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5
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0answers
53 views

Time reversal in classical electrodynamics

It is known that classical electrodynamics is time reversal invariant if one assumes that the transformation laws under such operation are $$\mathbf E(t,\mathbf x)\mapsto\mathbf E(-t,\mathbf x)$$ ...
3
votes
1answer
457 views

Width of a photon. And its length

Everyone is always talking about photon's wavelength. But what about its dimensions? What is length and width of it? And does it even have a point to think about such things? Or those dimensions are ...
0
votes
0answers
15 views

Charge movement in a rotating EM field (relativistic)

I have this problem let's see if anyone can help me advance a little. (No need to say that if my approach is ridiculous or too hard and anyone knows a better solution, I would like to know it). I ...
0
votes
1answer
17 views

Plasma frequency

I have a neutral plasma and I need to solve Maxwell equations given the charge and current densities on the plasma. In order to do it I need to know the electrical permittivity $\varepsilon$, I've ...
6
votes
1answer
74 views

Is the electromagnetic mass real?

In his Lectures on Physics vol II Ch.28-2 Feynman calculates the field momentum of a moving charged sphere with charge $q$, radius $a$ and velocity $\mathbf{v}$. He finds that the total momentum in ...
0
votes
0answers
9 views

Force on a small conductor in an EM wave

What forces act on a small, flat conductor subjected to electromagnetic radiation, if the conductor is much smaller than the wavelength? My guess is that the magnetic field component of the wave ...
1
vote
2answers
66 views

Energy conservation in electrodynamic system?

Consider two charged particles initially at rest in the configuration below. Let us assume the following: Starting at time $t=0$, we apply a constant force $f$ to the the bottom particle so that ...
1
vote
1answer
18 views

Non-constant potential distribution

I know that given a static charge distribution, the closed loop integral of the electric field is zero. But what if the charges are moving, i.e, the potential at a point a changing. Is the line ...
0
votes
0answers
28 views

Electric and Magnetic Field Created by Moving Electron

From a classical perspective, what are the electric and magnetic fields created by a single electron, initially located at the origin and moving along the $x$ axis with velocity $v \ll c$? I'm ...
0
votes
1answer
55 views

Momentum around an accelerated electron

Assume that an electron is accelerated along the +x-axis. The electron will radiate electromagnetic energy and momentum in every direction. But it seems to me that the EM momentum it radiates in ...
0
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0answers
17 views

Electromagnetic induction inside cylinder

Suppose we have a hollow cylinder whose walls conduct some alternating current. We also have a round wire inside cylinder with same axis as that of cylinder so my question is that can there be ...
2
votes
1answer
144 views

Poisson's equation for time dependent charge

Is Poisson's equation valid for a time dependent charge density? I think Poisson's equation is valid just for electrostatic fields. But I saw a paper that's used this equation for time dependent ...
1
vote
1answer
89 views

Why doesn't magnetic forces on current carrying wire depends on relative velocity?

We know that magnetic field arises due to relative velocity of charged particle . Electrons in wire move at very slow drift velocity but relativistic variation of magnetic field doesn't seem to apply ...
1
vote
2answers
69 views

Can magnetic force do work? [duplicate]

I have been told numerous times that magnetic force do no work at all but I have some trouble digesting this fact. Now suppose we have two straight wire with some current, they certainly can feel ...
0
votes
0answers
30 views

Induced potential in a metal

My problem is as follows: A metal whose response is determined by the Thomas-Fermi equation: $(\nabla^{2}-\lambda^{2})V(r)=0 $ , occupies the $z<0 $ infinite half-space: show that the general form ...
0
votes
2answers
53 views

Could we describe acids and bases using electromagnetism?

Why don't we use Maxwell's equations in acids and base theory? Surely the interaction between two charged species is readily described by this. The theory I have so far come across is HASB theory. ...
0
votes
1answer
42 views

Kittel solid state physics handbook - Plasma oscillation of a ball - Am I solving this right?

I'm self learning nanotechnology undergraduate and I'm trying to solve a problem from chapter "plasmons, polaritons and polarons". This is it: Frequency of uniform mode of plasmons in a ball is ...
2
votes
0answers
47 views

Are there limits to human/devices perception?

As far as i know, measurement devices present measurements based on something that affects the device's particles, for instance, forces, heat, tension, voltage... My question is, given that every ...
1
vote
0answers
53 views

Getting the electric field using Green's function [closed]

Let the Green's function for the gauge field be given (after gauge fixing) as $$G_{\mu \nu}(x,y) = \delta_{\mu \nu}G(x-y) \tag{1}$$ where $$G(x-y)= \int \frac{d^dk}{(2\pi)^d} \frac{e^{ik \cdot ...
1
vote
0answers
45 views

Partial Integration of outer product of del and position vector

I am trying to understand the solution I have been given to prove the following relation for a current density $\vec{j}(\vec{r})$ that is concentrated around the origin: $$ \int_V dV \, ...
1
vote
2answers
100 views

Problem with Maxwell's theory

What exactly is the problem with classical Maxwell theory and the blowing up of energy at $r=0$? Does it have any other problems on the classical level?
37
votes
1answer
10k views

How does this “simple” electric train work?

In this YouTube video, a dry cell battery, a wound copper wire and a few magnets (see image below) are being used to create what can be described as "train". It looks fascinating but how does this ...
0
votes
0answers
25 views

current and potentials in conductive sphere with shell

I would appreciate an explanation for calculating the electric potential in this scenario. Central conductive sphere, ends at diameter b, and conductivity $\sigma_1$ Shell (around the central ...
0
votes
1answer
77 views

What are the boundary conditions for EM waves normally incident on the interface between two dielectric media?

An EM wave, amplitude $E_0$, frequency $\omega_0$, is incident upon a material with relative permittivity (dielectric function) $$\varepsilon \left( z \right) = \left\{ \begin{gathered}{\varepsilon ...
0
votes
1answer
73 views

Electromagnetic field or direct interactions between charged particles?

Consider a small distribution of charged particles enclosed by an arbitrary volume $V$ with boundary $S$. It can be shown that the total mechanical momentum of the particles, $\mathbf{P_{mech}}$, ...
2
votes
0answers
37 views

Magnetic Multipole Tensor

When the electric scalar potential is expanded into spherical coordinates, one gets \begin{align} \phi (\vec r) = \frac{1}{4\pi\varepsilon_0} \sum_{l=0}^{\infty} \sum_{m=-l}^l ...
0
votes
1answer
24 views

Rate of work done by fields in a finite volume

In Jackson's Classical Electrodynamics, the rate of work done by fields in a finite volume is defined as $$\int _{v}\vec{J}\cdot\vec{E}\,d^{3}x^{'}$$ How?
1
vote
1answer
81 views

Traceless multipole moments vs non-traceless moments

There are two different possibilities to define the electric quadrupole tensor: On the one hand, one can define \begin{align}Q_{kl} = \int \rho(\mathbf r') \cdot r'_k \, r'_l d^3r',\end{align} while ...
1
vote
2answers
88 views

Momentum conservation in an electromagnetic system?

Suppose that I have two charged particles in the configuration below. Let us assume the following: We apply a constant force $f$ to the the bottom particle so that it has a constant acceleration ...
2
votes
1answer
77 views

Electromagnetic reaction force?

The classical (retarded) Lienard-Wiechert scalar and vector potentials describe the electromagnetic field due to an arbitrarily moving electric point charge. Thus given the motion of electron $A$ one ...
1
vote
1answer
45 views

Lagrangian of Non-Relativistic Charged Particle in a Magnetic Field

I'm trying to derive the Lagrangian for a non-relativistic charged particle under the influence of a magnetic potential. I'm assuming that $F=-grad(V)$ and so by the Lorentz force we have $-grad(V)=q ...
0
votes
1answer
53 views

Stopping current and Maxwell equation compliance

Preamble: Mathematically, the divergence of an eddy field is zero, thus for the magnetic field $$\nabla\cdot\nabla\times\boldsymbol B = \boldsymbol 0$$ and from the $\nabla\times\boldsymbol B$ Maxwell ...
1
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0answers
70 views

Online physics lecture [closed]

I'm looking for online courses "video" for Classical electrodynamics and nuclear physics for undergraduate students .. do you know where I can find it ?
2
votes
3answers
122 views

Self-energy of electron from classical reasoning

If it takes energy to group charge together(self energy) how can it be possible for every single electrons, etc, to have exactly same amount of charge? (think of if we hold some sand in our hand, then ...
10
votes
6answers
1k views

Recommended books for undergraduate electrodynamics

What books are recommended for an advanced undergraduate course in electrodynamics?
1
vote
1answer
71 views

Interaction Lagrangian forms

When a charge motion is given (known), the electromagnetic field can be explicitly found (Retarded potentials, etc.). The interaction Lagrangian density is $j\cdot A$ or in the action it may look like ...
0
votes
1answer
48 views

Field and Charge densities in two dimensional corners and along edges

In jackson's book, we can derive the equation as following. $\sigma(\rho)=\epsilon_{0}E_{\phi}(\rho, 0)\approx-\frac{\epsilon\pi a_{1}}{\beta}\rho^{(\pi/\beta)-1}---(2.75)$ My question is there are ...
4
votes
2answers
229 views

Deriving Heaviside-Feynman formula for the electric field of an arbitrarily moving charge from Lienard-Wiechert potential

I've been trying to derive this (which Feynman warns takes a lot of work) for a couple of days now, without success. My current best derivation which however doesn't give the right answer is: First, ...
0
votes
1answer
35 views

Optical Activity

I was wondering, does the optical activity of a material change under a magnetic field? Assuming it did, how would one analyze this phenomenon in the eyes of classical electrodynamics or classical ...
7
votes
2answers
668 views

Why are EM waves transverse?

I was reading Griffiths' Introduction to Electrodynamics, specifically the section on plane waves. I can see that if we want a transverse wave traveling in the $z$ direction that we are only going to ...
4
votes
2answers
335 views

Feynman's proof for Liénard-Wiechert's potential of a moving charge

Feynman's proof utilizes a geometrical and fundamental integration argument. I like it, except this bit: What makes me unconfortable somehow is that in (c) we are counting in some of the charge we ...
2
votes
0answers
50 views

Induced emf in a circular conducting wheel

Consider a conducting wheel with $N \in \mathbb{N}$ spokes which is completely in a homogenous magnetic field $\vec{B}$ perpendicular to the wheel plane. ...
0
votes
0answers
17 views

Penning Trap Simulation

I'm currently working on a particle tracker and I would like to implement a Penning trap. I think I might have a problem with the field of the electrical quadrupole. My idea was to place 2 dipoles and ...
9
votes
2answers
588 views

Trouble understanding the Bohr model of the atom

In this article it says: The electrons can only orbit stably, without radiating, in certain orbits (called by Bohr the "stationary orbits") at a certain discrete set of distances from the nucleus. ...
16
votes
4answers
2k views

Can two electrons get ever so close as to touch each other?

My friend and I were studying for our EM test when we started to think about what happens to the electric field near an infinite line of charge. $$E = \frac{\lambda}{2\pi\rho\epsilon_{0}}$$ As you ...
3
votes
1answer
75 views

Tensor notation

I'm trying to understand the Maxwell Stress tensor notation. I'm given that each element in the tensor is given by ...
1
vote
1answer
140 views

Using Ampere's Law without Right-Hand-Rule to derive an expression for the magnetic field around a current

I'm a little confused over the textbook example of applying Amperians to get the magnetic field around a current. I understand we take a loop which shares the rotational symmetry of the wire (a ...
0
votes
2answers
65 views

Electric field of spherical charge distribution

When solving the equation $$\boxed{ {1 \over r^2}{\partial \left( r^2 E_r \right) \over \partial r} + {1 \over r\sin\theta}{\partial \over \partial \theta} \left( E_\theta\sin\theta \right) + {1 ...
2
votes
2answers
144 views

Textbook on classical E&M in curved spacetime

Can anyone recommend a good reference for classical electrodynamics that goes over electrodynamics in curved spacetime that doesn't assume much knowledge of GR -- that is it builds up the tensor ...
4
votes
2answers
109 views

Charge vs Charge Density in classical electrodynamics

What is assumed to be a more fundamental physical quantity in classical electrodynamics. The charge density as a scalar field or the physical entity charge.