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Questions tagged [potential]

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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Some Questions regarding the Potential Difference

I have some questions regarding the potential difference : Question (1) : The potential difference is defined as the negative of the integral of E.dl with the lower limit being a and the upper limit ...
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Total charge for Dipole and Quadrupole moment

I have been struggling on what to put for $Q(total)$ in the equations for the dipole and quadrupole moment for the potential: $$ V_{quad}(\mathbf r) \approx \frac{2Qd^2}{4\pi\epsilon_0} \left( \frac{...
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Induced magnetic field in conducting sphere

The last day the teacher solved a problem and I did not follow all of his assumptions. We have a homogeneous conducting sphere in a magnetic field $$\vec{B}=B_0e^{i\omega t}\vec{e_z}$$. This applied ...
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Is this statement true for all conservative forces or just attractive conservative forces?

'Change in potential energy is always equal to the negative of the work done by a conservative force.'
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Energy measurement from position eigenstate

Given that the eigenstates of the position operator can be written as $\delta(x-x')$, and suppose we measure a particle in an infinite potential with walls at $x=0$ and $x=L$. I measure the particle ...
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Question about multipole expansion of electrostatic potential?

If I take a certain dipole and by dipole I mean that two charges of opposite sign differentiated by very small distance. And if I take the formula of multipole expansion of potential then I see no ...
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Electrical systems with multiple connections to earth - is earth modelled as one region of equal potential here?

In the picture we can see a realization of a TT-System, an electrical system with multiple connections to earth at different localiations. I allready know (from this question) that the coulomb-...
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1D Time independent Schrodinger eq. with limit

The one dimensional Schrodinger equation for an exponential potential $$-{\hbar^2\over 2m} \frac{d^2\psi}{dx^2}+-\alpha\frac{e^{-\vert x\vert\over\epsilon}}{2\epsilon}\psi=E\psi$$ I am interested ...
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Electric field and potential [duplicate]

Suppose we consider a point dipole i.e. an ideal dipole. At the origin the potential: $$ \phi(\mathbf r) = \frac{1}{4\pi\epsilon_0} \frac{\mathbf p\cdot\hat{\mathbf r}}{r^2}$$ is undefined due to ...
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Yukawa form of electrostatic potential with $\mu_{\gamma} \neq0$ (photon mass)

Yukawa form of electrostatic potential with $\mu_{\gamma}\ne 0$ (photon mass) is: \begin{equation} \varphi(r)=a\,\frac{e^{\mu_{\gamma}r}}{r}+b\frac{e^{-\mu_{\gamma}r}}{r} \end{equation} Since this ...
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Method of Images conundrum

My lecturer and I have found separately valid solutions to Poisson's equation in the region of interest for the following problem: Here is my interpretation of the boundary conditions: $$V(x,y,z \to ...
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Potential Flow integration (no-voice and very beginner!)

Let's say I managed to compute a velocity field that is divergence-free. How do I integrate it over time? meaning, I created a potential function, set v to be curl of potential function, so I have now ...
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Can we define potential for all conservative forces?

I know that defining potential for non-conservative forces is not possible and we can define potential and potential energy for conservative forces only. But can we define it for all conservative ...
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Electric potential inside a solid conducting sphere, next to other charges

The way I initially justified the potential inside a charged conductor to be $\frac{kQ}{R}\ for\ \ 0\le r\ <R$ was that from Gaus's law, you could determine that when you were a distance $r$ away ...
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Summing up very basic terms in basic electricity [closed]

My attempt to define following terms as per my understanding. I am currently at high school. Electromotive force (EMF): Potential between two terminals when open circuited. Wikipedia's ...
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Why does Jackson ignore the surface term in this integration by parts, in the electric potential of a polarized dielectric?

In Jackson's electrodynamics Page (153), it is given that the total potential is the sum of potential due to free charge and potential due to dipole. Therefore, \begin{align*} \phi(x) & = \frac{1}{...
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2answers
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Potential in open branch of a parallel circuit with grounding [closed]

If the switch is still open, what will the electric potential at Q be, i.e. negative, positive or zero? Is there a potential difference across the grounded point and point Q, or R3, even though the ...
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1answer
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Why is the magnetic potential inside the centre of a square wire zero?

Given a wire of square configuration, I found that the magnetic potential at the centre of that square is 0. I am a bit confused as to why this is the case, given that the magnetic field at the centre ...
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Does Ohm's law $V = IR$ mean voltage causes current, or does it just say that voltage and current are related?

I have read that Ohm's law, $V=IR ,$ just means that $V$ is equivalent to $IR ,$ not that voltage is the cause of current. This is similar to the interpretation of Newton's second law, $\mathbf{F} = ...
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1answer
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Particle in a box plus step (ground state)

I am trying to come up with a QM problem that: Can be solved analytically Contains a potential that is a sum of some analytically solvable potential and another contribution: $V'=V_0 + V$ Is then ...
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Would the voltmeters give different readings in a circuit with induced current?

$\def\vE{{\vec{E}}}$ $\def\vD{{\vec{D}}}$ $\def\vB{{\vec{B}}}$ $\def\vJ{{\vec{J}}}$ $\def\vr{{\vec{r}}}$ $\def\vA{{\vec{A}}}$ $\def\vH{{\vec{H}}}$ $\def\ddt{\frac{d}{dt}}$ $\def\rot{\operatorname{rot}}...
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Thermistor IV characterisitc

The circuit is a potential divider circuit with a NTC thermistor and fixed resistor. I know generally the IV characteristic for the thermistor however, I was given values of resistors voltage at given ...
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2answers
103 views

How does back emf occur if a system can’t do work on itself? [closed]

If a coil is connected to a battery and the current starts up, the electrons have to be moving at a certain speed through the wire and therefore have a certain kinetic energy. But if they are moving ...
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Why is the singularity not taken into account?

In this article "Reflections on Maxwell’s Treatise", Section 4.2, it says: He replaces $\mathbf{m}$ with a volume element of magnetization $\mathbf{M}\ dV$ , integrates over $V$ , and lets the same ...
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Why isn't electric potential infinite?

In my textbook, I've read that electric potential is the work performed to carry one unit of positive charge to electric field from infinite distance. We know that, W = Fs So here the distance is ...
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Question about the Lorenz gauge in classical electrodynamics

The Lorenz gauge is the gauge such that $$\nabla \cdot \mathbf{A} = -\mu_0\epsilon_0\frac{\partial\Phi}{\partial t}.$$ This condition dictates what $\lambda$ is in $$\mathbf{A}' = \mathbf{A} + \nabla \...
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Why can we pick the divergence of the vector potential? [duplicate]

I'm aware that the vector and scalar potential in E&M can be modified using a function $\lambda(t)$ in the following way: $$\mathbf{A}' = \mathbf{A} + \nabla\lambda,\;\; \textrm{ and } \;\;\Phi' =...
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What is the physical meaning of a pseudo-vector potential in a Dirac equation?

Consider a Dirac action with a pseudo-vector potential: $$S = \overline{\psi}(\gamma^\mu(\partial_\mu + i\gamma_5 A_\mu) + m_e)\psi$$ i.e. exactly like a Dirac equation with an electromegnetic ...
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Physics of Neuroscience - Action potential

I am confused about how to understand action potential in the context of physics. Are action potential and potential difference synonymous? If so why is it stated that an action potential 'travels' ...
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161 views

Sphere half-submerged on a dielectric

This is a classic problem in electrostatics with a twist, so I thought it could be useful for others here. I did have a problem with the integration at the end, but on general I think the idea can ...
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Relativistic Electric Potetnial

Suppose you have a particle of charge q circling the z axis in the xy plane. The orbit is centered at the origin and has a radius of $r_0$. The angular frequency of the orbit is $\omega$. Position of ...
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$\delta$ potential has highest probability for highest potential

I can't understand this intuitively. Figure 2.9 in Griffith's QM says that the wavefunction at $x=0$ for a delta function potential is $\sqrt{\kappa}$, and to the right it decays like $\psi_+=\sqrt{\...
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How can be $\frac{1}{4\pi R^2}\int_{S}V_{ext}(R)da= V_{ext}(0)$ physically explained?

I was working out problem 3.1 (4th edition) of Introduction to Electrodynamics by Griffiths, which asks you for the average potential over a spherical surface due to a charge located inside the sphere ...
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1answer
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Energy formula for finite potential well [closed]

The energy formula for infinite potential well is $$E=\frac{n^2h^2}{8ma^2},$$where $m$ is the mass of the particle, $a$ is the width of the well but in the case of finite potential well, I actually ...
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'Show that $E$ must exceed $V(x)$ for every normalisable solution of the TISE'. Surely you can show that this isn't true using exponentials?

In Griffith's this is a question, there's the clear answer which jumps out immediately: $$\frac{d^2\psi}{dx^2} = \frac{2m}{\hbar^2}(V(x)-E)\psi.$$ That is, if E is less than V the second deriviative ...
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Is there any physical scalar potential where $U$ is also depends on $\dot q_i$s?

In the book of Classical Mechanics by Goldstein, at page 21, while deriving the Lagrange's equation, when the external forces are derivable from a scalar potential $U$, the author implicitly assumes ...
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Why is a specific voltage limit needed to light a bulb in an electric circuit

The battery provides a potential difference between its terminals that allow acceleration of the electrons in the circuit, i.e the potential energy gets converted to kinetic energy, these electrons ...
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Confusion about Change in Integration Variable [closed]

I'm working through example 3.2 of Zangwill's Modern Electrodynamics and have come across a change in integration variables that I just can't seem to get. The example has two different change ...
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How do I connect a four way key in a potentiometer?

How do I connect (which wire to which terminal) a four way key to a Potentiometer to compare the EMF of two cells. Circuit diagram and a four wayway key is shown in the pictures.
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Determine electromagnetic potentials that satisfy Coulomb and Lorenz gauge condition

In our physics lecture, we did the following example of constructing potentials $\vec A$ and $V$ that supposedly satisfy both the coulomb ($\nabla \vec A=0)$ and the lorenz condition $(\nabla \vec A+ \...
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3answers
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Relationship between potential and electric field

There are a number of ways to solve this problem but was interested in doing it via the formula: $$ ∇V = -E$$ However the potential on the line due to -q is $$ \frac{-q}{4\pi\epsilon_0((0.5d)^2+y^...
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3answers
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General Definition of Potential in Circuits with Time-dependent Fields?

Electric potential is a very common observable to measure (especially in electro-engineering fields). It is measured using a multimeter, and thought of as the energy per charge that one charged ...
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Calculating the potential of a uniformly charged spherical shell

This question only really has to do with how to get the correct denominator in the integral. The object in question is a uniformly charged sphere of radius $R$. I'm going to choose as my reference ...
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2answers
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Is a *difference* of potential energy relative to a frame of reference?

If we consider an electrical field, or a gravitational field, and two points in this field, is the difference of potential between this two points depending of a frame of reference ? It seems to me ...
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Arriving at the Quantum Mechanial Potential From The Energy Eigenvalues [duplicate]

In Quantum Mechanics, we know that given a potential we can solve the eigen value problem to find out the energy eigen values and eigen functions. Now suppose in an experiment we have information only ...
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Understanding conformal mapping in electrostatics

I'm trying to understand the use of conformal mapping to solve problems in electrostatics. To better understand the idea, I'm trying to learn how to solve this example (but you can propose any other ...
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3answers
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Why do electrostatic potentials superimpose?

I've been trying to convince myself that the assertion that I've read in basic E&M books (Halliday & Resnick, Purcell), and even Griffiths, that the electrostatic potential at a point in space ...
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2answers
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Calculation of Gravitational Potential at the centre of the cube [closed]

I came across this problem in a test and have been able to come up with a solution however I am unsure if it is correct. I started by building a cube of twice the initial dimensions to bring point P ...
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3answers
95 views

Can Quantum Mechanical Potential have a Probability Distribution

I am currently in my second semester of undergraduate quantum mechanics. We have recently starting discussing two particle systems, usually in relation to spin interactions. In all of our calculations,...
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2answers
120 views

Central Forces: Newtonian/Coulomb force vs. Hooke's law

We know that a body under the action of a Newtonian/Coulomb potential $1/r$ can describe an elliptic orbit. On the other hand, we also know that a body under the action of two perpendicular Simple ...