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36 views

Deriving Lorentz force on a point charge moving perpendicular to external magnetic field using Maxwell stress tensor?

I heard that when we use Maxwell stress tensor to derive Lorentz force on a point charge moving perpendicular to external magnetic field, the result is not $qvB$ but $\frac{2}{3}qvB$. This should be ...
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0answers
45 views

Help understanding electromagnetism integral from exercise in MTW? [closed]

I was skimming through Misner, Thorne and Wheeler's book Gravitation looking for exercises to challenge myself with and came across the following exercise on page 178: Verify that the variational ...
3
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2answers
164 views

Why is there no induced electric field in the experiment (Faraday's Law)

Below are three circuit diagrams for each of Faraday's experiments that allowed Faraday to come up with Faraday's Law. In Griffiths' Introduction to Electrodynamics Griffiths states (on page 302 of ...
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0answers
51 views

Time reversed Abraham-Lorentz reaction force

The Abraham-Lorentz radiation reaction force on a charged particle is given by: $$\mathbf{F_{rad}} = \frac{q^2}{6\pi\epsilon_0c^3}\mathbf{\dot{a}}$$ I understand the situation where one fires a ...
1
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2answers
112 views

Why does the classical electrodynamics Lagrangian density equation have a “field” term and an “interaction” term?

On Wikipedia's page on classical electrodynamics, they state the Lagrangian density equation as follows \begin{equation} \mathcal{L} = \mathcal{L}_{\text{field}} + \mathcal{L}_{\text{int}} = ...
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1answer
121 views

Falling charged objects: energy conservation paradox?

Imagine that we start with two oppositely charged objects on the ground, separated by a distance $d$, with charges $+q$, $-q$ and masses $m$. We raise them both up to a height $h$. In doing so we ...
5
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1answer
108 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
505 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 ...
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0answers
29 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
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1answer
67 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 ...
9
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2answers
169 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 ...
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0answers
13 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
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2answers
111 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
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1answer
25 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 ...
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0answers
54 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 ...
2
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2answers
102 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
34 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
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1answer
202 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
112 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 ...
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2answers
84 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 ...
1
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1answer
117 views

Induced electric field due to a moving wire

An infinite wire carrying a constant current $I$ in the $\hat{z}$ direction is moving in the $y$ direction at a constant speed $v$. Find the electric field, in the quasistatic approximation, at the ...
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2answers
62 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
155 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 ...
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0answers
49 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 ...
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0answers
69 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 ...
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0answers
52 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
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2answers
93 views

Force on a loop with induced current

Consider an infinitely long ideal solenoid with current $I$, radius $a$, turns per unit length $n$. Put a closed conducting loop around it (radius $b > a$), on a common axis through their centers. ...
3
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2answers
168 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?
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1answer
26k 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
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0answers
48 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
189 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
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1answer
104 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
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0answers
45 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
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1answer
28 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
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1answer
108 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 ...
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2answers
97 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 ...
3
votes
2answers
125 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
92 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
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1answer
57 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 ...
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0answers
91 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
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3answers
150 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 ...
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6answers
3k views

Recommended books for undergraduate electrodynamics

What books are recommended for an advanced undergraduate course in electrodynamics?
1
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1answer
78 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
64 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
515 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
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1answer
39 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
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2answers
923 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
447 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
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0answers
71 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
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0answers
25 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 ...