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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438 views

Why electric potential requires absence of acceleration?

As of 28/05/2019, Electric Potential is defined in Wikipedia in the article with the same name as: The amount of work needed to move a unit of positive charge from a reference point to a specific ...
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1answer
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Is electric potential just the sum or measure of Electric Potential Energy for a given unit of matter with electric change?

I understand Electric Potential as follows (I "synthesized" the definition from different definitions I found online): The sum of Electric Potential Energy for a matter particle with an electric ...
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1answer
52 views

Showing $ \nabla \cdot \mathbf A = 0$ using integral formula

In Coulomb gauge the vector potential is chosen so that $ \nabla \cdot \mathbf A = 0$ and we find $$ \nabla^2 \mathbf{A}=-\mu_0 \mathbf j $$ The solution to which is $$ \mathbf A(r) = \frac{\mu_0}{4\...
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215 views

Even and odd solutions to time independent Schrodinger equation on symmetric potential

I have to solve the following problem: Consider the potential well: $$ V(x)=-V_0, \hspace{10px} |x|<a/2 $$ and $0$ everywhere else. $a$ is also a positive constant and so is $V_0$. Find the ...
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33 views

Connecting one lead of capacitor to a certain charged object (to get a potential difference)

Setup-A charged sphere , connected to one plate of capacitor , other lead of capacitor is free. Question-Will the capacitor plates go through a charge redistribution ? Arguments/Counterarguments-I ...
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3answers
80 views

Is a complete circuit required for capacitors to redistribute charges?

Suppose I have two capacitors of different capacitance $C_1$, $C_2$and they have been charged prior connecting by voltage of $V_1$ and $V_2$ respectively the positive plate of one capacitor is ...
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1answer
53 views

Work done in moving a charge in circuit?

Why is the work done in moving a charge from one point to another in a circuit through any path the same even though heat and other losses are there?
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1answer
52 views

How do you measure voltage from first principles? [closed]

I've always wondered if you were thrown back in time with just my cell phone, how could I charge it... I know how to make electricity, but how do I check the voltage if all I have access to is, shall ...
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Work done by battery?

Why the work done by a battery is Q*V where V is emf of battery and Q is charge that is made to flow in circuit?please explain detail? explain and write the formulas
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122 views

Why the electric field on the surface of charged spherical shell of radius $R$ and charge $q$ is $\frac{kq}{R^2}$?

As we know the electric field at a point due to charge $q$ is equal to $\frac{kq}{r^2}$ where $k$ is the constant of proportionality and $r$ is the distance between the charge and the point (where we ...
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57 views

Why do terms in a field theory Lagrangian that are polynomial in the fields collectively called the “potential”?

Field theory Lagrangians are often of the form of a kinetic term plus a source term minus a potential term. How do we know that the potential term is a polynomial in the fields? On a related note why ...
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243 views

Why is choosing a suitable thermodynamic potential important?

Say we are undergoing an isothermal process that eventually settles at equilibrium. $F$ will minimize at equilibrium, and if the entropy of the system is not held constant $U$ will not. Why do we care ...
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Proving thermodynamic potentials minimize at equilibrium

Is there a way to prove, for instance, $F$ minimizes at equilibrium for isothermal processes by looking at the equation $F = U - TS$ or must it be derived by using a thermal reservoir and analyzing ...
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What are 'external parameters' in Thermodynamics?

According to a Wikipedia article on Thermodynamic potential: When the entropy $S $and "external parameters" (e.g. volume) of a closed system are held constant, the internal energy $U$ decreases ...
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1answer
68 views

Energy density in electrostatics - definition [closed]

Background: It can be shown that the potential energy of charge distribution can be calculated by $U = \frac{1}{2}\int_V \rho(r')\Phi(r') d^3r' $ by means of integration by parts and the poisson ...
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Please clarify a doubt in the article: Reflections in Maxwell's treatise

While going through an article titled "Reflections in Maxwell's treatise" a misunderstanding popped out at page 227 and 228. Consider the following equations $(23\ a)$ and $(23\ c)$ in the article (...
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Problems in calculating potential of uniformly charged infinite plane or wire

From $\int_Vd^3x \rho(\vec x)\mathrel{\mathop{=}\limits^!}Q_V$ and by use of Dirac's delta distribution one finds that the charge density for the uniformly charged infinite plane is $\sigma\cdot\delta(...
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Different definitions of the EMF of a device - None of them applies to devices in a circuit

Wikipedia gives two formal definitions of the electromotive force: One in case of a closed loop, in which case the the EMF is supposed to be the path integral of the electric field (and all other ...
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2answers
124 views

Direction of gravitational field given equipotential lines

I've attached the question as an image below as it's a graphical question. It simply states: "The diagram shows equipotential lines near a group of asteroids. Which arrow shows the direction of the ...
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1answer
44 views

Electric potential and voltage

A capacitor is connected to a battery with constant voltage. If you approach one of the plate to the other, what happens to electric potential? I already have an answer to this question but it's ...
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1answer
190 views

Why do we assume the potential is independent of time in the Schrödinger equation?

In just about every text I read (online or in paper), when they handle the time-dependent Schrödinger Equation, I see something along the lines of "we always assume the potential is independent of ...
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1answer
57 views

Schrödinger equation in unknown potential well [closed]

Have a question from my class which I'm struggling with. We have a particle $m$ with wavefunction $φ=Ax \exp(-ax)$ when $x≥0$, and $φ=0$ otherwise. We are asked to show that the double derivative $...
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For degenerate perturbation theory, how do we interpret the eigenvectors and eigenvalues of $\hat V$?

For the eigenvectors that are unmixed by the matrix $\hat V$, the eigenvalues are the energy corrections of this eigenbasis. However, the eigenbasis tends to always be (as far as I'm aware) a linear ...
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Why is it possible to write the electrical potential as a sum of $\int dV \,\rho/R$ and $\int da \,\sigma/R$?

I'm trying to understand why one can write the electrical potential as follows \begin{equation} 4\pi\varepsilon_0\phi(\mathbf r) =\int d^3 r\,\dfrac{\rho(\mathbf r')}{\|\mathbf r - \mathbf r' \|} + \...
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2answers
118 views

Why wavefunction becomes exponentially smaller during quantum tunneling?

I am interested in quantum tunneling and I am wondering why the wavefunction of a particle would becomes smaller so that there is a slight possibility of finding it at the other side of a big energy ...
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2answers
164 views

When to use Poisson's equation in electrostatics

When does when elect to use Laplace's equation when dealing with charge distributions. For example, if I had a metallic sphere of radius $R$ and charge $Q$, then $$\mathbf E = \begin{cases} 0, & ...
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92 views

Potential of a polarized hollow spherical shell due to uniform electric field

A hollow spherical shell has inner radius $a$, outer radius $b$ and is made with a material with dielectric constant $\epsilon_r = \epsilon / \epsilon_0$. It is placed in a uniform electric field $\...
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1answer
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Why does a voltaic cell induce an electric force proportional to voltage?

I'm trying to understand the intuition behind Ohm's law (that current is proportional to voltage). I understand the basics of the Drude model: if the electrons frequently collide and on average reset ...
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159 views

Why can't Gauss surface be a cube?

For calculating field outside a charged plane conductor, a gaussian surface of Cylinder is considered. I have been said that we consider cylinder because the circle in its upper end is in equal ...
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1answer
36 views

Will a led, connected to a long conducting rod, shine when the rod is falling through the magnetic field of the Earth?

Visualize a long conducting rod of length $l$ falling towards the Earth (after being released from a hight of say $5(km)$) perpendicularly to the Earth's magnetic field. Near the earth's equator, ...
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1answer
29 views

Why is force 0 either side of an inflexion point in neutral equilibrium?

In Tipler & Mosca 5th edition p173 it defines neutral equilibrium as a point in a U-x curve where $\frac{dU}{dx}=0$ and also $\frac{dU}{dx}=0$ for a small displacement either side of the point. ...
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1answer
137 views

Differing definitions of Gibbs free energy and Helmholtz free energy

I am trying to understand, to me, the difficult concepts of thermodynamic potentials, and I find their definitions numerous and hard to connect between each other. For instance, here are two ...
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1answer
48 views

Calculating electric potential — denominator going to zero [closed]

Calculate the potential inside a uniformly charged solid sphere of radius $R$ and total charge $q$. My attempt: There are several ways to solve this problem but I'm curious as to whether this ...
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1answer
36 views

How is voltage (potential difference) like gravitational potential energy? [closed]

How is voltage (potential difference) like gravitational potential energy? What are their similarities
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Natural variables for state functions

The Helmholtz function $F$ is defined: $$F = U - TS$$ $$\implies dF = dU - TdS - SdT$$ Since by the Thermodynamic identity, $dU - TdS = - PdV$: $$\implies dF = -PdV - SdT$$ My textbook then notes ...
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While applying or deriving electric field and potential relation why is the field considered constant?

The relation is : $$\text dV = -\mathbf E\cdot \text d\mathbf R$$ (both of $E$ and $\text d\mathbf R$ are vectors ) . I have seen some questions and derivations where it is assumed constant. Please ...
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3answers
162 views

Direction of $d\mathbf{l}$

A solid sphere has charge $q$ and radius $R$. Find the potential at a point a distance $r$ from the center of the sphere where $r>R$, using infinity as the reference point. My attempt: From Gauss'...
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55 views

How to calculate energy of conduction band - fermi energy (Ec-Ef) - semiconductor

I am learning shottky diodes and i want to work out the built in potential barrier using: $$V_{bi} = \phi_m - [E_c - E_f] $$ now i come across 2 equations when working out Ec-Ef. the first: $$E_c -...
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1answer
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Find its radius and location of its Centre [closed]

Two fixed charges $-2Q$ and $Q$ are located at the points with coordinates $(-3a,0)$ and $(+3a,0)$ respectively in the x-y plane. Show that all the points in the x-y plane where the electric potential ...
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1answer
81 views

Infinite field but finite potential Is it possible?

I calculated the electric potential at any point (assuming zero potential at infinity) on the circumference of a uniformly charged ring (non conducting) and after evaluating that integral it turns out ...
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3answers
415 views

Surface charge density formula

We know for an infinite plane sheet, electric field from the sheet is given by: $$ E = \frac{\sigma}{2\epsilon_0} \hat n$$ Therefore potential is given by $$ - \frac{ \partial V}{\partial n} = \frac{\...
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Is it necessary that the potential difference between any two equipotential surfaces in a system be constant?

Is keeping $dV$ constant a necessary condition in the formula $$E=-\frac{dV}{dr}$$ for equipotential surfaces ?
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1answer
355 views

Electric field due to an infinite long, current carrying wire with potential difference $V_0$

I'm confused with the following: I am meant to model a standard co-axial cable as an infinite length of straight wire of radius $a$ symmetrically surrounded by a thin conducting cylindrical shell of ...
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1answer
149 views

How can direction of electric field due to a moving charge be from the present position of charge?

According to Maxwell's Equations, the electromagnetic waves in vacuum travel at the speed of light $c$. While solving Maxwell's equations using Lorenz gauge conditions (or basically evaluating scalar ...
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56 views

Electric field of a line of Charge on it axis using electric potential

We have a line of charge with length $L$ and charge density $\lambda$ and we want to find its Electric field on a point $p$ with distance $d$ from one end of it using potential. I drew a picture like ...
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2answers
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How Do I Calculate the Potential of System?

I was doing my homework when I came across this question: Three equal point charges, each with charge $1.40 \, \rm\mu C$ , are placed at the vertices of an equilateral triangle whose sides are of ...
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2answers
511 views

Why does electrostatic potential inside a conducting spherical shell seem to violate superposition principle?

I want to find the potential at the centre of a conducting spherical shell; The conducting shell bears a total charge of $Q$. The shell has a radius $R$, and there is a point charge of magnitude $q$ ...
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2answers
72 views

Why do 2 charged conductors gain same potential when connected via wire

Why do 2 charged conductors gain same potential when they are connected via a wire.Can somebody also give a mathematical proof of it?
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1answer
86 views

Why does potential decrease when a dielectric is introduced?

Here is a problem that I have encountered: A parallel-plate capacitor has the space between the plates filled with a slab of dielectric with constant $K_1$ and one with constant $K_2$, each of ...
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1answer
369 views

What do we mean by positive terminal and negative terminal?

What do we mean by positive terminal and negative terminal of battery ? What is the electric potential of both positive terminal and negative terminal ? Does positive terminal mean positive electric ...