All Questions
Tagged with physics electromagnetism
101
questions
2
votes
2
answers
1k
views
Finding the distance from a point a distance $z$ above the center of a square to any point on the edge
I was working on an electrostatics problem that I thought I was doing correctly. However, upon reading the solution I see I was not. I will post my attempt and the solution below and then ask a few (...
- 2,220
1
vote
1
answer
59
views
"Double" relativistic variant of the same classical mechanics equation
This question is about my curiosity about the relativistic Kepler equation of which I am reading in a recent paper. Actually, I am only interested in an introductory concept stated in paper.
Let
$$ m\...
- 3,277
0
votes
1
answer
119
views
Help with a physics problem about the magnetic field
Text of the problem:
A circular loop of radius $R$ carries a current $I_1$. Perpendicular to the plane of the coil, and tangent to it, there is an indefinite rectilinear wire, traversed by a current $...
0
votes
0
answers
82
views
Electric Field felt at the origin of a hemisphere
I want to calculate the Electric Field that is felt at the origin $O$ provoked by a hemisphere of radius $R$ with uniform charge density $\sigma$.
I used spherical coordinates: $\vec{r} = -R(\sin(\phi)...
- 653
0
votes
0
answers
34
views
Translational invariance of sources/materials implies translational field invariance
Let's say we have an electromagnetic problem where $\epsilon = \epsilon(x,y)$, $\rho = \rho(x,y)$, and $J = J(x,y)$. The physicist argument is that by the symmetry of the problem we also have $E = E(x,...
- 613
4
votes
1
answer
158
views
Properties about an elliptic integral of the first kind.
In polar coordinates, the electric potential of a ring is represented by the next relation
$$
\frac{\lambda}{4\pi\varepsilon_0}\frac{2R}{|r-R|}\left( F\left(\pi -\frac{\theta}{2}\Big|-\frac{4 r R}{(r-...
- 51
1
vote
2
answers
71
views
Boundary Problem for Electrostatic Potential
I have been working on a exercise that asks me to resolve the 2nd order differential equation for a electrostatiic problem. Here it is the exercise statement:
Letting u be the electrostatic potential ...
- 13
4
votes
2
answers
145
views
Flux integral of Gauss law
Consider a point charge enclosed by some surface, using spherical coordinates, and taking $\hat a$ to be the unit vector in the direction of the surface element, flux is
$$\oint\vec E\cdot d\vec A = ...
3
votes
2
answers
318
views
Is curl of a particle's velocity zero?
The question
Consider the motion of a particle specified by $\mathbf{x} (t): \mathbb{R} \mapsto \mathbb{R}^3$, where $\mathbf{x} = (x_1,x_2,x_3)$ in cartesian coordinates. The curl of its velocity $\...
- 33
2
votes
0
answers
60
views
Approximate value of hyperbolic tangent in certain case
I am reading Thé Nature of Magnetism. While reading, I came across a particular approximation of hyperbolic tangent
while in first case $T>T_c$ , it is just Taylor series,
in case $T < T_c$ ( ...
- 21
0
votes
1
answer
249
views
Using "Maxwell's curl equations" to get $H_y = \dfrac{j}{\omega \mu} \dfrac{\partial{E_x}}{\partial{z}} = \dfrac{1}{\eta}(E^+ e^{-jkz} - E^- e^{jkz})$
I am currently studying the textbook Microwave Engineering, fourth edition, by David Pozar. Chapter 1.4 THE WAVE EQUATION AND BASIC PLANE WAVE SOLUTIONS says the following:
The Helmholtz Equation
In ...
- 4,322
2
votes
1
answer
126
views
What does it mean to say that "$h$ is a coordinate measured normal from the surface"? How does this work in practice?
I am currently studying the textbook Microwave Engineering, fourth edition, by David Pozar. Section Fields at a General Material Interface of chapter 1.3 FIELDS IN MEDIA AND BOUNDARY CONDITIONS says ...
- 4,322
2
votes
1
answer
187
views
Calculating the average of the square of the magnitude of an electric field
Let the sinusoidal electric field polarised in the $\hat{x}$ direction be $\overline{\mathcal{E}}(x, y, z, t) = \hat{x}A(x, y, z)\cos(\omega t + \phi)$, where $A$ is the amplitude, $\omega$ is the ...
- 4,322
1
vote
1
answer
102
views
Can we have vectors with vectors as components?
I was working on my course on Electrodynamics earlier today, when I was tasked with computing the eletric field of a non-trivial charge distribution, and it struck me that I had a field with ...
- 487
1
vote
1
answer
437
views
How does $\sqrt{-\omega^2(\epsilon - j\sigma/\omega)\mu}$ having either a positive or negative sign determine $\alpha_0$ and $\beta_0$?
I am told that Maxwell's equations take the form
$$\text{curl} \ \mathbf{E} = - \mu j \omega \mathbf{H}, \ \ \ \ \ \text{curl} \ \mathbf{H} = (\sigma + \epsilon j \omega) \mathbf{E},$$
where $\sigma$ ...
- 4,322