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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 ...
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3answers
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 ...
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1answer
167 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 ...
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1answer
179 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 ...
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2answers
476 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. ...
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1answer
148 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 ...
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1answer
60 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 ...
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1answer
64 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 ...
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2answers
112 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 ...
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1answer
63 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 ...
2
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2answers
118 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 ...
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2answers
40 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 ...
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1answer
33 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?
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0answers
98 views

Complex integration by shifting the contour [migrated]

In section 12.11 of Jackson's Classical Electrodynamics, he evaluates an integral involved in the Green function solution to the 4-potential wave equation. Here it is: $\int_{-\infty}^\infty dk_0 ...
3
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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 ...
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1answer
102 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 ...
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1answer
269 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 ...
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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 ...
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2answers
120 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 ...
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2answers
128 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} = ...
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1answer
43 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
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1answer
78 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.
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1answer
62 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 ...
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1answer
47 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 ...
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2answers
147 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, ...
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2answers
337 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} = ...
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2answers
329 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) ...
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5answers
230 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 $q$ ...
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0answers
32 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 ...
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2answers
55 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 ...
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0answers
56 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 $B$ ...
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1answer
90 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 ...
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2answers
85 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 ...
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2answers
97 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 ...
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2answers
136 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 ...
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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 ...
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2answers
56 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 ...
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2answers
43 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
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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
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0answers
134 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 ...
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1answer
51 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 ...
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1answer
125 views

The workings of the Hall effect?

I want to ask about the workings of the Hall effect. Why do the electrons come to rest on the edge of the wire? The magnetic field pushes them up, and the electric field pushes them forward. Shouldn't ...
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0answers
13 views

Where does $R/\gamma^3$ come from in relativistic E&M?

I am starting to read many papers on electron beam physics; more specifically its motion in a magnet i.e. curved motion. The term $R/\gamma^3$ comes up a lot, but I don't know where they are coming ...
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0answers
30 views

Polarizable molecule in E-field

If we have a linear molecule with a dipole moment $\mu$ in a static electric field $E$, the potential is given by $V = - \langle \mu,E \rangle$. What is the appropriate equation for the potential if ...
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9answers
776 views

Metallic and glass sphere of same size released at a height

This question was in my exam today : A metallic and glass sphere of same size were dropped at same height. Which sphere would hit the ground first and why? I have thought about several things and ...
3
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1answer
80 views

A question about the Thomson experiment

Recently, I was studying about Thomson's experiment with cathode rays. My textbook shows it like this. It says: When only electric field is applied, the electrons deviate from their path and ...
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2answers
92 views

Velocity of a Charged particle in a magnetic field according to Biot-Savart Law

According to Biot-Savart Law, if there is a charged particle in motion, there will be a magnetic field. My question is whether the counterpart of this law also holds true, i.e. if there is a magnetic ...
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1answer
84 views
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1answer
161 views

Chern-Simons Energy-Momentum Tensor

I'm assuming the following statement is true. I'm not finding any reference which shows that explicitly. Statement: Chern-Simons term is a topological one and does not contribute to the ...
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4answers
236 views

Why ONLY Maxwell's equations are the basic equations of electromagnetism?

In electromagnetism we say that all the electromagnetic interactions are governed by the 4 golden rules of Maxwell. But I want to know: is this(to assume that there is no requirement of any other ...