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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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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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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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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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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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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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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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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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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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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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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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117 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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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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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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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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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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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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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 ...
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Deriving the formula of potential difference duo to a solid conducting sphere

The doctor in university was deriving a formula and I can't understand how it works A sphere with charge Q The Sphere's radius is R, and we are trying to derive a formula for potential difference at ...
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How can there be a voltage across an inductor if the voltage through any conductor is zero?

It's commonly taught that the electric field in a conductive material is zero. Hence the voltage through a perfectly conductive material is zero. I however when learning about inductors in physics ...
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How to cast dipole point charge force expression from cylindrical to Cartesian coordinates

Background I am currently building simulations of molecular dynamics and one thing I want to model is dipole interactions. I recently came across this post about calculating the force between a point ...
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Elasticity of an object [closed]

I was studying elasticity, and I thought of certain questions that I couldn't find an answer to. I'll will try to explain my queries If in the elastic limit, the strain on say a rectangular block of ...
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The formula of voltage

Definition from Wikipedia: An electric potential (also called the electric field potential, potential drop or the electrostatic potential) is the amount of work needed to move a unit of positive ...
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Proving continuity of potentials and fields due to a surface charge

Is there a way to show: $(1)\ \displaystyle \phi=\int_{S'} \dfrac{\sigma}{r} dS'$ is continuous all over space $(2)\ \mathbf{E}=\displaystyle\int_{S'} \dfrac{\sigma}{r^2}\ \hat{\mathbf{r}}\ dS'$ is ...
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Direction of propagating wave in quantum barrier

Consider a step potential $V(x)$ where \begin{align} V(x) & = 0; \quad x\leq 0 \\ V(x) & = V_0; \quad x> 0 \end{align} Now consider the case where $E_0<V_0$. The solutions of the ...
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What is the electric potential inside a point charge?

We know that electric potential of spherical charge is inverse proportion with $r$ from $V = \frac{kq}{r}$ , So if $r$ is getting less then electric potential will be higher. But , What about point ...
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How do I solve this Laplace equation? [closed]

I'm stuck with the following problem: Suppose we have an infinitely long box whose cross-section has a rectangular shape of dimensions 2×3. Take the four last digits of your student ID number as a ...
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Calculating electric field in cylindrical symmetry- - Trying to understand electric field/potential in 3D with cylindrical coordinates

Trying to work through this question I am sure that I am doing something wrong. We start with a uniform electric field $$ E = E_o \hat{i} $$ and then find that the potential is given by $$ V=-E_0 ...
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Why the electric potential inside a conductor doesn't equal zero?

Assume that a negative charge in the space near of it a small positive charge, Then for sure that the negative charge will attract the positive charge naturally because it has an electric field around ...
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Why does the potential along a uniform current-carrying wire vary with the distance along it?

Is it because as the electrons move further through the wire they lose more energy due to resistance? Also, in this context, I believe potential refers to the electric potential energy but I am unsure,...
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Spectrum of sinusoidal potential

In 1D quantum mechanics problems, the energy spectrum is often determined by the limits of the potential at $\pm$ infinity. Generally, the spectrum is continuous non-degenerate when energy is above ...
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How to verify generally that the formula for electric potential is a solution to Poisson's equation?

$$V(\vec{a})=\frac{1}{4 \pi \epsilon_0}\int_\tau \frac{\rho(\vec{r})}{l}d\tau$$ This is the formula for the potential at a general point $\vec{a}$. Note that $l$ in this formula is the magnitude of ...
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Doubts about interpretation of the curves of effective potential energy

The image shows a graph of the effective potential energy. Where,$K=-Gm_{1}m_{2}$ and $L$ is the angular momentum. The graph of the effective potential energy that can be seen in this publication was ...
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electric potential of electric dipole in 2D

I have the homework question as follows. What I did was first find that $$\phi = \frac{-\lambda}{2\pi\epsilon_0}(\ln(r_+)-\ln(r_-))=\frac{-\lambda}{2\pi\epsilon_0}\ln\left(\frac{r_+}{r_-}\right).$$ ...
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Potential by Assembling Charges

For finding electric potential energy of a uniformly charged sphere, we can assemble the sphere by brining charges from infinity to that point. So to make a uniformly charged sphere of radius $R$ and ...
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Retarded vector potential and transverse current

While studying some topics on retarded potential, I came across the following statement, and I have some trouble understanding why this is true. When we use the Coulumb gauge (instead of the Lorentz ...
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Relation between the propagator and probability for the infinite well

This may be an easy question, but I am really confused about it. For the infinite square well, the (time-dependent) energy eigenfunctions are (inside the well):$$\psi_n(x,t) = \sqrt{2/L}\:e^{-iE_nt/\...
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Effective potential in a time-dependent spacetime

My question is regarding an arbitrary time-dependent spherically symmetric spacetime with line-element, in co-moving coordinates, to be $$ds^2 = -f(R) dt^2 + a(t)\bigg\lbrace\frac{dR^2}{f(R)} +R^2d\...
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Is the voltage between the two points $A$ and $B$ denoted as $U_{AB}$ or $U_{BA}$? And why?

Consider the following circuit Is the voltage between the two points $A$ and $B$ denoted as $U_{AB}$ or $U_{BA}$? And why?
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Doubt in a derivation for electric potential at a point

My physcis teacher in school has given me this derivation for electric potential at a point. What bothered me the most was why the small work was negative but the large work positive.Could anyone ...
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How can theories about 1D or 2D systems be generalized for 3D systems?

I was watching a lecture video from MITx $^\dagger$ by professor Barton Zwiebach. He proved a pretty cool theorem "every attractive 1-dimensional potential has a bound state"; however, that only holds ...
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Does this example contradict Earnshaw's theorem in one dimension?

This is basically a continuation of the post here. Consider electrostatics in $1$-dimension (say, the $x$-axis). Now consider a positive charge $+q$ located at $x=0$, and two equal negative charges $...
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Facing a paradox: Earnshaw's theorem in one dimension

Consider a one-dimensional situation on a straight line (say, $x$-axis). Let a charge of magnitude $q$ be located at $x=x_0$, the potential satisfies the Poisson's equation $$\frac{d^2V}{dx^2}=-\frac{\...
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Electric potential and field due to a continuous charge distribution

(1) The electric potential due to a continuous charge distribution is: $$\psi=\int_V \dfrac{\rho}{r}\ dV$$ To calculate this integral $\rho$ must be continuous over $V$. But $\rho$ is discontinuous ...
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About density charged in the Liénard - Wiechert Potential to Point Charge?

I'm reading Griffiths Ch. 10. In the 10.3.1 section, there's a proof of this integral $$ \int \rho(r^\prime, t_r) \mathrm{d} \tau^\prime $$ which is not equal to the charge of the particle, but ...
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Qualitative understanding of negative step potential problem

In QM textbooks the single step potential problem is explained in great detail. However, it is hard to understand what happens when $V_{0}<0$. Could anyone please explain qualitatively, how the ...
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Problem based on Laplace and Poisson's Equations. How to find the charge from electric field and potential?

In the above problem, I have found out the potential and the electric field in the medium between the two conductors. From here, how can I calculate the approximate charge per plate?
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Difference between voltage, electrical potential and potential difference

I am having hard time to visualize these two concepts in my mind seriously. First of this confusion came from two parallel plates that was connected to a power supply, charged then disconnected from ...