All Questions
29
questions
4
votes
2
answers
2k
views
Derivatives of Dirac delta function and equation of continuity for a single charge
For a single charge $e$ with position vector $\textbf R$, the charge density $\rho$ and and current density $\textbf{j}$ are given by:
\begin{equation} \rho(\textbf{r},t)= e\,\delta^3(r-\textbf{R}(t))...
- 1,352
4
votes
1
answer
225
views
Is there a quick way to calculate the derivative of a quantity that uses Einstein's summation convention?
Consider $F_{\mu\nu}=\partial_{\mu}A_\nu-\partial_\nu A_\mu$, I am trying to understand how to fast calculate $$\frac{\partial(F_{\mu\nu}F^{\mu\nu})}{\partial (\partial_\alpha A_\beta)}$$
without ...
- 838
4
votes
1
answer
108
views
What does $\mathbf{A}\cdot\nabla$ mean here?
What does $\mathbf{A}\cdot\nabla$ mean in an expression like $(\mathbf{A}\cdot\nabla)\mathbf B$?
I found this in Griffiths’ Classical Electrodynamics book and cannot figure it out.
3
votes
3
answers
113
views
Finding the vector potential
$$\nabla\times\mathbf{B}=\nabla\times\left(\nabla\times\mathbf{A}\right)=\nabla\left(\nabla\cdot\mathbf{A}\right)-\nabla^2\mathbf{A}=\mu_0\mathbf{J}\tag{5.62}$$
Whenever I try to work this out and ...
- 220
3
votes
1
answer
435
views
Heaviside-Feynman formula derivation
I want to discuss derivation of Feynman-Heaviside formula.
The topic has already been discussed here but I can not put there any question that's why I'm making new post.
Deriving Heaviside-Feynman ...
2
votes
1
answer
2k
views
Derivatives with upper and lower indices
I'm studying classical and quantum field theory, but evaluating derivatives of fields (scalar and/or vector) described with upper and lower indices is somewhat new to me. I'm trying to evaluate
$$\...
- 187
2
votes
2
answers
4k
views
Total time derivative of magnetic vector potential $A$
I am looking at this document, which tries to establish the Lagrangian of the Lorentz force. Everything is fine, but I don't see why:
$$\frac{dA_i}{dt}=\frac{\partial A_i}{\partial t}+\frac{\partial ...
- 594
2
votes
1
answer
213
views
Tensor Differentiation
In the book "Tensors, Relativity and Cosmology" the author derived Maxwell's Equation in covariant form using the EM field tensor Lagrangian $L=-\frac{1}{4}F^{jl}F_{jl}$ (source=0). One of the steps ...
- 1,047
2
votes
3
answers
498
views
About field gradient
I read the term field gradient in most of the article about magnetic field. I search it online but most of the explanation is about the math. I wonder in physics, what the gradient field really mean? ...
- 2,383
1
vote
2
answers
4k
views
Derivative of the magnetic field to the vector potential
So the magnetic field is defined with the vector potential A as:
$$\mathbf{B}=\nabla\times\mathbf{A}.$$
How would I calculate the derivative:
$$\frac{\delta}{\delta\mathbf{A}}|\mathbf{B}|^2$$
I ...
- 3,112
1
vote
3
answers
143
views
Passing from curl to vector product
I don't understand how to obtain second equation with first part in the equation
$$
\nabla \times \vec A_0 e^{-j \vec k\cdot \vec r} = -j\vec k\times \vec A_0 e^{-j \vec k\cdot \vec r}.
$$
Can you ...
- 13
1
vote
1
answer
226
views
Four-vector differentiation (E-M Euler-Lagrange eq.)
$$\partial_{\mu} \frac{\partial(\partial_{\alpha}A_{\alpha})^2}{\partial(\partial_{\mu}A_{\nu})} = \partial_{\mu}\left[2(\partial_{\alpha}A_{\alpha})\frac{\partial(\partial_{\beta}A_{\gamma})}{\...
- 139
1
vote
1
answer
90
views
How to show the equivalence between Lagrangians?
I have a Lagrangian of a form:
$$\mathcal{L}=\frac{1}{2}\left (A_\mu g^{\mu\nu}\partial^2 A_\nu-A_\mu \partial^\mu \partial^\nu A_\nu\right ) $$
And I want to show that it is equivalent to the ...
- 47
1
vote
1
answer
836
views
Derivation of curl of magnetic field [closed]
I am having trouble in one part of derivation of curl of magnetic field, from Biot-Savart law. The attached picture is from Griffiths - Introduction to Electrodynamics.
I got all the parts, but only ...
- 327
1
vote
1
answer
285
views
Help with relativistic notation (Derivative of Lagrangian)
I am trying to learn QFT, but I haven't taken a course in general relativity so the relativistic notation stuff is taking me a bit to get used to. I do not understand how to do the following.
For a ...
- 1,001