end{cases}$$ The stationary state energies for a ...
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Particle in a box: value for wave function $u(x)$ when potential $V(x)$ is infinity

The time-independent Schrödinger equation (TISE) is: $$ -\frac{\hbar^2}{2m}\frac{d^2 u(x)}{dx^2}+V(x)u(x)=Eu(x) \hspace{15pt}$$ where $E$ is a constant. Imagine now a infinity potential well as ...
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1answer
66 views

Why does the Gravitational Potential energy formula indicate that heavier masses in the same point in the field have lower potentials?

$$ U = -\frac{Gmm_E}{r} $$ Intuitively, it'd appear that the further away two objects are, the greater their gravitational potential, and this is confirmed by the gravitational potential formula. The ...
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1answer
63 views

What is voltage in a circuit?

What is voltage in a circuit? We just started learning about electricity in my school. From what I understand; potential is potential energy per Coulomb and voltage means difference in potential. So, ...
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172 views

How to compute Gravitational potential energy

Find the potential energy of a system of four particles placed at the vertices of a square of side $\ell$. Also obtain the potential at the centre of the square. In the question above can ...
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66 views

Deriving Konopinski's Operational Definitions of Scalar and Vector Potential

In "What the electromagnetic vector potential describes", E. J. Konopinski asserts: Operational definitions of Φ, A should now be expected to stem from the equation of motion (2) when it is ...
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1answer
256 views

Electric Potential for Concentric Spherical Shells

If you have a charged point ($q_1=+1$) inside an initially neutral spherical shell ($q_2=0$), how would you find the following: (A) Potential at the outer surface of the spherical shell? Would it be ...
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90 views

Electric Potential for concentric spheres and charged surface

A few conceptual questions about a charged sphere inside an initially neutral spherical shell and about uniform E for a charged plane. (A) How would I go about calculating potential at a certain point ...
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2answers
466 views

Can the electric or gravitational potential be discontinuous? Why?

I was solving the Laplace's equation for the charger thin spherical shell and noticed that the field is discontinuous at the surface (inside it is zero and outside it is proportional to $1/r^2$) but ...
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3answers
138 views

Why doesn't the volume integral vanish?

I am reading Galactic Dynamics by Binney and Termaine, and I'm struggling with the following passage. According to Poisson's equation the resulting change in potential $\delta\Phi(\mathbf x)$ ...
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2answers
59 views

Gravitational potential and intensity

Why don't we calculate gravitational field/intensity of a point due to a disc directly? We first calculate the potential then calculate the field by differentiating with respect to $dr$. Why don't we ...
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1answer
40 views

Electrolysis and actual electrode potential (using a supercapacitor)

For an electrolytic cell, the voltage source Vs, does not contribute directly to the potential on the electrolytic electrodes. Vs determines the current and can add charges to the electrodes. This can ...
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Electric field and electric potential

I have a question about electric field inside hollow spherical conductor. I think I understand the concept of Faraday Cage that protect the cavity to get any electric field from an external source. ...
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94 views

Finite square wall with $E > V_0$

I'm working through a problem for homework and feel as if there is a typo or I am confused. The problem is with a one sided finite square wall such as this: So the energy is more than $V_0$. I'm ...
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1answer
96 views

Is it okay to put singularities into the wave function to test behavior around unstable potentials? [closed]

$$ \psi(r)=\sqrt[4]{\frac{ a}{8\pi^3 }}\frac{ \exp (-a r)}{r^{1.25}} $$ The wave function above is an example of a function that is normalizable in 3D space and $r=\sqrt{x^2+y^2+z^2}$. $$ -\psi ''(r)...
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The dipole moment P in a metallic sphere

A metallic sphere is in a homogenous field $\vec{E}=E \cdot \vec{e_z}$. Put a dipole moment P at the origin, so the total potential is constant on a surface of a sphere with radius $a$. Which $p$ is ...
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220 views

Potential difference between 2 points in a loop containing changing magnetic field = 0?

I came across this question in an exam. The answer to this was given as YES. But I think otherwise. They say between A and B, there is zero potential difference. But if i simply alter the diagram a ...
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Why do wider double wells have a lower $\Delta E$ than thinner ones?

In this diagram, in which an $n=1 (E_{1})$ and $n=2 (E_{2})$ wave have been superimposed, the probability density of the new, combined wave changes with time. The period of its shifting density is ...
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movement of water in plants

Books say that water moves from places with a high water potential to places with a low water potential. The movement of water in plants are explained because water potential is lowest in leaves and ...
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1answer
50 views

Lower Voltage = Higher Potential?

I am doing problems from a textbook and one of the questions asks to determine where the higher potential is. (b) Find the potential difference between the points on the axis at and which of ...
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95 views

How do you find potential by Lagrangian formalism?

Suppose a ball is falling towards earth and hence by Lagrange equation we can find $T$ and $V$ where $V$ is $mgh$. But we know $V$ only because we know $F = mg$. Now since Lagrange equation doesn't ...
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1answer
19 views

What are the potentials of a battery with respect to earth?

Assume an open-circuit voltaic cell. We know that the cell maintains a potential difference between its terminals. That is $V_+ - V_- = E$. Now, if I connect $(-)$ to earth using the earth terminal ...
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217 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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280 views

Why not use the magnetic scalar potential?

In electricity and magnetism, we use the scalar potential to derive the electric field and the vector potential to derive the magnetic field because $\nabla\cdot B=0$ and $\nabla\times E=0$. I was ...
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1answer
83 views

What mistake am I making in plotting this graph of effective potential for the Earth-Moon system?

I am trying to create a graph of effective potential for the Earth-Moon system in Excel. It should result in a graph that looks like this: But this is not what I end up with. (I've made a Google ...
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What does Potential Difference between a load/resistor mean?

Guys this has been bugging me for ages and all the answers i found online were unsatisfactory. My questions is, what does difference in potential or potential drop after current passes through a load/...
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1answer
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Potential on a uniform

My doubt is in the part where he sets $V=V_s - \int{E dr}$. My idea is that he is summing two potentials, from the surface, and the one he's trying to calculate with the integral. Is that right? If so:...
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Does magnetic induction produce potential across zero resistance wire?

If magnetic field is increased at a constant rate inside a zero resistance wire loop, then, according to Faraday's law , $$\varepsilon = \frac{dΦ}{dt} $$ Thus, a potential difference is produced. ...
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Significance of imaginary mass

Can real mass be thought of as producing a deformation in spacetime leading to a stable equilibrium (valley curve in gravitational potential energy) of the massive body, and imaginary mass as similar, ...