Questions tagged [electromagnetism]
For questions on Classical Electromagnetism from a mathematical standpoint. This tag should not be the sole tag on a question.
407
questions
1
vote
1
answer
60
views
How to prove this vector identity? [closed]
I've seen this vector identity from the book[1] in page 89,
$$ (\nabla p)\times\nu =0,\ \text{on}\ \partial\Omega,$$
where $\nu $ is the outer normal vector of $\partial \Omega$, $ p \in H_0^1(\Omega)....
- 45
2
votes
0
answers
29
views
Does this family of curves appearing in the magnetic field of a coil have a name?
While attempting to express the magnetic field induced by a single coil of current (at any point in space, not just on the coil's axis), I tried visualising the set of the infinitesimal contributions $...
- 165
0
votes
0
answers
34
views
Boundary Conditions on the Magnetic Flux Density (B-field)
My question is similar to this one (Boundary conditions magnetic field) in that it is related to the boundary conditions of the magnetic field (B-field). However, my question focuses on mathematically ...
- 665
0
votes
0
answers
67
views
Solving a funky differential equation.
I'm currently trying to solve the DE that defines charge in a circuit containing an Inductor, Capacitor, Resistor and (crucially) a Memristor. This needs to be able to work for any variable values and ...
- 1
3
votes
1
answer
220
views
Show that $\partial_\mu\phi^\ast A^\mu\phi- A_\mu\phi^\ast\partial^\mu\phi=A^\mu\phi\partial_\mu\phi^\ast - A^\mu\phi^\ast\partial_\mu\phi$
The following is loosely related to this question:
[...], the most general renormalisable Lagrangian that is invariant under both Lorentz transformations and gauge transformations is
$$\mathcal{L}=-\...
- 419
5
votes
1
answer
156
views
What is the correct sign for the four-vector potential gauge transform; $A_\mu\to A_\mu\pm\partial_\mu\lambda$ and where does this gauge originate? [closed]
I have three questions regarding the following extract(s), I have marked red the parts for which I do not understand for later reference. The convention followed for the Minkowski metric in these ...
- 419
0
votes
1
answer
44
views
Partial differential equation with Faraday's equation
We were asked to find what equation is satisfied by $\Psi(x,y,z,t)$ given that $\textbf{B} = \nabla \times (\textbf{z} \Psi)$ and
$\textbf{E} = -\textbf{z} \frac{\partial \Psi}{\partial t}$ while ...
- 103
6
votes
2
answers
131
views
Fubini's theorem for differential forms? Why does $\int_{t_0}^{t_1}(\oint_{\partial\Omega}j)dt=\int\limits_{[t_0,t_1]\times\partial\Omega}dt\wedge j$?
In an electrodynamics book I came across the following claim for the electric current density (twisted) 2-form $j$ along the boundary of some 3-dimensional volume $\Omega$:
$$\int_{t_{0}}^{t_{1}}\left(...
- 1,490
1
vote
2
answers
77
views
What does $\vec{\nabla}^2 \vec{E} = \vec{\nabla}^2 \left[ f(\vec{k} \cdot \vec{r} - \omega t) \vec{E}_0 \right]$ mean?
$\vec{E} = f(\vec{k} \cdot \vec{r} - \omega t) \vec{E}_0$ with the constant vector field $\vec{E}_0$
I only know the case if I apply the Laplacian operator on a scalar field, in this case it is a ...
1
vote
0
answers
55
views
Writing momentum 4vector as an integral over the EM stress-energy tensor
I have been watching a series of lectures on general relativity by Neil Turok and I have run into a problem.
In one of the lectures, the professor writes the momentum 4-vector as a contraction of the ...
0
votes
0
answers
17
views
if divergence of a vector is zero, how to find the spherical coordinate of the vector?
The perturbed part of magnetic field is $\mathbf{\delta B}$ where $\mathbf{\delta B} = \delta B_x(x,y), \delta B_y(x,y)$ and
$\nabla \cdot \mathbf{\delta B} = 0$.
To prove $\mathbf{\delta B} = \delta ...
- 37
-1
votes
1
answer
116
views
Polar coordinates: What unit vectors span the $(r,\theta)$ space? [closed]
Polar coordinates: What unit vectors span the $(r,\theta)$ space?
I am thoroughly confused. If in the Cartesian system, the associated orthonormal polar vectors at different points on a circle keep ...
- 419
1
vote
2
answers
176
views
Book Recommendation: One that has a lot of problems and theory associated with polar coordinates and spherical polar coordinates
I would like to "master" polar coordinates and spherical polar coordinates. In the sense, I would like to become as well versed with them as I am with cartesian coordinates.
I have gone ...
- 419
2
votes
1
answer
85
views
How to evaluate the integral $\int_{-r/2}^{r/2} \int_{-r/2}^{r/2} \frac{1}{x^2+y^2+r^2/4} dx dy$
I came across this integral while trying to evaluate the electrical force exerted by a charged plate in the form of a square with side length $r$. I tried the usual method of first keeping $y$ ...
- 409
14
votes
3
answers
3k
views
What is the sum of an infinite resistor ladder with geometric progression?
I am trying to solve for the equivalent resistance $R_{\infty}$ of an infinite resistor ladder network with geometric progression as in the image below, with the size of the resistors in each section ...
- 1,111