# What is Coulomb potential: Definition and 26 Discussions

The electric potential (also called the electric field potential, potential drop, the electrostatic potential) is the amount of work energy needed to move a unit of electric charge from a reference point to the specific point in an electric field with negligible acceleration of the test charge to avoid producing kinetic energy or radiation by test charge. Typically, the reference point is the Earth or a point at infinity, although any point can be used. More precisely it is the energy per unit charge for a small test charge that does not disturb significantly the field and the charge distribution producing the field under consideration.
In classical electrostatics, the electrostatic field is a vector quantity which is expressed as the gradient of the electrostatic potential, which is a scalar quantity denoted by V or occasionally φ, equal to the electric potential energy of any charged particle at any location (measured in joules) divided by the charge of that particle (measured in coulombs). By dividing out the charge on the particle a quotient is obtained that is a property of the electric field itself. In short, electric potential is the electric potential energy per unit charge.
This value can be calculated in either a static (time-invariant) or a dynamic (varying with time) electric field at a specific time in units of joules per coulomb (J⋅C−1), or volts (V). The electric potential at infinity is assumed to be zero.
In electrodynamics, when time-varying fields are present, the electric field cannot be expressed only in terms of a scalar potential. Instead, the electric field can be expressed in terms of both the scalar electric potential and the magnetic vector potential. The electric potential and the magnetic vector potential together form a four vector, so that the two kinds of potential are mixed under Lorentz transformations.
Practically, electric potential is always a continuous function in space; Otherwise, the spatial derivative of it will yield a field with infinite magnitude, which is practically impossible. Even an idealized point charge has 1 ⁄ r potential, which is continuous everywhere except the origin. The electric field is not continuous across an idealized surface charge, but it is not infinite at any point. Therefore, the electric potential is continuous across an idealized surface charge. An idealized linear charge has ln(r) potential, which is continuous everywhere except on the linear charge.

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1. ### Relativistic correction to Coulomb Potential in SQED

I have derived the Coulombian potential as an effective potential between two spinless charged particle taking the non-relativitic approach on the scattering amplitude obtained in terms of the Feynman rules in SQED. The scattering amplitudes are: I'm using the gauge in which xi = 1. How could...
2. ### I The atomic Coulomb potential extends to infinity?

I'm studying nuclear physics in a text, but at one point that is said: "Both the Coulomb potential that binds the atom and the resulting electronic charge distribution extends to infinity" , I don't understand what is that "resulting electronic charge distribution extends to infinity" what they...
3. ### QED, chapter 4 P&S page 125 (Coulomb Potential)

$$\bar u(p') \gamma^i u(p) = u^\dagger(p') \gamma^0 \gamma^i u(p)$$ if ##p = p'## we can use $$u^\dagger(p) u(p) = 2m \xi^\dagger \xi$$ but how can we conclude the statement?
4. ### Phase shifts for a localized Coulomb and harmonic potential

I am struggling over a problem and i could really use some help in this. So it's about finding phase shifts in a localized sphere of coulomb and harmonic potential. I tried solving the radial Schrodinger equation for both of them by using power series method, but still i am having problem...
5. ### I Probabilities Associated with Sudden Changes in Potential

Hi, I have a question about calculating probabilities in situations where a particle experiences a sudden change in potential, in the case where both potentials are time independent. For example, a tritium atom undergoing spontaneous beta decay, and turning into a Helium-3 ion. The orbital...

9. ### Rayleigh–Ritz method - Yukawa coulomb potential

Hello everyone Homework Statement I have been given the testfunction \phi(\alpha, r)=\sqrt{(\frac{\alpha^3}{\pi})}exp(-\alpha r) , and the potential V(r,\theta, \phi)=V(r)=-\frac{e^2}{r}exp(\frac{-r}{a}) Given that I have to write down the hamiltonian (in spherical coordinates I assume), and...
10. ### Coulomb potential as an operator

I want to calculate the commutator ##{\Large [p_i,\frac{x_j}{r}]}## but I have no idea how I should work with the operator ##{\Large\frac{x_j}{r} }##. Is it ## x_j \frac 1 r ## or ## \frac 1 r x_j ##? Or these two are equal? How can I calculate ##{\Large [p_i,\frac 1 r]}##? Thanks
11. ### SO(4) symmetry in the Coulomb potential

In chapter 4 of "Modern Quantum Mechanics" by Sakurai, in the section where the SO(4) symmetry in Coulomb potential is discussed, the following commutation relations are given: ## [L_i,L_j]=i\hbar \varepsilon_{ijk} L_k## ## [M_i,L_j]=i\hbar \varepsilon_{ijk}M_k## ## [M_i,M_j]=-i\hbar...
12. ### Coulomb potential in hydrogen atom nomenclature

I'm seeing a version of the potential as -Ze^2/4πεr. My question is what exactly does the Ze^2 refer to? I think the e^2 is supposed to represent the proton and the neutron, and the Z is supposed to represent the number of protons, but I'm not sure how to read it. Does e refer to the charge...
13. ### One dimensional Coulomb potential

Consider the potential below: V(x)=\left\{ \begin{array}{cc} -\frac{e^2}{4\pi\varepsilon_0 x} &x>0 \\ \infty &x\leq 0 \end{array} \right. The time independent Schrodinger equation becomes: \frac{d^2X}{dx^2}=-\frac{2m}{\hbar^2} (E+\frac{e^2}{4\pi\varepsilon_0 x})X I want to find the ground...
14. ### Coulomb potential in Kohn-Sham DFT

In Kohn-Sham DFT, the Coulomb potential, which is a component of the Kohn-Sham potential, is given by: v_H(\mathbf{r}) = \int \frac{\rho(\mathbf{r'})}{|\mathbf{r}-\mathbf{r'}|}d\mathbf{r'} where \rho(\mathbf{r'}) is the electron density. For molecular systems with exponential densities...
15. ### Monte-Carlo simulation Coulomb potential scattering

Dear all, I just started learning about the Monte-Carlo methods of simulating particle interactions. I would like to ask a question about simulating potential scattering. In particular I think that the simulating scattering by Coulomb potential, and writing a corresponding MC test program might...
16. ### Relativistic Coulomb potential - how to understand the equation

Hi, I need a formulation of the equation for Coulomb's potential. It needs to be an integral that applies to densities (so no delta functions). (I think the relevant densities are charge densities?) Also, it needs to be relativistic. So far I have: ? = \int\frac{ρ(r'...
17. ### What is Coulomb potential and energy?

is it just potential and potential energy? but if so, why is it given as V(r) = - Ze2 / 4πεr ? and E = Z2e2 / 4πεr i am having trouble understanding how come for potential V, Q = Ze2 while for E, Q2 = Z2e2 thanks!
18. ### Unusual coulomb potential

I have seen the Fourier transform of the coulomb potential quite often. However, I have come across a sum expression for an electrostatic potential V_{cb}(r-r') = \frac{1}{V}\sum_{q \neq 0} \frac{4\pi}{q^2}e^{iq(r-r')} It is equation (2.6) here...
19. ### Expectation value of Coulomb potential depends on relative spin

Homework Statement Show that the expectation value of the Coulomb potential v(\vec{r_1},\vec{r_2})=\frac{e^2}{|\vec{r_1}-\vec{r_2}|}, between two electrons depends on the relative orientation of spin of the two electrons. Assume each electron is in the product state form...
20. ### Relativistic particle in Coulomb potential - any analytic solution?

Is there a general analytic solution to the classical motion of a relativistic charged particle in a static Coulomb potential? Of course, the non-relativistic limit is simply Kepler's problem. Quantum effects should be ignored, but relativistic effects (such as E field transforming into B field)...
21. ### Coulomb Potential Energy - discrepancy between like and opposite charges

The Coulomb potential energy between two point charges is defined as: V=[(q_1)(q_2)]/[(k*r)] Suppose that you have two equal, like charges at a distance L, then V_like=q2/(k*L) Similarly, for two equal, opposite charges, V_opp=-q2/(k*L)=-V_like Both situations experience a force of...
22. ### Coulomb potential removes the degnerecay of states

Hi every one this is the first time in this wonderful forum :) and i have a question i hope i find an answer ? how can the additiona of a smalll (c/r square)term to the coulomb potential removes the degnerecay of states with different (small) L. (quantum defect)? :confused: thanks
23. ### Propagating planar wave of the Coulomb potential

Homework Statement There is a propagating planar wave of the Coulomb potential, \phi = sin(kx - \omega t) . What other fields result when it is assume the magnetic potential, \textbf{A} is everywhere constant? \phi, Coulomb potential \textbf{B}, magnetic field strength \textbf{E}...
24. ### Coulomb potential twice problem

If I describe a system by a Lagrange's function L=-\frac{1}{2}\int d^3x\;(\partial_{\mu}A_{\nu}(x))(\partial^{\mu} A^{\nu}(x)) - \sum_{k=1}^N \Big(q_k A^0(x_k) - q_k v_k\cdot A(x_k) + m_k\sqrt{1-|v_k|^2}\Big) (I'm just coping this from my notes. I'm sure the not gauge fixing Lagrangian with...
25. ### Coulomb Potential Barrier: Is This Calc Right? What's fm?

The Coulomb potential barrier of a system of two nuclei X and Y is approximately given by VC = ZX*ZY*e2/RN where ZX and ZY are the charge numbers of the nuclei, e2 = 1.44 MeV*fm, RN = (AX1/3+AY1/3) × r0 is the sum of the nuclear radii. r0 is a constant usually estimated to 1.2 to 1.3 fm and AX...
26. ### Anyone prove Fourier representation of the Coulomb potential

I've seen the Fourier representation of the Coulomb potential is -\frac {Ze} {|\mathbf{x}|} = -Ze 4\pi \int \frac {d^3q} {(2\pi)^3} \frac {1} { |\mathbf{q}|^2} e^{i\mathbf{q}\cdot\mathbf{x}} Will anyone show me how to prove it? (yes, it's the Coulomb potential around an atomic nucleus.)...