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7
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5answers
239 views

Recommended books for undergraduate electrodynamics

What books are recommended for an advanced undergraduate course in electrodynamics?
2
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2answers
121 views

What is the area in Faraday's law if we have only a piece of metal moving in a magnetic field?

If a piece of metal of length $l$ is moving with a speed $v$ in a region where there is a uniform magnetic field $B$ perpendicular to it, there will be a potential difference across its terminals ...
1
vote
1answer
56 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 ...
9
votes
1answer
366 views

Recovering all of Maxwell's equations from the variational principle

Whether you can get the first couple of Maxwell equations from a variational principle? In the second volume of the Landau theoretical physics said that it is impossible.
1
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1answer
40 views

Particle in Oscillating Field

Ignoring quantum effects, what are the dynamics of an electrically charged particular placed with zero initial momentum in an oscillating electromagnetic field, e.g. light?
2
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2answers
198 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 ...
3
votes
1answer
124 views

Physical interpretation of Green's theorem with Dirichlet boundary condition

The potential is given by $$\Phi(\mathbf{x})=\int_V d^3x' G_D(\mathbf{x},\mathbf{x'})\rho(\mathbf{x'})-\frac{1}{4\pi}\oint_S d^2x'\frac{\partial G_D(\mathbf{x},\mathbf{x'})}{\partial ...
0
votes
1answer
33 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 ...
1
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0answers
44 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
24 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
463 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 ...
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 ...
1
vote
1answer
51 views

calculating electrodynamic momentum of a dumbbell (consisting of two point charges) in longitudinal motion

I'm working through a paper on momentum in electrodynamics that requires the integration below and would greatly appreciate any help. I'm pretty sure it evaluates to $2/d$ but I can't quite figure ...
20
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3answers
3k views

What is the answer to Feynman's Disc Paradox?

[This question is Certified Higgs Free!] Richard Feynman in Lectures on Physics Vol. II Sec. 17-4, "A paradox," describes a problem in electromagnetic induction that did not originate with him, but ...
2
votes
0answers
32 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
12 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 ...
5
votes
1answer
233 views

Maxwell's Stress Tensor

What really is the Maxwell Stress Tensor? I understand that it's derived from $$\mathbf {F} = \int _V ( \mathbf E + \mathbf v \times \mathbf B )\rho \ d \tau$$ Griffiths describes this as "total EM ...
1
vote
1answer
183 views

Frequency of rotating coil

Given a coil initially in the x-y plane, rotating at angular frequency $ \omega $ about the x-axis in a magnetic field in the z-direction. This uniform time varying magnetic field is given by $B_z ...
8
votes
2answers
502 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. ...
1
vote
1answer
157 views

Total Momentum From a Standing Electromagnetic Wave

How does one show the momentum imparted to a perfect conducting resonance cavity (boundary) of any shape by a classical standing electromagnetic wave inside is zero? It should be by conservation of ...
1
vote
1answer
72 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 ...
1
vote
1answer
66 views

Angular momentum of light

Can someone explain the classical angular momentum in electromagnetic theory of light? If I shine elliptically polarised em wave on a black disc it rotates. I would like to know how to calculate ...
0
votes
2answers
115 views

Drift Speed and Current in Two Different Inertial Frames

We have a long, cylindrical wire carrying a constant current I in an inertial frame. At a distance of R from the center of the wire, the magnitude of magnetic field is $μI/2πR$. What is the magnitude ...
3
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1answer
70 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 ...
0
votes
2answers
43 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 ...
3
votes
1answer
99 views

Motion in a Paul trap: $2n$th harmonic with larger amplitude than $n$th harmonic

Using a Paul trap, we captured the motion of a light charged particle (based on a rotating potential applied by AC current). Our rotational frequency was 50 Hz, and so when used FFT on the data, we ...
4
votes
1answer
289 views

Is there a Hamiltonian for the (classical) electromagnetic field? If so, how can it be derived from the Lagrangian?

The classical Lagrangian for the electromagnetic field is $$\mathcal{L} = -\frac{1}{4\mu_0} F^{\mu \nu} F_{\mu \nu} - J^\mu A_\mu.$$ Is there also a Hamiltonian? If so, how to derive it? I know how ...
2
votes
1answer
70 views

Far Field Diffraction of EM waves: what does the zero frequency signify?

If you have a system of independently radiating electrons/point-charges, the far field distribution of the EM waves can be approximated by the fraunhoffer diffraction integral, or simply by the ...
2
votes
2answers
126 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
130 views

Instantaneous Coulomb interaction in QED

It seems I am stuck with a (at a first sight) trivial problem. It's from the "Quarks and Leptons" (Halzen, Martin) book page $141$, where one considers the following integral: $$\tag{1} T_{fi} = ...
2
votes
1answer
44 views

Demagnetisation by throwing a magnet

I tried to answer this question in a book about electrodynamics: How to demagnetise a permanent magnet, ie. described by $ D_T$ change into described by (0,0) I figured out about heating it up ...
2
votes
1answer
81 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.
1
vote
1answer
66 views

Relating Quantum Mechanics to Classic Electromagnetism [duplicate]

I've been directed to a few articles, and I am sure there is a related post, but can someone explain the procedure by which we can view classic electromagnetism through quantum mechanics? Indeed we ...
1
vote
2answers
205 views

Grounded conducting sphere inside uniform electric field

The problem of a grounded conducting sphere inside a uniform $E$ field in the $z$ direction can be solved by imagining the field be produced by a pair of charges $Q$ and $-Q$ put on the $z$ axis, ...
4
votes
2answers
345 views

Aharonov–Bohm effect on a non-contractible manifold

The Aharonov–Bohm effect shows the vector potential $\mathbf{A}$ is more fundamental than magnetic flux density $\mathbf{B}$. However, vector potential is introduced by $$ \nabla \times \mathbf{A} = ...
4
votes
2answers
337 views

What is the magnitude of the force on a charged particle due to electromagnetic radiation?

Suppose there is an electromagnetic wave moving forward in the $\mathbf{\hat{k}}$ direction. Its electric/magnetic field components are given by: $$\mathbf{E} = E_0 \sin(kz - \omega t) ...
2
votes
5answers
256 views

Is the canonical momentum conserved when a particle moves in magnetic field?

Here is a question about the canonical momentum that I had asked some days ago, but I still have one point that I am not understand. Considering a particle moves in a magnetic field with charge $q$ ...
0
votes
0answers
36 views

My model of Conductors in “static” condition - Please analyze

My textbook presents an idealization of a conductor as made up of infinitesimal units of charge and derives results. I was not convinced, so I started thinking of how electric fields are in real ...
0
votes
2answers
58 views

Inductor's energy

I have some knowledge about LC circuits, like I know Maxwell's equations, the differential equations of circuit oscillator and so on. I am armed with equations to solve physical problems involving ...
1
vote
0answers
58 views

Poynting Vector Volume Integral Inside a Cavity

Given an electromagnetic wave in resonance mode in a vacuum cavity inside a perfect conductor, on the boundary, the parallel component of $E$ field vanishes, and the perpendicular of component of $B$ ...
1
vote
1answer
96 views

Ion Optics: Electric and Magnetic field. A comparison with Light Optics

When we compare ion optics with light optics, normally we consider electric field. For example Snell's law. $n_1\sin\theta_1$=$n_2\sin\theta_2$. When an electron move from one electric potential to ...
3
votes
2answers
91 views

Utility of gauge four-potential $A_{\mu}$ (as opposed to electric and magnetic fields ${\bf E}$ and ${\bf B}$) in E&M?

The action for an electromagnetic field with source charges is given by $$S= \int \left\{ \frac{1}{4\mu_0}F^{\mu\nu}F_{\mu\nu} - J^\mu A_\mu \right\}dx$$ By setting $dS=0$ and taking the Lorenz ...
0
votes
2answers
98 views

Can the Lorentz force stabilize the Hydrogen atom?

I've recently been working on relative equilibria for some systems of particles. (ie. studying equilibrium solutions in a rotating frame. Saturn's rings for example.) This has evolved into some ...
3
votes
2answers
137 views

Classical Viewpoint on Electromagnetism

Note: This question may be difficult or impossible to answer within the rules of these forums due to its philosophical nature. I will delete the question if I am violating the rules. Onto the ...
24
votes
5answers
4k views

Does a magnetic field do work on an intrinsic magnetic dipole?

When you release a magnetic dipole in a nonuniform magnetic field, it will accelerate. I understand that for current loops (and other such macroscopic objects) the magnetic moment comes from moving ...
3
votes
2answers
70 views

Showing that Coloumb and Lorentz Gauges are indeed valid Gauge Transformations?

I'm working my way through Griffith's "Introduction to Electrodynamics". In Ch. 10, gauge transformations are introduced. The author shows that, given any magnetic potential $\textbf{A}_0$ and ...
2
votes
2answers
44 views

Reference on electrodynamics with tempered distributions

Back in my undergrad I had a course on classical electrodynamics where the fields had values in the space of tempered distributions. In this way one could correctly treat self-interaction and ...
3
votes
2answers
55 views

Why is radiation for an ultrarelativistic charge zero on axis?

I attribute it to the fact that for an ultrarelativistic charge the field is contracted and essentially there are only fields in the transverse direction and nothing longitudinally (wrt the charges ...
3
votes
0answers
138 views

Free charge movement in an electric field - including bremsstrahlung

Let us imagine a free, negatively charged object that is in rest and placed in an elecric field of a point positive charge. The positive charge has a huge mass and cannot move, so we consider only the ...
1
vote
1answer
53 views

Why can we allow the speed of light being infinite in case of Surface Plasmons?

I have a problem with understanding of these sentences: We have indicated in the opening paragraph of the Introduction that surface plasmon polaritons are solutions of Maxwell’s equations in ...