Coulomb Definition and 219 Threads

This is Problem 10.6 in page 422 of "Introduction to Electrodynamics" Edition 2 by David Griffiths. The question is: Which of the potentials in the following is in the Coulomb gauge? Which is in Lorenz Gauge?( Notice that these gauges are not mutually exclusive.) This is what the solution...

Does anyone know of a dimensional formula for the Coulomb in SI that does not involve amperes as in A*s? I am looking at some equations and the dimensional analysis is leaving me with C (Coulomb unit charge) and left over m, kg, s to various powers. Just curious if anyone has come across some...

Homework Statement A gauge transformation is defined so as to leave the fields invariant. The gauge transformations are such that \vec{A}=\vec{A'}+\nabla\Lambda and \Phi=\Phi'-\frac{\partial\Lambda}{\partial t}. Consider the Coulomb Gauge \nabla\cdot\vec{A}=0. Find out what properties the...

Homework Statement 2 questions regarding the answer I have been given for this problem. Attachments are the problem & relevant worked answer I disagree with. Problem Three charges are arranged in the xy-plane as shown in attachment. A charge Q is at the point A with (x, y) coordinates...

I'm starting my study in eletromagnetism and I would like to know how do you deduce the eletric field produced by a single particle of charge q placed in the origin. The magnetic field is constant so by Maxwell equations, the rotacional is 0 and the divergence is constant. Is this enough to...

Homework Statement I am trying to directly calculate the electric field (using Coulomb) at some arbitrary point P(0,0,z). The charge is evenly distributed over the surface of a sphere (radius R, charge density σ). Here I use θ for the polar angle and p for the azimuthal angle. I will leave...

Basically I'm trying to find out how to find the maximum distance between two deuterium nuclei in order to overcome the coulomb barrier, causing them to fuse. Thanks

The ionization of potassium is 4.34 eV; the electron affinity of iodine is 3.06 eV. At what separation distance will the KI molecule gain enough Coulomb energy to overcome the energy needed to form the K^+ and I^- ions? I'm looking at the solution to this problem and I'm not understanding how...

I'm new to forums and after I typed all this out and tried to submit, it cleared everything. I really need to get this problem finished tonight. 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...

Hello, Could someone help me finish this train of thought? This is how we think in SI units: First, just because we like the value of 1 Ampere as it is now, we choose the force between two parallel conductors to be exactly 2×10^{-7}N= const ×\frac{1A×1A}{1m} Then, purely as choice, we decide...

It is known from the Coulomb's law (F = q E) that if an electric field is applied on a charge, it will accelerate it, i.e. the position of the particle changes macroscopically. But why mechanical displacement? why not a change in particles internal energy, say for example excitation of an...

Why is it that neutrons evaporate from nuclei more easily than protons do? Intuitively, since protons are electrostatically repelled (in addition to whatever nuclear forces they have in common with neutrons), one would expect protons to be ejected more readily than neutrons. (Maybe this is...

I am studying Physics Vol2 by halliday, resnick and krane. I was attempting the coloumb force exercises..If we put one charge negative and other positive in the formula..then the force comes out to be negative but the instructor manual for the book ignores the negative charge, and take it as...

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...

I know that the electron has an electric charge of 1.6x10^-19C and a magnetic moment of 9.3x10-24J/T. If you placed two electrons 1 angstrom apart in such a way as their north poles are pointing at each other, the coulomb force would attract them and the magnetic force would repel them. Which...

Homework Statement There isn't an exact problem I'm struggling with, it's one small part of a larger problem, which involves finding the probability protons will penetrate the Coulomb barrier. I'm trying to understand an example in my notes, and the bit that confuses me is attached as an...

This may be a pretty dumb question. How is it possible for ions and electrons to coexist in plasma state. Shouldn't be there Coulomb force between them so that they would be bound together and become atoms?

My book has introduced the idea of gauge invariance in terms of classical electrodynamics (attached file). However, I am not sure I completely understand how it works. On the one hand they use a lot of time on specifying how you can add to the vector potential the gradient of any scalar, whilst...

Homework Statement Hi, I'm on the first part of this question and I've got to the end but I have an extra factor of two which I can't seem to explain! Any insight would be much appreciated, thank you! Homework Equations The Attempt at a Solution I resolved the forces around one ball and came...

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'...

Under the influence of the coulomb field of charge +Q, a charge −q is moving around it in an elliptical orbit. Find out the correct statement(s). (A) The angular momentum of the charge −q is constant (B) The linear momentum of the charge −q is constant (C) The angular velocity of the charge...

I am working on the following. A point charge of √3Q is at point (3a, a, 2a) Find charge at (2a, 2a, 3a) I'm using Coulomb's Law E(r) = q / 4∏ε0 (r-r0)3 ([B]lr-r0l[B] & can get through most of it, but looking at my book I can't see why the last step occurs. See attachment. I can find r-ro &...

I'm having some difficulty resolving the units (unit conversions will be my great un-doing) for calculation of the Coulomb energy between nuclei. Given that \Delta E = \frac{3e^{2}}{5r} (2Z-1) with the value for r in fermis (~10^-13cm), the elementary charge e in coulombs, and Z is...

I am trying to workout the drift of a charged particle from another particle using coulomb law. but the problem is the further the particles move, the less the force between them, so how can I work out the drift in such case? We know that the force between two charged particles is: F = (k Q1...

Does anyone know why Coulomb chose 1.6x10^-19 for the charge of an electron? (or why he chose 6.25x10^18 electrons for 1 coulomb)

Hey, A coulomb is the amount of charge that passes a point through a wire carrying one ampere for one second. Voltage is a measure of electrical potential energy in units of volts or joules per coulomb (energy/charge). Then 1 volt means 1 joule per coulomb; 2 volts mean 2 joules per coulomb...

differential cross section of coulomb scattering can be expressed as a form factor times Rutherford one, we model the charge we used spherically symmetric charge density, if we replace this point charge with other distribution like Gaussian , what is the difference between these two models, is...

Homework Statement 224Ra --> 220Rn + \alpha 224Ra --> 212Pb + 12C 224Ra --> 210Pb + 14C Calculate the Q-Values (in MeV) for these decays given their atomic mass excesses (in MeV) are 88225Ra = 18.818 86220Rn = 10.604 82212Pb = -7.557 \alpha = 2.425 82210Pb = -14.743...

I'm just curious, in the Coulomb gauge changes made locally to the scalar and vector potential fields are propagated instantaneously, classically we wave off this problem since the potentials aren't directly observable... except they are in Aharanov-Bohm. Presumably there's something that saves...

I understand the conceptual meaning of gauge transformation which "can be broadly defined as any formal, systematic transformation of the potentials that leaves the fields invariant". I understand for example the U(1) and S(3) gauge symmetry in Gauge Theory. But what is this got to do with...

Hello, A typical problem assigned to students is where there are two charges on the x-axis and find the location of a third charge so that the net force on it is zero or some other force value given. I am wondering what is the idea behind this problem? It can get really complicated when...

I presented a way to derive Coulomb force via the canonical mechanism. One uses Coulomb gauge \partial_i A^i = 0 derives \Delta A_0 = -4\pi\,\rho which can be inverted formally A_0 = -4\pi\,\Delta^{-1}\,\rho and calculates the interaction term in the Hamiltonian density...

I have a technical question and at the time being I can't ask it to a professor. So, I'm here: If I try to quantize the vector field in the Coulomb gauge (radiation gauge) A_0(x)=0,\quad \vec\nabla\cdot\vec A=0. by imposing the equal-time commutation relation...

Homework Statement If conducting a Coulomb Balance experiment, and a question asks to estimate the total excess charge on a sphere with a conducting surface charged to 2,000,000V potential. Is there a specific equation I should be using to estimate this? Thank you. P.S. why are...

How much energy particles must have in order to overcome the Coulomb Barrier? Or the correct way to ask this is how much temperature is required for this?

Homework Statement What temperature would be required for two protons to collide if quantum mechanical tunneling is neglected? Assume that nuclei having velocities ten times the root mean square (rms) value for the Maxwell-Boltzmann distribution can overcome the Coulomb barrier (which you can...

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!

The definition of Δ (difference,drop of) Electrostatic Potential Energy (D E-PE) says it 'is the work done on a unit charge (e) to bring it from r to r1 (against the force) with constant (without acceleration) velocity and extremely low absolute value of velocity (quasistatic, vanishingly...

Hi How can I calculate the Coulomb friction load torque of a rolling spear on a surface with a coulomb friction coefficient of 0.1? Other details: Mass: 1Kg Radius: 0.1m Thanks in advance

Homework Statement Two charges, q1 = 4.9 e C and q2 = -3.6 e C are located 105nm apart, what is the size of the force between the two charges?Homework Equations F=kqq/r^2 The Attempt at a Solution I did it according to the formula and I got the answer wrong, so I checked it using an online...

Coulomb Law and Vectors - How do you find a scalar answer from the vector form?? Two small metal spheres carry equal charges q. They are located at positions r1 = (1,1,0) nm and r2 = (0,0,0) nm and feel a repulsive force of magnitude (mod) F = 0.05 N How much charge is on each sphere...

This is exact copy from Griffiths Introduction to Electrodynamics 3rd edition page 421. This is regarding to information travel in space. In time varying situation, E depend not only on V, but on A also.

I'm just curious, as space offers the huge length scales that could substantially lengthen the attractive interaction between positive and negative charges (although charges will still be repelled from other like charges)

Homework Statement Hey everyone, i have a homework question I'm completely stuck on. Coulomb Vector Force Q1= 20nC Q2= -96nC Q3= +250 nC A(y axis)= .30 meters B(x axis)= .40 meters Layout: Q1 . .A . . Q2--------Q3 B Calculate: Vector force F21 on Q1 due...

Just like the answer to mole is amount of atoms in 12 grams of carbon12. I wonder, is there a reason behind the amount of electrons in a coulomb?

Homework Statement 1. [1pt] What is the total charge of the radon nucleus? (The neutral radon atom has 86 electrons.) 1.38 * 10^-17 C 2. [1pt] What is the magnitude of its electric field at a distance of 9.6 x10-10 m from the nucleus? +1.34 * 10^11 V/m 3. [1pt] What is the...

Hello I have been having trouble understanding equation 14.25 in Bjorken and Drell "Relativistic Quantum Fields" and how exactly it gets to it. Also I would like to explicitly find/derive what the operator gauge function is. Can anyone help please?

1. Homework Statement Calculate the magnitude and direction of the Coulomb force on each of the three charges shown in Figure P15.10. http://www.webassign.net/sf5/p15_10.gif thats 3 cm if its to small to see. 6.00 µC charge Correct answer 46.76N Magnitude to Left 1.50...

I'm having a difficult time understanding how the coulomb came to be around as a unit of charge. The definition that a coulomb is equal to the charge of 6.24151×10^18 electrons and that the charge of one electron is -1.602176487(40)×10^19 seems to me like circular reasoning. The other definition...

Hello, I'm having a little trouble with this: Coulomb Force Point Charges on Cube Homework Statement Identical charges of Q (C) are located at the eight corners of a cube with side L (m). Show that the coulomb force on each charge has magnitude: 3.29Q^2/4\pi\epsilon_0l^2 Homework Equations...