# Electro dynamics Definition and 72 Discussions

The Electro-Dynamic Company manufactured electric motors and generators 1880-2000, principally as a subsidiary of the Electric Boat Division of General Dynamics and its predecessors.

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2. ### Kramers-Kronig, parity and delta function

Hi, First of all, I'm not sure to understand what he Kramers-kronig do exactly. It is used to get the Real part of a function using the imaginary part? Then, when asked to add a peak to the parity at ##\omega = -\omega_0##, is ##Im[\epsilon_r(\omega)] = \delta(\omega^2 - \omega_0 ^2)## correct...
3. ### Radiation emitted by a decelerated particle

Honestly, folks, I don't even know how to start. I included in the Relevant Equations section the relativistic generalization of the Larmor formula according to Jackson, because that's the equation for the power emitted by an accelerated particle, but I don't see how that gets me very far. The...
4. ### I How do I find the Direction of an induced electric field?

Faraday's law tell's you about the line intergal of the electric field, but you have to know the direction of the induced electric field first in order to properly apply it. How can I find its direction? Is it in the same direction as the induced current?
5. ### A Penetration depth of a ion beam coupled with an EM wave

A Ion source is a device that allows creating ion beams (e.g. argon ions) and to project them outside the device, for example to be further processed by a particle accelerator, or to irradiate materials or biological tissues etc. Now, suppose the ion beam is coupled with an EM wave, especially...
6. ### I Polarizing filter synthesis and dynamics

I have found a fair amount of sources for studying polarized light but I haven't found sources discussing synthesis of polarizers in detail along with mechanistic discussion.
7. ### Zangwill Modern Electrodynamics Lectures?

Summary:: Courses in electrodynamics Any online lectures or courses keyed to this book? Thanks very much
8. ### I Linear EM wave transmitted

Hi, I have an expression in my textbook that I don't really understand. I have 2 questions regarding this expression for a linear EM wave## \tilde{\vec{E_{0i}}} = (E_{0x} \hat{x} \pm E_{0y} \hat{y}) e^{i(kz- \omega t)}## ## \tilde{\vec{E_{0t}}} = (\sum_j E_{oij} e_{pj}) \hat{e_p} ## ##...
9. ### Classical Electrodynamics Recommendations

I'm currently studying quantum mechanics from MIT opencourseware, just about to finish 8.05, quantum physics 2. I have little knowledge of electrodynamics, but I want to learn enough to be comfortable studying quantum electrodynamics in the future. My math background is pretty strong, so I've...
10. ### I Moving charges in electrostatics

According to a popular book on electrodynamics a special case of electrostatics is- ''source charges are stationary (though the test charge may be moving)''. My question is- now that the test charge is moving, how is it a special case of electrostatics anymore? Also many times we deal with...
11. ### Capacitance of a parallel-plate Capacitor with non uniform dielectric

Hey guys! I'm having trouble with the solution that I arrived at. Through boundary conditions I'm able to determine ##\vec{D}## as $$\vec{D}=-\frac{4Q}{R_0^2}\hat{e_z}$$ (In CGS units) Trough that I'm able to get the electric field as $$\vec{E}=-\frac{1}{\epsilon(r)}\frac{4Q}{R_0^2}\hat{e_z}$$...
12. ### I Relation between blackbody radiation and spontaneous emission

I'm wondering what the relationship between blackbody radiation and spontaneous emission is. As far as I know, there are three sources of EM radiation - thermal radiation, oscillating dipole (multipole?), and LASER. And it seems like light emission from an atom can be separated into two...
13. ### Classical explanation for microwave door shielding

What is the classical explanation for why the microwaves won't pass through the microwave door?
14. ### Induced voltage difference in a magnetic field

Hi everyone, I'm currently working on the problem listed above. I'm pretty new to electrodynamics, and I'm learning on my own through a book. I was wondering if someone can please help me through this problem. Here are my thoughts: I think I need to use Faraday's Law of Induction for part...
15. ### The motion of a charged particle in a magnetic field

qvB=mv^2/R R=mv/qB= p/qB ! As you can see, the difference between this relation and the relation in question is in 'c'. Maybe my way is wrong. Maybe I should get help from relativity because the speed of light is involved here. Please help. Thankful
16. ### Intuition about electromotive force (EMF)

My understanding of emf Let us consider 2 parallel plates with charges (opp. but equal in magnitude) stored on it. When we connect both the plates from the outer side, the electrons from the lower potential (i.e., negatively charged plate) moves to the higher potential (positively charged plate)...
17. ### Can the displacement current be equal to and opposite in sign to the conduction current so the total current will be zero?

If so, what will I measure in the Ampermeter, the zero total current or the value of the conduction current? I was thinking of the following example- a circuit consist of a current source, an Ampermeter, a switch, and a semiconductor. The semiconductor can have both conduction and displacement...
18. ### DIY Electromagnetic Induction Experiment

So I was watching this video containing DIY experiments on electromagnetic induction . At minute 4:45, the dude pretty much creates a transformer without using an iron core. He runs 30-50 kHz AC in a coil (forming the primary circuit) and then brings another coil with its ends attached to a...

20. ### Interaction between the induced magnetic field and a changing magnetic field

Hello, If you have an appropriately oriented conductive ring in a constantly changing magnetic field, current will flow in the ring. There will also be a magnetic field associated with the current in the ring. I understand (maybe ... ) that the current is due to the electric field which is...
21. ### How to deduce the image method solution for a charge outside of a sphere

I was wondering if there is a way to deduce the solution of the potential of a charge outside a sphere given by the image method, though Green functions. Because of a Dirichlet condition (GD(R,r')=0), I know that a solution can be written as GD=Go+L, where ∇2L=0. But in order to approach this...
22. ### Charges in a Gas Discharge

As I understand both cations and electrons are produced between cathode and anode in a gas discharge, but what is their imminent fate, during and post discharge event? The majority of information I could find only covers the electrons from the time of the first ionization event to impacting the...
23. ### Work Done, by what on what? [electrical/mechanical]

I have been reading older posts containing "work done", but they don't seem to answer my doubts, or maybe I don't understand the answers because I need some visual pedagogical aids. I can sort of take the concept in, when we are dealing with a charge in an electric field, but when it comes to...
24. ### I Personal COMSOL challenge (EM)

Hi Y'all For the purpose of exploring COMSOL, I challenged my self to plot the E/M-fields of a piece of current carrying wire in 3D. It's quite a simple task to plot the fields inside the wire, but I fail when plotting the fields outside the wire. For plotting the outside fields I have...
25. ### A Compactification of spatial extra dimensions

Hi everyone, I am looking at a paper on compact dimensions. Equation 65 makes sense except for the term of 4*pi*n*R in the denominator. Why is it 4*pi and not 2*pi? I cannot rationalize this. Please help. Thank you. https://arxiv.org/ftp/hep-ph/papers/0609/0609260.pdf
26. ### Studying Self-Studying Electrodynamics- Am I doing it correctly?

So I am self-studying electrodynamics using Wangsness' Electromagnetic Fields textbook. Now, I have completed till chapter 21 (Maxwell's Equations). From the electrostatics part, out of the total end chapter problems for each chapter, I was able to solve all excluding 2 or 3. That is, if there...
27. ### The Angular Momentum of an Electric and Magnetic Charge

Relevant Equations: Angular momentum density stored in an electromagnetic field: $$\vec{l}_{em} = \epsilon_0[\vec{r} \times (\vec{E} \times \vec{B})]$$ Electric field of an electric charge: $$\frac{q_e}{4\pi\epsilon_0}\frac{r - r'}{|r - r'|^3}$$ Magnetic field of a magnetic charge...
28. ### Constructing an equation for the induced EMF in terms of the radius of the circular loop

In order to calculate for the curl of the induced electric field for a loop moving in a uniform magnetic field, and using the cylindrical coordinate system for a curl, it's my understanding that since the B field is in the 𝑧̂ direction, then so is the partial time derivative of B, and therefore...

30. ### If a magnet does not feel the Lenz force, will there be a violation of energy?

Consider the following, a magnet and a charge is attached to a platform, which is constrained to move only up and down direction. Now, if magnet is moved towards charge, due to changing magnetic field, an electric field will be created. This electric field will impart force on charge. since the...
31. ### Finding the induced EMF in a solenoid-wire system

I know that ##B = \mu n I## and ##\phi = B \pi R^2##. So with have ##d\phi / dt = \mu n \alpha \pi R^2##. But I don't know what to do with this? is this the answer? I don't think so but I don't know what to do after this.
32. ### Jackson E&M: Power loss in waveguides for TE & TM modes

Hi. I'm having trouble with calculating (8.59) from (8.58) (## \vec H_{//} ## is simply ## \vec H ## in Jackson, but that shouldn't matter.) in Jackson. Specifically I think I'm not sure about parallel component of H field here. For example, shouldn't I have two terms for the...
33. ### Electrodynamics: Vector Calculus Question

Why are the red circled Del operators not combining to become 'Del-squared' to cancel out the second term to give a net result of 0?
34. ### Kramers-Kronig Relations: Principal Value

I'm kind of confused on how to evaluate the principal value as it's a topic I've never seen in complex analysis and all the literature I've read so far only deals with the formal definition, not providing an example on how to calculate it properly. Therefore, I think just understanding at least...
35. ### I Hamiltonian for a field

Hi, I hope this is in the right section. It's for EM which I guess is a relativistic theory but the question itself is not to do with any Lorentz transformations or anything similar. I'm reading through Jackson with my course for EM and I'm on the section where he is generalising the Hamiltonian...
36. ### System of charges

Homework Statement Two charges, ##-q_1## and ##q_2## are fixed in the vacuum and separated by a distance ##a##. What should be the velocity ##v## of a particle with mass ##m## and charge ##q##, traveling from an infinitely far point along the line which unites ##q_1## and ##q_2## in order to...
37. ### Interesting Magnetic Field Induction Problem

Homework Statement Suppose we have an isolated, long, narrow straight wire with low electrical resistivity. A constant current ##I## is sent through this wire. We know that if an electron is sent on a path which is perpendicular to the wire, towards it, with an initial speed ##v_0##, and the...
38. ### I Falling electric dipole contradicts the equivalence principle?

Consider an electric dipole consisting of charges ##q## and ##-q##, both of mass ##m##, separated by a distance ##d##. If the dipole is given an acceleration ##a## perpendicular to its moment the total electric force on it, due to each charge acting on the other, is given approximately by...
39. ### What happens to the Electrical Potential the closer we are to a point charge?

So I have been wondering: The potential for a point charge at the origin, is described as: (Using the reference point at infinity): V=1/(4πε) * q/r My question is, what happens to this Potential the closer we are to the point charge, and so the closer we would get, the Potential seems to go...
40. ### Show that the radiation field is transverse

Homework Statement Show that the radiation field is transverse, ##\vec{\nabla}\cdot\vec{A}=0## and obeys the wave equation ##\nabla^2\vec{A}-\frac{1}{c^2}\partial_t^2\vec{A}=0##. You should start from the expansion of the quantum Electromagnetic field. Homework Equations ##H=\frac{1}{2}\int...
41. ### Spherical Capacitor Discharging Through Radial Resistor

Homework Statement A spherical capacitor has internal radius ##a## and external radius ##b##. At time ##t = 0##, the charge of the capacitor is ##Q_0## Then the two shells are connected by a resistor in the radial direction of resistance ##R##. Find the Poynting vector and the energy...
42. ### Trying to understand a derivation in a paper

Hello PF, first of all I don't know where to put this post as it's not exactly a homework question but a clarification question for a project. I'm going through the derivation of the effective permeability of two stacked medias, given the polarization of an incoming EM wave but I'm stuck at the...
43. ### Free surface charges on concentric cylinders

Homework Statement Consider an infinitely long cylindrical rod with radius a carrying a uniform charge density ##\rho##. The rod is surrounded by a co-axial cylindrical metal-sheet with radius b that is connected to ground. The volume between the sheet and the rod is filled with a dielectric...
44. ### Field strength tensor for a moving charged particle

Hi, I am studying Chapter14 in Jackson. My attached file is about field strength tensor. My question is how can I obtain the radiation and the non-radiation terms in the field strength tensor for a moving charged particle. Many thanks.
45. ### Deriving magnetic dipole moment from multipole expansion

Homework Statement This is from Griffith's Introduction to Electrodynamics, where the book is deriving the magnetic dipole moment from multipole expansion of the vector potential The vector potential of a current loop can be written as \mathbf{A(r)}=\frac{\mu_0 I}{4\pi} \left[ \frac{1}{r}...
46. ### Vector potential of a plate with a uniform, time-harmonic current density

Hi all, i tried to do this question but got stuck on the last point . Can anyone help me please? The general form of vector potential: I got the answer for A1 vector potential but don't know what assumptions i need to get the expression for the A2. Does anyone know how one can derive it...
47. ### Direction of induced electric field?

If there is a very very big(infinitely big) region of space where ## \frac {dB} {dt} = constant ## what would be the E field at any point? Obviously ## \nabla x E = constant ## but what after that ?
48. ### Motion of Charged Particles in E&B Fields

Homework Statement Problem Statement: A system consists of a long cylindrical anode of radius a and a coaxial cylindrical cathode of radius b (b < a). A filament located along the axis of the system carries a heating current I producing a magnetic field in the surrounding space. Find the least...
49. ### I Particle Focusing using EM fields

Good day all! I have a question that has been in my head bouncing around for a while and I figured the best resource would be here as I can't find anymore related information (Or I am just looking in the incorrect spot). My apologies if this is in the wrong section I wasn't too sure where to...
50. ### Electric Field of a solid sphere of non-uniform surface density

A solid sphere has surface charge density, Rho (r) Rho(r) = k 1 ( 0 < r < a) k2 x ( a < r < R) 2) Find the electric field in all region i.e 1) r < a and 2) a < r < R and 3 ) R < The attempted solution and the question with the diagram is attached below Could the answer be verified...