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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Applying boundary conditions due to an arbitrary current density to a scalar magnetic field in cylindrical coordinates

The general solution to the Laplace equation in cylindrical coordinates in the context of a scalar magnetic potential is of the form: $\phi = c e^{\pm k z} \cos{n \theta} \{c_1 J_n (rk) + c_2 Y_n ...
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Why is $F=-\nabla V$?

I came across this equation $F=-\nabla V$ where $V$ is gravitational potential. I do understand that $F(r)=-\frac{dV}{dr}$. Hence does this mean the nabla operator in this case means derivative? ...
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Analytical non-separable solution for schrodinger equation

I am an undergraduate with the background of a first course in Quantum Mechanics. I want to find out if there exist non-unique solutions to Schrodinger equation. So I have to find potentials ...
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Proving assumptions used in 'method of image charges'

While studying the method of images for an infinite grounded plate, I came upon two assumption I can't seem to find the logic for: The test charge doesn't induce a charge density on the plate which ...
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Is the scalar magnetic potential continuos?

If we have two current-free spaces and separated by a surface current, we can solve the magnetic problem by solving two magnetic scalar potentials and then using matching conditions. My question is, ...
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Vector potential of a linear current

First of all, I apologize in advance for my English, as I know it is not very good. So thank you for making the effort of understanding me. Well, here is my problem. I am trying to prove that if I ...
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Q: Goldstein chapter 1 problem 16: Finding the generalized potential from the force

I have started to work through Herbert Goldstein's, Charles Poole's and John Safko's Classical mechanics, and I am having a bit of trouble with one of the problems (chapter 1 problem 16). The problem ...
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Why the electric potential energy the charges carry in a electric circuit does not vary with its distance to the opposite terminal?

I understand that with wires assumed to be ideal, there is no resistance and subsequently no force acting on electrons, hence no work done and p.d. across any segment of wire. However, as the ...
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Resistance and potential difference across it

I have this question that has baffled me for hours now. My question is what really happens when charge passes from one point to another in a circuit for eg what happens when it passes over a ...
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How to decide if a potential is a scalar?

I know that ${\vec E}=-{\vec \nabla} V$. If a potential is scalar, I can find its electric field strength. The question is how can I know if a potential is scalar? Do all point charges result in ...
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Electron's Frame Aharonov-Bohm Effect

In the electron's inertial frame the solenoid moves past it in the Aharonov-Bohm Effect. That means the electron sees a time varying vector potential which, by: $\vec{E}$ = ...
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Time dependent solution to infinite well

A particle of mass $m$ is confined within an infinite, one-dimensional potential well, $U(x)$, of width $a$. $$ U\left(x\right) = \left\{ \begin{array}{lr} \infty &\: x \leq ...
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Electric potential difference

From what I have read, since electrical potential is essentially EPE/unit of charge, it would be position dependent (relative to the electric field). Electrical potential difference is then defined ...
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electric potential at the other end of diode

I was brushing my basics about diode & got stuck at a point...my question is Consider a diode let the positive terminal of the diode be connected to +ve of battery Now in the figure let the ...
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Understanding electric field and potential inside an half-connected wire

Let's say we have a 9 V battery and a wire as shown in the image below: Let's assume H is the reference for measuring potential. I know the potential in F is 9 V, and I know the electric field in F ...
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Why do electric field lines point in the direction of decreasing electric potential?

Why do electric field lines point in the direction of decreasing electric potential? I came across this sentence in my school book but am trying to understand this ever since. I know that dV=-E.dr ...
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Potential (which only depends on the length of a position vector) [closed]

a) A potential $U$ only depends on the length $r=|\vec{r}|$ of the position vector $r$. Show that $$\vec{\nabla}U(r)=U'(r)\frac{\vec{r}}{r}. $$ What properties does this vector field have? ...
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Parallel-plate capacitor working voltage $V={Qd\over{\epsilon_0 A}}$ relationship with plates' distance

I don't understand why the working voltage of a capacitor increases with the plates' distance. Suppose we have 2 capacitors in series where $C_1=12,0\mu F$ and $C_2=4,0\mu F$. The voltage over both ...
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Angular momentum & Energy using Yukawa's potential [closed]

I was doing my Gravitation problems and I found this one that I'm unable to solve. Yukawa's theory for nuclear forces states that the potential energy corresponding to the attraction force ...
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Electric field of two infinitely long and thin, straight wires

I know the formula of the electric field, however: suppose that we put two infinitely long and thin, straight wires symetrically into the coordinate system, so that y axis is between them. Now ...
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Is it possible for two polarizable bodies to induce dipoles in each other in the absence of an external electric field?

If there exist two initially neutral bodies (say atoms) some distance apart, with no external electric field applied, can they induce dipoles within each other?
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Potential and Electric field

I'm trying to find the electric field from the potential and vise-versa but I'm having trouble I know the electric field of a ring with radius a and charge Q to be $$E=\frac{Qx}{4\pi ...
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why isn't the net force considered while calculating potential due to a system of charges?

The textbook I'm reading defines potential at a point as work done per unit charge by an external agent to move the test charge from the reference point to the point under consideration (without ...
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Equipotential inside a conductor ring, but how do I determine the value?

I was mapping the potential lines of 2 cylindrical electrodes - one at 0 V, the other at 5 V. I have a metallic ring midway between the 2 electrodes. I know that the electric field inside the ring is ...
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Confusion with potential difference [closed]

I was trying to solve a hard problem involving a circuit like this: Find the reading on the voltmeter (red ones are resistors) I don't know how to think about potential difference across branches ...
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Point with zero electric potential inside triangle [closed]

If we have three equal point charges placed on a two dimensional plane at $(a_x, a_y)$, $(b_x, b_y)$ and $(c_x, c_y)$, what would then be the coordinates of the point at which the electric ...
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Potential difference of conductor with induced load

If a metallic sphere is grounded and close to a positive charge q, it will be charged with -q. Let's say that the electrons will arrive through the grounding. This charge will cover the surface of the ...
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Metastable $E=0$ s-wave bound state in a spherical potential well

I am currently dealing with scattering theory. I looked up the scattering on a spherical well potential. $$V(r) = \begin{cases} -V_0 & , r \leq R\\ 0 & ,r > R \end{cases} $$ where ...
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Potential of an infinitely long cylinder

Suppose I have an infinitely long cylinder with radius $R$, charged with longitudinal density $\lambda$. I want to calculate the potential outside the cylinder. The field induced by the cylinder is ...
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68 views

Why is the ground state energy of a 2DEG higher compared to the 3DEG?

I am reading something about a 2DEG (2-dimensional electrongas model) and can not understand it. My book says the ground state of the 2DEG is higher compared to a 3DEG because the confinement to 2D ...
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Can Ampere's Circuital law be used on an infinite number of alternating Helmholtz coils?

I have the following surface current density $$ \bar{\sigma}_s = \hat{\phi} \sin(kz) |\bar{\sigma}_s| $$ to approximate an infinite number of alternating Helmholtz coils stacked along the z-axis with ...
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Why does the potential difference between two charged plates increase as they move further apart?

Suppose a uniform electric field $E$ exists between to oppositely charged metal plates (one is positively charged and one is negatively charged). If the plates move apart, and the charges on each ...
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Why does the sphere with the smaller radius (r1) have the greater charge density?

Suppose two charged conducting spheres of different radii $r_1$ and $r_2 > r_1$ are very far apart but connected by a conducting wire. Why does the sphere with the smaller radius $(r_1)$ have the ...
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Dipoles and Potential Energy

I was pondering about electrostatics, particularly dipoles. How would one go about calculating the difference in potential energy of a dipole an arbitrary distance away from an arrangement of another ...
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58 views

Calculating the potential of 2 spherical perfect conductors with the image method

I am searching for a way to calculate the potential on the surface of two perfect conductors that are spheres. I am not sure my method is correct. Here is a diagram of what I am studying : They ...
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Kinetic energy and Potential of a photon

How does the potential and kinetic energy of a photon relate? Do they mean the same thing? Also how does De broglie wavelength and Potential relate?
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Electric potential at midpoint?

I understand that if you assume the field is uniform between R and S then you can use E=V/d to get E=(30-20)/(0.5)=20Vm^(-1), so the answer is C (which is correct according to the mark scheme). But ...
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Calculation & derivation of de-Broglie wavelength [duplicate]

How to calculate the de Broglie wavelength of an $\alpha$ particle that is accelerated through a potential difference of $V$ from rest.
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Need help on electric potential definition

I'm having trouble understanding electric potential. In my book it says "an electric force acts on a charge situated in an electric field." I understand this part. Then it goes on to say "If a charge ...
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Why is the zero of electric potential taken to be $r = \infty$, rather than $r = 0?$

Wouldn't it make more sense if it was taken to be zero at $r = 0$? This seems to imply that with a negative test charge at $r = 0$ from a positive point charge, $V = -\infty$, which I have trouble ...
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A Method of Images Problem from Electrodynamics (Cylindrical Surfaces)

This problem is from Introduction to Electrodynamics 4th Edition , Griffiths, problem 3.12 Two long, straight copper pipes, each of radius $R$, are held a distance $2d$ apart. One is at potential ...
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How to determine if a potential admits bound states?

According to Griffith's Quantum Mechanics, "$E$ must exceed the minimum value of $V(x)$, for every normalizable solution to the time independent Schroedinger equation" As an example, there is no ...
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At what distance is lightning dangerous for someone lying down?

My 8 yo child told me that they learned at school that they should lay down flat on the ground in case of lightning. I told him that the more correct position is crouching down with feet together, but ...
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How do the electrons know the route?

I've learnt in classroom that the requirements for electrical current to flow in a circuit are as follows: there must be a closed conducting path between negative and positive terminals there must ...
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What state does the particle in a box occupy?

My textbook derives the equations for the different energy states $E_n$ of the particle in a box. But my professor in class said this example was a good one because it spoke about the "superposition ...
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Why do we not require higher derivatives to match at boundary when solving the Schrödinger equation in a given potential?

When solving the time independent Schrödinger equation for a given potential in 1D, the main part of the solving involves matching boundary conditions. Usually, we require the value and the first ...
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How can I physically demonstrate potential difference in a circuit to a 14 year old?

Children of this age have a fair idea about current, resistance, and batteries. Potential difference is a thing that cannot be felt or physically visualized. A teenager asked me if he can touch ...
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Use of termination in solving quantum harmonic oscillator, hydrogen atom etc

I can't seem to understand the use of termination to make the series solutions physically acceptable (when solving the linear harmonic oscillator etc.). So what if the series does not terminate, it's ...
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Calculating the electric charge of two spheres knowing their potential

I have a system of two spheres, the first one is at a potential of $ V_1 = 1 V $ and the second one is at a potential of $ V_2 = 0 V $ The distance between them is $d$ and the radius are respectively ...
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Infinite Energies of a particle in a rectangular box

For a particle trapped inside a rectangular box of side lengths $l_x$ $l_y$ and $l_z$, the energies are ...