I am given an initial vector potential let's say:
\begin{equation}
\vec{A} = \begin{pmatrix}
g(t,x)\\
0\\
0\\
g(t,x)\\
\end{pmatrix}
\end{equation}
And I would like to know how it will transform under the Lorenz Gauge transformation. I know that the Lorenz Gauge satisfy...
The problem says I have a spherically symmetric spinning constant charge distribution of charge Q and angular momentum w; I saw two possible explanations but none of them has made me realize why it is zero, one mentions thata constant w somehow implies a constant E which would mean there is no B...
The problem is shown above, the hint to solve the problem is below. See the hint if it is difficult for you to imagine what is going on.
I am assuming the diagram in the hint shows what's happening when the mass is falling at terminal velocity. I have quite a few questions.
1. How do the wheels...
I have not studied the Fourier transform (FT) in great detail, but came across a problem in electrodynamics in which I assume it is needed. The problem goes as follows:
Evaluate ##\chi (t)## for the model function...
Let ##(r,\phi, \theta)## be the radial, polar and azimuthal coordinates respectively.
As ##\vec{B}## is confined to ##xz## plane such that ##\theta = \alpha## I assumed ##\vec{B}## on the surface of shell to be ##\vec{B} = a\sin(\alpha) \hat x + \cos(\alpha) \hat z \tag{1}##
Surface area...
I am prepping for my spring Graduate E/M I course (official textbook: Jackson) and will like to know what math topics in PDE/Math-Methods/ODE/Linear-Algebra to brush up on or hone down on as I prep? Which topics are most frequently needed for Graduate Electrodynamics I?
In SR, we know that ##\vec E \cdot \vec B## and ##E^{2}-B^{2}## are invariant.
Although I can prove those two invariant physical quantities mathematically, I do not know how to find at least
one example to demonstrate that ##\vec E \cdot \vec B## and ##E^{2}-B^{2}## are invariant.
Many thanks!
My professor told that poission equation has a unique solution even for mixed boundary conditions( i.e. Dirichlet bc for some part and Neumann for the remaining part). But how is this possible? As different boundary conditions for the same problem will give different solutions.
Point Particle in Relativity and Electrodynamics:
“The Classical Theory of Fields” – by Landau and Lifshitz, in its discussion about classical size of a particle, concludes that:- Thus we come to the conclusion that in classical (non-quantum) ‘relativistic mechanics’, we cannot ascribe finite...
A friend mine of gave me a problem :
Calculate the Emf b/w the axis and surface of a long current carrying wire of radius ##r## and current density ##J##.
I am not able to understand why there would be a potential difference between the axis and surface but i think that either of these could...
Homework Statement
Two parallel plates of metal sandwich a dielectric pad of thickness d, forming an ideal
capacitor of capacitance C. The dielectric pad is elastic, having a spring constant k. If an
ideal battery of voltage V across its terminals is connected to the two plates of this...
Hi, friends! Under particular conditions on ##\phi:\mathbb{R}^3\times\mathbb{R}\to\mathbb{R}## - I think, as said here, that it is sufficient that ##\phi\in C_c^1(\mathbb{R}^4)##: please correct me if I am wrong - the following equality holds$$\frac{\partial}{\partial r_k}\int_{\mathbb{R}^3}...
Dear friends,
I have found a derivation of the fact that, under the assumptions made in physics on ##\rho## (to which we can give the physical interpretation of charge density) the function defined by
$$V(\mathbf{x},t):=\frac{1}{4\pi\varepsilon_0}\int_{\mathbb{R}^3}...
I have a t-shirt with a next print:
But I am not sure what equation is. I only know that is something related with light. But I haven't found it. I am not sure if it is one from quantum electrodynamics or some advanced course in physics. I would appreciate that somebody could tell me which...
Homework Statement
The following circuit is given.
I intend to calculate the current in every resistor (every quantity except i1, i2, i3, is known).
My textbook states that ℰ3-ℰ1 = (R1+R2+R3+R4+2r)*i, but I think it should be -ℰ3+ℰ1 on the left-hand side, since the current enters the negative...
Having a big issue working through this problem and was wondering if somebody, much smarter than I, could give me a few pointers. Anyway here's the problem:
Given that k2=εμω2-iωμσ
By writing the wave number as k=kr-iki.
Show that ki, which determines attenuation, can be expressed by...
Hey guys,
Can you please refer some good books to refer to in studying relativistic Electrodynamics (introductory parts),
covering the Maxwell's equations in tensor form the L-W potentials and other aspects.
FYI am just a beginner in relativistic Electrodynamics.
Thanks for the help.
Homework Statement
Let $$\vec H = ih_4^{(1)}(kr)\vec X_{40}(\theta,\phi)\cos(\omega t)$$
where ##h## is Hankel function of the first kind and ##\vec X## the vector spherical harmonic.
a) Find the electric field in the area without charges;
b) Find both fields in a spherical coordinate system...
I am reading Jackson's book on classical electrodynamics.
It said in page 412 to 415 (3rd edition) that the total power radiated by a
dipole is proportional to k^4 (equation 9.24)
quadrupole is proportional to k^6 (equation 9.49)
But why does the linear antenna at page 412, which is a dipole...