In this image of Introduction to Electrodynamics by Griffiths
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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 ...
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...
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}}...
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...
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...
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...
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...
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...
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
$$\mathbf{A} \propto \iint \frac{d^3 p}{\sqrt{2\omega_p}}\sum_{\lambda} \Big(e^{i\mathbf{p}\cdot...
I'm trying to understand how we set up the lagrangian for a charged particle in an electromagnetic field.
I know that the lagrangian is given by $$L = \frac{m}{2}\mathbf{\dot{r}}\cdot \mathbf{\dot{r}} -q\phi +q\mathbf{\dot{r}}\cdot \mathbf{A} $$
I can use this to derive the Lorentz force law...
Hi everyone,
I am trying to calculate the equation of motion of a charged particle in the field of a monopole.
The magnetic field of a monopole of strength g is given by:
\textbf{B} = g \frac{\textbf{r}}{r^3}
And the Lagrangian by:
\mathcal{L} = \frac{m\dot{\textbf{r}}^2}{2} +...
Homework Statement
So my teacher, as we made the multipole expansion of Vector Potential (\vec A) decided to proof that the monopole term is zero doing something like this:
∫∇'⋅ (J.r'i)dV' = ∮r'iJ ndS' = 0
The first integral, "opening" the nabla: J⋅(∇r'i) + r'i(∇⋅J) this must be equals 0
J =...
Homework Statement
Homework Equations
Provided in the questions I believe. Here's the triangle from question two.
The Attempt at a Solution
QUESTION SET 1 TOP OF PICTURE
A.) I didn't know how to just "guess" what the constant should be so I actually worked it out. I found the constant...
Hello,
I was wondering if anybody knew of any material (books, papers etc..) which considers a possible connection between longitudinal waves and vector potentials, at least mathematically. I have been scouting about, but failed to find anything substantial. I understand that there seems to be...
So its been a while since I studied maxwells equations, anyway:
So From my ignorant perspective, trying to derive conceptual meaning from these, I can see that the time dependant study there is some conductivity x the partial differential of the magnetic vector potential plus the cross product...
I've having trouble understanding one of the consequences of using the length gauge.
The length gauge is obtained by the gauge transformation ##\mathbf{A} \rightarrow \mathbf{A} + \nabla \chi## with ##\chi = - \mathbf{r} \cdot \mathbf{A}##. Starting from the Coulomb gauge, we have
$$...
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...
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...