# Tagged Questions

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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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 ...