Read about vector potential | 18 Discussions | Page 1

  1. Adesh

    I'm not getting the curl of vector potential equal to magnetic field

    In this image of Introduction to Electrodynamics by Griffiths . we have calculated the vector potential as ##\mathbf A = \frac{\mu_0 ~n~I}{2}s \hat{\phi}##. I tried taking its curl but didn't get ##\mathbf B = \mu_0~n~I \hat{z}##. In this thread, I have calculated it like this ...
  2. R

    Vector potential of current flowing to a point from all directions

    I am having problem with part (b) finding the vector potential. More specifically when writing out the volume integral, $$A = \frac{\mu_0}{4\pi r}\frac{dq}{dt}\int_{0}^{2\pi}\int_{0}^{\pi}\int_{0}^{?}\frac{1}{4\pi r'^2} r'^2sin\theta dr'd\theta d\phi$$ How do I integrate ##r'##? The solution...
  3. TheBigDig

    Magnetic field of vector potential

    So I was able to do out the curl in the i and j direction and got 3xz/r5 and 3yz/r5 as expected. However, when I do out the last curl, I do not get 3z2-3r2. I get the following \frac{\partial}{\partial x} \frac{x}{(x^2+y^2+z^2)^\frac{3}{2}} = \frac{-2x^2+y^2+z^2}{(x^2+y^2+z^2)^\frac{5}{2}}...
  4. It's me

    Dirac hydrogen atom vs spin symmetry

    Homework Statement Exact spin symmetry in the Dirac equation occurs when there is both a scalar and a vector potential, and they are equal to each other. What physical effect is absent in this case, that does exist in the Dirac solution for the hydrogen atom (vector potential = Coulomb and...
  5. V

    Vector potential of a plate with a uniform, time-harmonic current density

    Hi all, i tried to do this question but got stuck on the last point . Can anyone help me please? The general form of vector potential: I got the answer for A1 vector potential but dont know what assumptions i need to get the expression for the A2. Does anyone know how one can derive it...
  6. allison west

    Vector Potential of a Rotating Mangetic Dipole

    Homework Statement A rotating magnetic dipole is built by two oscillating magnetic dipole moments, one along the y-axis and one along the x-axis. Find the vector potential at a point: (0, 0, ##z_0##) along the z-axis. Then find the magnetic field at ##z_0## . As the magnetic field is a function...
  7. Q

    I Christoffel Symbol vs. Vector Potential

    As far as I can tell, in GR, the Chirstoffel symbol in the expression of the Connection is analogous to the vector potential, A, in the definition of the Covariant Derivative. The Chirstoffel symbol compensates for changes in curvature and helps define what it means for a tensor to remain...
  8. 1

    Finding the magnetic field of a loop at far distances

    Homework Statement Loop of current ##I## sitting in the xy plane. Current goes in counter clockwise direction as seen from positive z axis. Find: a) the magnetic dipole moment b) the approximate magnetic field at points far from the origin c) show that, for points on the z axis, your answer is...
  9. M

    A Quantized E field, Coulomb Gauge with Interactions

    The common presentation for free field quantization proceeds with the Lorentz and Coulomb (##\phi = 0, \,\nabla \cdot \mathbf{A} = 0 ##) constraints. Then ##A## can be defined $$\mathbf{A} \propto \iint \frac{d^3 p}{\sqrt{2\omega_p}}\sum_{\lambda} \Big(e^{i\mathbf{p}\cdot...
  10. brad2292

    I How do we formulate the electromagnetic Lagrangian?

    I'm trying to understand how we set up the lagrangian for a charged particle in an electromagnetic field. I know that the lagrangian is given by $$L = \frac{m}{2}\mathbf{\dot{r}}\cdot \mathbf{\dot{r}} -q\phi +q\mathbf{\dot{r}}\cdot \mathbf{A} $$ I can use this to derive the Lorentz force law...
  11. I

    A Lagrangian of a monopole (Einstein notation is used)

    Hi everyone, I am trying to calculate the equation of motion of a charged particle in the field of a monopole. The magnetic field of a monopole of strength g is given by: \textbf{B} = g \frac{\textbf{r}}{r^3} And the Lagrangian by: \mathcal{L} = \frac{m\dot{\textbf{r}}^2}{2} +...
  12. P

    Multipole expansion of Vector Potential (A)

    Homework Statement So my teacher, as we made the multipole expansion of Vector Potential (\vec A) decided to proof that the monopole term is zero doing something like this: ∫∇'⋅ (J.r'i)dV' = ∮r'iJ ndS' = 0 The first integral, "opening" the nabla: J⋅(∇r'i) + r'i(∇⋅J) this must be equals 0 J =...
  13. DrPapper

    Vector Potential: Infinite Wire and Infinite Solenoid

    Homework Statement Homework Equations Provided in the questions I believe. Here's the triangle from question two. The Attempt at a Solution QUESTION SET 1 TOP OF PICTURE A.) I didn't know how to just "guess" what the constant should be so I actually worked it out. I found the constant...
  14. muscaria

    Longitudinal waves and vector potentials.

    Hello, I was wondering if anybody knew of any material (books, papers etc..) which considers a possible connection between longitudinal waves and vector potentials, at least mathematically. I have been scouting about, but failed to find anything substantial. I understand that there seems to be...
  15. T

    Layman explanation of some simple EM equations

    So its been a while since I studied maxwells equations, anyway: So From my ignorant perspective, trying to derive conceptual meaning from these, I can see that the time dependant study there is some conductivity x the partial differential of the magnetic vector potential plus the cross product...
  16. DrClaude

    Length gauge

    I've having trouble understanding one of the consequences of using the length gauge. The length gauge is obtained by the gauge transformation ##\mathbf{A} \rightarrow \mathbf{A} + \nabla \chi## with ##\chi = - \mathbf{r} \cdot \mathbf{A}##. Starting from the Coulomb gauge, we have $$...
  17. G

    How Fourier components of vector potential becomes operators

    Hello. I'm studying quantization of electromagnetic field (to see photon!) and on the way to reach harmonic oscillator Hamiltonian as a final stage, sudden transition that the Fourier components of vector potential A become quantum operators is observed. (See...
  18. P

    Curl of the vector potential produced by a solenoid

    Homework Statement / Homework Equations[/B] I was looking at Example 5.12 in Griffiths (http://screencast.com/t/gGrZEPBpk0) and I can't manage to work out how to verify that the curl of the vector potential, A, is equal to the magnetic field, B. I believe my problem lies in confusion about how...
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