All Questions
55
questions
1
vote
1
answer
31
views
Effect of incident angle on wavelength of transmitted wave for normal polarisation?
In my electrodynamcis assignment I'm being asked to derive the wavelength of a normally polarised wave transmitted through a glass/air interface as a function of $n_1$ (the refractive index of the ...
- 11
0
votes
1
answer
66
views
Direction of propogation of a EMW [closed]
If let say i have an EMW given by- (Note the difference between $k$ and K)
B(x,y,z)=$B_0sin[(x+y)\frac{K}{√2}+wt]\hat k$
i got confused in 2 different outcomes when i wanted to find out the direction ...
- 367
1
vote
0
answers
72
views
Electromagnetic waves in medium with strange polarization vector
I have an exercise in Electromagnetic waves, basically to find the refractive index of a wave in a medium with polarization $\mathbf{P}=\alpha \nabla \times \mathbf{E}$. I used the Maxwell equations ...
- 147
1
vote
0
answers
55
views
How is $E×B$ zero? [closed]
I was reading Feynman lectures vol. 2 pg no. 291. There I found the general solution of one dimensional planar waves along $x$ direction. My question is the when I apply dot product on $E$ and $B$ ...
- 157
0
votes
1
answer
157
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Unpolarized light incidence
A beam of unpolarized light carries 2000W/m2 down onto an air–plastic interface. It is found that of the light reflected at the interface 300W/m2 is polarized with its $E$-field perpendicular to the ...
- 980
1
vote
0
answers
44
views
When and how will charged oscillating pendulum in vacuum and Earth gravity stop?
Let's say there is a positively charged metallic sphere hanging on a thread in Earth's gravity and in vacuum. There is no electric field (except for the field from the sphere itself), no friction etc. ...
- 11
0
votes
1
answer
223
views
Electric field strength $d$km from a television transmitter of power $P$kW, assuming isotropic radiation
I think I need to use the Poynting vector to do this, as it is equal to the power per unit area flowing through a surface.
At a distance $d$km from the transmitter, the surface will have a surface ...
- 75
0
votes
1
answer
320
views
Can both magnetic and electric fields induce current from an EM wave?
I was reviewing a homework problem I completed for class, but I saw different explanation that contradict each other.
My teacher says that this position for the waves is optimal for maximum induced ...
1
vote
0
answers
79
views
Proof $\Delta \vec{E} = \frac{1}{c^2} \frac{\partial ^2\vec{E}}{\partial t^2}$ [closed]
Here's what I'm doing, but I'm not sure if this is correct.
Furthermore, I think $c^2$ is the speed of light, however is $c^2 = (\mu_0\epsilon_0)^{-1}$ as follow?
$$\nabla \times (\nabla \times \vec{...
- 29
-1
votes
1
answer
136
views
Radiating quadrupole [closed]
I'm trying to solve the following problem.
Two charges $+q$ are located along the $z$ axis at $z=\pm a \sin \omega t$. Determine the lowest non-vanishing multipole moments, the vector potential and ...
- 685
-1
votes
1
answer
179
views
Electromagnetics - how to choose a proper normal vector? [closed]
In D.K.Cheng's equation 8-29 he makes the following correlation between the magnetic field intensity $\mathbf{H}$ and the electric field intensity $\mathbf{E}$ in an electromagnetic wave.
Where $\eta$...
- 246
1
vote
0
answers
16
views
When do travelling (accelerating) charged particles emit radiation in their direction of travel and when perpendicular to their velocity? [closed]
I have read numerous things saying that a travelling charged particle emits radiation primarily in a cone in the direction of travel, and other places say the radiation is emitted and polarized in an ...
- 4,509
0
votes
1
answer
86
views
Troubles verifying $\langle \omega \rangle = \frac{1}{2}\epsilon \epsilon_0 |\vec{E}_0|^2$
I'm trying to prove that the time average of the energy density $\omega$ is equivalent to
$$\langle \omega \rangle = \frac{1}{2}\epsilon \epsilon_0 \|\vec{E}_0\|^2$$
for a plane EMW. My approach is to ...
- 254
-1
votes
1
answer
362
views
Calculating the Poynting vector for a line charge moving along its length [closed]
The problem reads:
An infinitely long thin wire carrying a uniform linear static charge density $\lambda$ is placed along the z-axis. The wire is set into motion along its length with a uniform ...
- 133
2
votes
1
answer
1k
views
Confusion even over such a simple application of the Right-hand rule to determine direction of magnetic field
After reading this question on this site I learned that the direction of the magnetic field is given by $\boldsymbol{B}=\frac{1}{\omega}\boldsymbol{k}\times \boldsymbol{E}$
The left diagram below is a ...
- 295
1
vote
0
answers
58
views
How do I know if a solution of Maxwell Equations is caused solely by the charges?
My question is very general and it isn't limited to the system that I calculated the fields. I need a general answer or a particular answer for my problem. I found two fields $\mathbf E,\mathbf B$ ...
- 277
1
vote
3
answers
13k
views
Deriving the wave equation for electromagnetic waves
I'm currently referring to the wave equation derivation given in "Introduction to Electrodynamics" by David J. Griffiths. It follows something like this:
The electromagnetic wave equations are given ...
- 87
1
vote
2
answers
60
views
Calculating at what time electromagnetic wave reaches highest and lowest value? [closed]
I thought electromagnetic waves travel forever and that the peak (both positive and negative) only decreases when the magnitude decreases cus of attenuation but it would never reach 0?
How is it ...
- 13
3
votes
2
answers
2k
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Proof that $||\vec{E}|| = c||\vec{B}||$ for electromagnetic waves from maxwells equations in vacuum
Starting from Maxwell-equations in vacuum :
$$
\nabla \cdot \vec{E} = 0
$$
$$
\nabla \times \vec{E} = - \frac{\partial \vec{B}}{\partial t}
$$
$$
\nabla \cdot \vec{B} = 0
$$
$$
\nabla \times \vec{B} =...
- 297
0
votes
1
answer
68
views
Effect of a linear medium on a plane wave's electric and magnetic fields using wave impedance
A homework problem provides that a plane wave is traveling through a medium with a electric permittivity of 2.54 and has an electric field strength $E$ of $5V/m$. I am asked to find the magnetic field ...
0
votes
1
answer
1k
views
Propagation of EM waves in non-conducting medium
Let's say I produce a thin electromagnetic wave beam that is directed towards a non-conductive large plastic block (let's say 30cm x 30cm x 30cm).
Let's say that the EM beam enters into the solid ...
- 13
0
votes
0
answers
341
views
Electric field on the surface of dielectric sphere and outside sphere
Let a dielectric sphere of radius $r_0$ and permittivity $\epsilon_1$ is placed in medium of permittivity $\epsilon_2$. The electric field inside sphere is $\mathbf{E_1(\mathbf{r})} = E_0 \hat{z}$. ...
- 1,335
1
vote
1
answer
3k
views
EM-Wave: Calculate magnetic field $H$ from electric field $E$
In an exercise I am supposed to calculate the magnetic field from the electric field for a plane, harmonic wave in vacuum.
$$\vec{E} = - E_0 \cdot \sin(\omega t - k z) \cdot \vec{e_y}$$
Using the law ...
- 247
0
votes
1
answer
90
views
EM- waves in anisotropic medium
When ElectroMagnetic waves from vacuum enter the anisotropic medium. If the $\epsilon$(permittivity) matrix is diagonal (with not all diagonal entries being equal). There'll be two waves in the ...
- 101
0
votes
2
answers
944
views
Expressing Maxwell's equations as scalar equations involving differentials in Euclidean space
I am trying to convert Maxwell's equations from the well known differential form (found on Wikipedia Maxwell's equations) into scalar equations involving partial derivatives (more than four equations)....
- 469
1
vote
1
answer
89
views
I am studying polarization of EM waves. Where does this general form come from?
This is a snapshot from The Physics of Waves by Georgi. I am wondering if anyone could explain where this general form of polarization vector comes from? Thank you very much.
- 23
0
votes
0
answers
187
views
Pressure radiation using Lorentz force
We know from theory and experiment that an electromagnetic wave that incides on a surface will generate a radiation pressure normal to that surface as a result of the change in momentum of the wave ...
- 1,172
1
vote
0
answers
156
views
Electromagnetic wave in a prism
Imagine an electromagnetic plane wave entering perpendicular to one of the faces of a prism with the form of a triangle rectangle, which is made of a certain material of refraction index $n$. The wave ...
- 1,172
1
vote
4
answers
3k
views
Can a wave's Poynting vector be in the opposite direction compared to its direction of propagation?
Can a wave's Poynting vector be in the opposite direction compared to its direction of propagation, and if so, what physical implications does it have?
As I understand, the poynting vector s can be ...
- 11
1
vote
0
answers
22
views
Does the absorption intensity for vibrational transition depends on the angle between the electric field vector and the transition moment vector?
Is the transition possible even if there is a certain angle between the electric field vector and the transition moment, given that the photon and molecule are in resonance. My notion is that the ...
- 21
0
votes
1
answer
99
views
Glint effect in electromagnetic waves [closed]
Two plane waves having the same frequency and different intensities:
$$E_0=Ae^{i(\omega t-kr_0)}$$ and
$$E_1=Be^{i(\omega t-kr_1)}$$
arrive at point $P=(x,y)$ from two point sources located at a ...
- 593
1
vote
1
answer
536
views
Non-radiation charge density
For all $l,m$ but $l=0,m=0$, can we find $r_0,w_0$ such that the following charge distributions can represent a charge field that does not radiate:
$$
\rho(r,\theta,\phi) = \Re(c_{l,m} Y_{l,m}(\theta,...
- 371
0
votes
3
answers
2k
views
Calculation of Poynting vector of standing electromagnetic wave
I have this question in my homework where I have the following phasor of the electric field (we assume that all waves have $\omega$ frequency):
$$\overline{\mathbf{E}}_{1}\left(x,y,z\right)=E_{0}\left[...
- 202
0
votes
1
answer
910
views
Why is the lowest TM mode 1,1?
I'm working on Griffiths problem 9.31 and he asks us to find the lowest TM mode in a rectangular wave guide… First, I need to deduce $E_z$. Using separation of variables I found that
$$ E_z(x,y) = E_0 ...
- 356
1
vote
1
answer
861
views
Electric field of uniformly moving charge ; misprint in Feynman textbook? (28.3)
I doubt about formula (28.3) from this Feynman's lecture.
$$\textbf{E} = - \frac{q}{4 \pi \epsilon_0 } \Big{[} \ \frac{e_{r'}}{r'^2}+ \frac{r'}{c} \frac{d}{dt} \Big( \frac{e_{r'}}{r'^2} \Big) + \...
- 115
3
votes
3
answers
621
views
Tricky question involving finding the magnetic field given the wave equation for the electric field and it's solution
Consider the wave equation for linearly $x$ polarized waves travelling in the $\pm z$ directions:
$$\frac{\partial^2\vec E_x}{\partial t^2}=c^2\frac{\partial^2\vec E_x}{\partial z^2}\tag{1}$$
...
- 2,470
1
vote
0
answers
74
views
How should one generalize the proper radiation reaction force of a charge to any Lorentz frame?
In section 8 of Medina's paper Radiation reaction of a classical quasi-rigid
extended particle, he writes
The motion equations of the dressed mass, (56) and (57), show that the radiation reaction ...
- 5,318
1
vote
1
answer
60
views
Dirac's paper on classically radiating electrons: scalar product of $ev_{\gamma}f^{\nu}_{\mu}$ with $v$ is zero?
In Dirac's paper, classical Theory of Radiating Electrons, he analyzes electromagnetic radiation entering and leaving a world tube surrounding the world line of a charge moving under the influence of ...
- 3,108
1
vote
1
answer
1k
views
Derivation of the electric dipole radiation
An harmonic oscillating source will emit fields of the form
\begin{align}
&\mathbf{H}=\frac{ck^2}{4\pi}(\mathbf{n}\times\mathbf{p})\frac{e^{ikr}}{r}\left( 1-\frac{1}{ikr} \right) \tag{1}\\
&\...
- 937
1
vote
1
answer
248
views
Derive the form of the fields for TEM waves in a waveguide
In my book it says that for TEM waves in a waveguide, with: $$\textbf E = \textbf E_0(x,y)e^{i(kz-\omega t)}$$ and $$\textbf H = \textbf H_0(x,y)e^{i(kz-\omega t)},$$ where $z$ is the direction of the ...
- 789
0
votes
2
answers
2k
views
Maxwell's equations for electromagnetic wave
Good day, I am a student of Physics at the university of Padova, I must solve this problem for my exam of electromagnetic fields, but I have got different problems. The text is the follower:
The ...
- 3
0
votes
0
answers
71
views
Longitudinal waves in matter
What would be the best way to show that longitudinal waves satisfy the following equation: $$\nabla ^2 \textbf E\space - \space \frac{1}{c_0^2}\frac{\partial^2 \textbf E}{\partial t ^2}=\frac{1}{c_0^2}...
- 789
1
vote
0
answers
82
views
Radiation of a circular orbit intensity and polarisation [closed]
Consider a (non-relativistic) particle with charge q on a circular orbit with radius $r$ and angular velocity $\omega$.
I would now like to calculate and draw the radiation profile due to the dipole ...
- 415
5
votes
1
answer
545
views
Why do planets not radiate EM waves in their orbits?
Despite being overall near-netural, I would expect the individual electrons and proton to radiate long EM waves as we accelerate around the Sun or rotate around our poles. Is the acceleration so small ...
- 163
-1
votes
1
answer
96
views
How I can prove refractive index in an environment is this? [closed]
in "Applied Quantum Mechanics" by A.F.J. Levi, is a problem that I couldn't solve it can any solve it:
if electrical filed is:
$$
\mathbf{E}\left(\mathbf{r}, \omega \right) =\mathbf{E}_{0}\left(\...
- 189
1
vote
1
answer
61
views
Charge affected by EM-pulse. What is the equation of motion?
I'm studying for my test on radiation for Tuesday. I came across this exercise. Thought it looked interesting but now I'm stuck and I can't move forward before I finish this one.
Exercise:
A ...
- 35
0
votes
0
answers
134
views
Gradient of Greens function
This question is about Jackson's equation (10.75) and (10.77) I don't know the step in between these two equations.I'm not sure what our unit vector $n'$ will be here and how can we take gradient of ...
- 385
1
vote
1
answer
294
views
How do integral representations of $\mathbf A$ and $\Phi$ satisfy Lorenz condition?
The following are the integral solutions of the potentials, obtained from the retarded potentials (by a Fourier transform):
$$\mathbf A (\mathbf r) = \frac{\mu_0}{4\pi}\int_V \frac{\mathbf J (\mathbf ...
- 903
-3
votes
2
answers
7k
views
How to determine the angular velocity of a particle with mass $m$ and charge $q$ in a constant B field? [closed]
$\textbf{PROBLEM:}$
A particle with mass $m$ and charge $q$ moves in a constant magnetic field $B$. Show that, if the initial velocity is perpendicular to $B$, the path is circular and the angular ...
0
votes
2
answers
147
views
Wave number of $\mathbf{E}$ field
If I have an $\mathbf{E}$ field:
$$ \mathbf{E}_1 = x E_0 e^{-j(y-z) } $$
I think I can find its wave vector direction by finding the $\mathbf{H}$ field and then solving for the Poynting vector $\...
- 143