Coulomb Definition and 233 Threads

Dear all, In my quantum mechanics book it is stated that the Fourier transform of the Coulomb potential $$\frac{e^2}{4\pi\epsilon_0 r}$$ results in $$\frac{e^2}{\epsilon_0 q^2}$$ Where ##r## is the distance between the electrons and ##q## is the difference in wave vectors. What confuses me...

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...

Homework Statement Assume that there is a deviation from Coulomb’s law at very small distances, the Coulomb potential energy between an electron and proton is given by V_{mod}(r)=\begin{cases} -\frac{q^{2}}{4\pi\varepsilon_{0}}\frac{b}{r^{2}} & 0<r\leq b\\...

Homework Statement A circular rod has a radius of curvature R = 8.11 cm, and a uniformly distributed positive charge Q = 6.25 pC and subtends an angle theta = 2.40 rad. What is the magnitude of the electric field that Q produces at the center of curvature? Homework Equations E = kQ/r^2 6.25 pC...

Homework Statement A metal sphere of radius 15 cm has a net charge of 4.2x10^-8C. At what distance from the sphere's surface has the electric potential decreased by 500V? Homework Equations V = kQ/r The Attempt at a Solution \Delta V\quad =\quad \frac { kQ }{ r } \\ \\ r\quad =\quad \frac {...

Homework Statement A charged particle (either an electron or a proton) is moving rightward between two parallel charged plates separated by distance d=2.87mm. The plate potentials are V1=-75.8V and V2=-49V. The particle is slowing from an initial speed of 90.0 km/s at the left plate. What is...

Homework Statement A metal sphere of charge +6μC is surrounded by a metal shell of net charge +6μC. Which of the following diagrams represents the electric field lines of the system? Homework EquationsThe Attempt at a Solution The correct answer provided by my teacher is a figure with 12...

Homework Statement a) Calculate the difference in binding energy between the mirror nuclide ##^{15}O## and ##^{15}N##. b) Calculate the radius of both nuclide’s assuming the difference in binding energy exclusively depends on difference in Coulomb energy. Homework Equations Mean nuclear radius...

Homework Statement My question relating to physics and electric circuits, is "If a circuit consists of a 12 volt battery and two ohm resistors connected in series, then how many Coulombs pass through each resistor in a second". Thank you all so very much. Homework Equations V=IR The Attempt...

When we say "1 coulomb is equal to charge on 6.24 x 10^18 electrons" does "charge" mean elementary charge or simply -1 ?

Charge on one electron (elementary charge) = 1.60217662 × 10-19 coulombs. Charge on 6.241509745 x 10^18 electrons is equal to 1 coulomb. So the two values above are multiplied to give one coulomb of charge ?

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

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...

Hello, I've been trying to answering this question but my answer is always wrong. Two point charges, -9.10 μC and 21.29 μC, are placed at x = 0 cm and x = 8.00 cm, respectively. (a) At what point along the x-axis is the electric field zero? What i did: i figured that the point should be on the...

Hi, I am a little confused of derivation of Coulomb Gauage. (2) First, prime notation is adopted to describe the magnetic field density source current. Non-prime notation is for position that we are specifically interested in (ex. the position magnetic force acts on)...

Homework Statement A charge (q) is placed in-between two other equal charges named Q. Q-----q-----Q a) If both Q's are positive, is charge q in equilibrium? If yes, is it a stable or unstable equilibrium? b) What about if one Q is negative while the other is...

Coulomb experiment torsion balance. I know that electrical force is inversely to the square of the separation r ...My question is why we take r square? why we need square? And another question, why Q1Q2(multiplication of charges) is proportional to electrical force? (why we need to multiply...

Hey there - I think I have an issue with my 3D density plots of the probability density of the Coulomb wave function. The reason I think something is going wrong is because my plots of |ψ(n=2, l=1, m=-1)|² and |ψ(2, 1, 1)|² are identical, while I would expect them to have the same shape but be...

Hey there, I used Mathematica to find the (non-normalised) wave function of an electron in the vicinity of a Hydrogen nucleus, and converted the answer from one involving Whittaker functions to one involving generalised Laguerre polynomials. My result is shown below: This agrees with the...

Homework Statement Find the force on a point of charge of 30μC at (0,0,5)m due to a 4m square int he z=0 plane between x=±2m and y=±2m with a total of 500μC, distributed uniformly. Homework EquationsThe Attempt at a Solution R=-x,-y,+5z dQ=ρdydx=500/4 dydx dE=dQ(5az) / (4πε0((x2+y2+25)3/2 ) x...

Homework Statement I need to find the magbitude of charges Lenght of string - 50 cm mass of balls - 0.2 grams theeta - 37 degrees Homework Equations K-8.99x10^9 [/B]The Attempt at a Solution I found that half the distance between the balls is 15.9 cm but i don't know how to continue[/B]

Hi Is it possible to convert coulomb to joule without knowing volt?

why isn't the number of e or p making a Coulomb the same as the reciprocal of the 'basic' charge if the basic charge is defined as a fraction of a Coulomb? basic charge = 1.6 x e-19C, but number of p or e constituting a C is 6.25 x e18

Homework Statement Find the electric field of a sphere of radius R and charge Q outside sphere. Use only a Coulomb integral to do this. Homework Equations I know that I have to use a triple integral to find the E-field. I am just unsure of my whole setup really. The Attempt at a Solution...

What is the unit value of coulomb constant(k)? I just want to know the CGS unit value of k. In my book it is said the CGS unit value of k is 1. By i don't know how it come.?

We are doing an experiment to verify coulomb's law, and we are currently using a stable voltage source. However, we were assigned to do it using static electricity, and we were wondering how to establish inverse r^2 dependence if the amount of the charge on the ball isn't the same every time we...

Homework Statement What is the distance between two charges of -5.00 C each if the force of electrostatic repulsion acting on them is 5.00 x 10^3 N?[/B]Homework Equations Is this rearrange formula correct? r^2=k(q1q2) / F[/B] The Attempt at a Solution 6704m

Homework Statement I was given a task to model (using Matlab) 3 identical particles in external field and find spectra of lowest system energy states using gradient descend method for each particle in the system. I did a run of 500 random generated coordinates and found this distribution...

How to prove that e(the charge of proton)=1.6E-19 Mev.fm

Homework Statement The temperature in the interior of the Sun is about 1.5E7 K. Consider one of the reactions in the thermonulcear synthesis chain: p+p->H_2 + e^+ neutrino. In order for this reaction to occur two protons have to be at the distance of about 1 fm (10E-15 m). Estimate the...

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...

Hi, i have been struggling to find some good resources on variational principle , I have got an instructor in advanced quantum course who just have one rule for teaching students- "dig the Internet and I don't teach you anything".. So I digged a lot and came up with a lot reading but I need...

Homework Statement A mass m is attached to a spring with spring constant k. There is a coefficient of static friction, us The coefficient of kinetic friction is uk Suppose you pull the mass to the right and release it from rest. You find there is a limiting value of x = A0 > 0 below which the...

Homework Statement Hi guys! I have a problem pertaining to the kinetic energy gained by a point charge from interacting with a another point charge. Here's the problem: A point charge of mass m1 and charge q is placed near another point charge with mass m2 and charge Q. Both charges are of...

Definition/Summary A particular choice of "gauge fields" in which the vector potential has no divergence. Equations \nabla\cdot\vec A=0 Extended explanation As explained elsewhere, one introduces "gauge fields" in order to identically solve two of the four Maxwell equations...

One of the observation noted in connection with coulomb interaction is that, it is not affected by the presence of other charges. Why? Thanks.

How do you write out the potential of an ion in a Penning trap? Specifically, how does the inter-ionic Coulomb interaction come to be written as a Green's function? I found it here : http://journals.aps.org/rmp/pdf/10.1103/RevModPhys.71.87 They do say something about interactions with image...

Hi I'm wondering: The symbol of charge is Q but the SI unit of charge is coulumb which is the Charge of approximately 6.241×1018 electrons. But charge is not itself defined, only in terms of Coulomb, and coulomb is defined in termes of Charge. Its SI definition of Coulomb is the charge...

What's the original definition of Ohm, ampere, volt and coulomb, And which unit was defined according to the other ??!

Homework Statement Evaluate the so-called Direct (or Coulomb) Integral, C, which occurs in the theory of the 2-electron atom. C=\int\int d\vec{r}_1d\vec{r}_2\left|\phi_a(1)\right|^2\left|\phi_b(2)\right|^2 \frac{e^2}{\left|\vec{r}_1-\vec{r}_2\right|} You may assume that both...

Homework Statement The engine delivers 12 kW. Per second it can shift the m = 800 kg car over a vertical distance of 1.5 m. Find the current delivered by the batteries. Homework Equations P = U * I I = P/U = 12 000 W / 168 V = 71.4 A The Attempt at a Solution My Problem is...

We have a system of two orbitals 'a' and 'b'. The Hamiltonian is given as: $$H=\sum_{\sigma=\uparrow,\downarrow}(\epsilon_a A_\sigma^\dagger A_\sigma+\epsilon_b B_\sigma^\dagger B_\sigma) -t\sum_{\sigma=\uparrow,\downarrow}(A_\sigma^\dagger B_\sigma+B_\sigma^\dagger A_\sigma)+U...

Homework Statement You have two charges, q1= -15uC and q2= 3uC, separated by a distance d= 3m. We want to calculate the electric field, E, at a location x relative to charge q2 located on a line connecting the two charges. Note that x could be anywhere on that line. Also need to calculate the...

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...

Hi, I am trying to decide on a topic for my senior project, and my professor and I fleetingly discussed my idea of writing a program that models collisions of macroscopic objects using the mutual repulsive forces of their valence electrons rather than standard conservation laws. My question is...

Homework Statement We study the free electromagnetic field in a charge and current free cubic box with with edge length L and volume V. The vector potential in such a system is given via Fourier series: Homework Equations \vec{A}(\vec{r}, t) = \sum\limits_{k} \vec{A}_k(t) e^{i...

The well-known connection between the electric field and Coulomb's law is that The magnitude of the electic field at distance r from a point-charge Q is E=Q/r^2The definition of E is that the force exerted the field on a point-charge q is F=qE. These two equalities yield the F=qQ/r^2...

What k mean in coulomb law? it's 1/(4π*ε) but why is in this form? 4π it's related to the shape of an atom?

Hello, I'm new in the realm of numerical analysis. I need to find the local probability density of energy P(E) of a single electron on site i from a self-consistent equation for the energy (mean field equation of energy)...

I'm struggling to understand why 'amps' is a base unit. An amp is defined as one coulomb per second, correct? Then surely it isn't a base unit! It clearly relies on the coulomb. Like, if the coulomb didnt exist, or the amp was discovered before the coulomb was discovered, what would the amp be...