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1answer
139 views

Traditional Kirchoff voltage law in AC circuit?

The traditional (not taking into account phasor addition or complex addition) application of Kirchoff Voltage law, i.e. $\Sigma\Delta V=0$ along a loop, does not work for AC circuits. We can sum the ...
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1answer
47 views

Is there a heuristic argument for the expression $ \textbf{g} = \frac {\mathbf{S}}{c^2}$?

Electromagnetic momentum density and the Poynting vector are related by the simple expression: $$ \textbf{g} = \frac {\mathbf{S}}{c^2}$$ It can be rigorously derived from Maxwell's equations, but is ...
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1answer
264 views

Difference between Poynting vector and energy flux density?

Are those two terms the same, or...? My book says that the Poynting vector is an energy flux density given by: $$\mathbf{S} = \frac{1}{\mu_{0}}(\mathbf{E} \times \mathbf{B})$$ So that alone should ...
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2answers
230 views

Non-linear dynamics of classical hydrogen atom

I'd like to know if there have been attempts in solving the full problem of the dynamics of a classical hydrogen atom. Taking into account Newton equations for the electron and the proton and Maxwell ...
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2answers
63 views

Connection between $\textbf E$ and $\textbf D$ can be non-local ? - Electrodynamics

In J.D. Jackson's first chapter, he says the proper equation connecting $\textbf E$ and $\textbf D$ $$ D_\alpha = \sum_\beta \int d^3x'\int dt' \epsilon_{\alpha\beta}(\textbf x',t')E_\beta(\textbf x ...
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2answers
39 views

If the net force on a current loop in a magnetic field is zero, why is torque independent of choice of origin?

Im trying to show that the integral over a closed loop of a crossproduct stays the same if I choose a different origin with $\overrightarrow{r}=\overrightarrow{r}\prime+\overrightarrow{r_0}$ and ...
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1answer
115 views

What happens to a conducting ring when exposed to an electric field?

It might be a silly question, but one of my friends just got asked this question at an oral exam, and he could not answer it, and didn't receive the answer either (Or at least he forgot). And I've ...
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1answer
162 views

Can inertia be explained by Bremsstrahlung?

Considering that on the atomic level objects consists of densely spaced positively and negatively charged particles, does not the acceleration of those objects lead to Bremsstrahlung of those ...
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2answers
80 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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3answers
110 views

How the electric field or magnetic field itself contain momentum?

I have recently come to know that the electric and magnetic field contain both the translational and angular momenta in it given by some particular formulas at any given instant of the space....But I ...
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1answer
39 views

Greens reciprocity theorem

The Greens reciprocity theorem is usually proved by using the Greens second identity. Why don't we prove it in the following "direct" way, which sounds more intuitive: $$\int_{\text{all ...
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1answer
66 views

Canonical Stress Tensor for the Free Electromagnetic Field

I have the followwing Lagrangian for the free electromagnetic field, $$\mathcal{L} = -\frac{1}{4} F^{\mu \nu}F_{\mu \nu},$$ and the canonical stress tensor is, $$T^{\alpha \beta}=\frac{\partial ...
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1answer
42 views

How is Transition Radiation different from EM waves crossing a boundary?

Just confused my self again :(. Transition radiation is the radiation produced when a charge crosses a boundary between two dielectric materials (http://en.wikipedia.org/wiki/Transition_radiation). As ...
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1answer
63 views

electromagnetic induction. Does charge matter?

Just wondering. I know a negative electric charge moving though a coil will induce a voltage in the coil. My question is, would a positive charge, say an ion beam, moving though a coil also induce a ...
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2answers
113 views

A question about canonical momentum and arbitrariness for potential in magnetism

The following question confuses me: There exists magnetic field $B_z =- \beta x$ where $x > 0$, and a particle is incident from origin point $(0,0)$ with pisitive charge $q$, mass $m$, and ...
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1answer
87 views

Accelerated charge inside sphere (again!)

Sorry to go on about this scenario again but I think something is going on here. Imagine a stationary charge $q$, with mass $m$, at the center of a stationary hollow spherical dielectric shell with ...
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1answer
369 views

General solution to the Helmholtz wave equation with complex-valued frequency in cylinderical coordinates

The Helmholtz equation is expressed as $$\nabla^2 \psi + \lambda \psi = 0$$. This equation occurs, for eg., after taking the Fourier transform (with respect to the time coordinate) of the wave ...
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1answer
236 views

Understand equations of a conducting sphere

Can somebody explain to me, when the following two equations (equations 2.48 and 2.50 in this document) are applicable and what $\Phi_s$ and $\Phi$ actually are? The thing is, I want to find general ...
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1answer
82 views

Conducting surface inside conducting surface

Let's say there's a closed conducting surface. Then by Gauss's Law the E field bound by the surface must equal the charge inside. There's no charge inside, so the E field cancels. This is a Faraday ...
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4answers
290 views

Interaction of matter with EM fields

For the interaction between electromagnetic fields and matter, when do we have to include quantization of the EM field and when we can ignore it? when do we have to include quantization of atomic ...
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1answer
40 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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1answer
40 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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1answer
55 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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0answers
29 views

Do plasmons depend on the ambient EM field?

Imagine a situation: There's an illuminated metal slab in vacuum. Normally, there are some plasmons created running all over the slab. What would happen if we had turned a giant magnet near the slab? ...
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0answers
29 views

Computing the Electric and Magnetic Field Distribution of a Funnel Waveguide

In our undergraduate E&MWaves class, we learned about a rectangular waveguide, and how to calculate the electric and magnetic field distribution throughout the waveguide using finite element ...
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1answer
81 views

Step in a proof that $\textrm{div} \ \mathbf{B} = 0$ from Biot-Savart's law

Notation: The magnetic field $\mathbf{B}$ generated by a point charge $e$ moving with velocity $\mathbf{v}$ is given by Biot-Savart's law $$\mathbf{B} = \frac{\mu_0 e\ \mathbf{v} \wedge ...
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1answer
97 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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1answer
163 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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0answers
127 views

Complex polarizability of a dielectric sphere in a homohenious electric field

It is well known that complex polarizability of uniform dielectric sphere with radius $r$ and complex permittivity $\hat\epsilon_{in}(\omega)$ placed in a medium with complex permittivity ...
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0answers
68 views

Time derivative to energy equates $0$

Following up on a related question. This implies that, From the reference we can write \begin{align*} E(\lambda) &= I_F [g_\lambda ] + I_K [f_\lambda , g_\lambda ] + I_V [f_\lambda ] \\ & ...
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0answers
39 views

Question about “quadrupole radiation” vector potential formula derivation

I tried to get an expression for $\mathbf A (\mathbf x )$ in quadrupole approximation. After some transformations of Liénard–Wiechert vector potential I got, as in many books, $$ \mathbf A \approx ...
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0answers
69 views

Electric field screening for arbitrarily formed charge

if I have a not necessarily homogenous electric field of a charge distribution in an electrolyte and i want to find out what the electric field at some position in the electrolyte is. is there any ...
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0answers
299 views

Properties of electric field

I have the following vector field: $E=E_0(-sin(\phi),cos(\phi),0)^T$ and $E_0$ is some constant. Does anybody here have an idea what this electric field does to a metallic sphere that is in it? ...
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0answers
24 views

Two charges in a medium where different permittivity is adjacent

I was thinking about the following: Assuming that you have NON SPHERICALLY SYMMETRIC charges and they are both in medium 1. Does it make a difference(whereby I am referring to the total force) if ...
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2answers
102 views

is action integral Lorentz invariant?

I need to find the Lagrangian for charged particles in EM fields considering relativistic effects. Is action integral Lorentz invariant. $$A = \int_{t_1}^{t_2} L (q_i, \dot q_i, t) dt $$ According ...
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1answer
54 views
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1answer
22 views

How to account for the huge difference in susceptibility of liquid and gaseous oxygen?

I noticed this while studying magnetic fields in matter from Griffiths' Electrodynamics book. A table is provided in the chapter which shows the materials with their respective susceptibilities. Under ...
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1answer
46 views

What is the mechanism for the production of the electromagnetic radiations due to accelerated charge particles?

I have recently read in Griffiths that when a charge particle get accelerated the electromagnetic field associated with it get " ditatched " from it and this detatched electromagnetic field is what we ...
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2answers
90 views

Prerequisites for Griffiths electrodynamics [duplicate]

I want to start reading Griffiths electrodynamics during my holidays. But I am not sure of the math I need to know to start reading and understand the text thoroughly. So any advice would be ...
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1answer
111 views

Electric dipole, error in calculation

Currently I am calculating the dipole moment of a metal sphere in a uniform electric field $E_0$ in z-direction. From here I know that the charge density look at page 15 is given by $ 3 \epsilon_0 ...
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1answer
39 views

Electromagnetic waves and group velocity

I have three questions about electromagnetic waves and was wondering whether anybody here could comment on these things: Wikipedia says that there are no longitudinal EM waves, although TM and TE ...
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1answer
60 views

Online course on theoretical electrodynamics [duplicate]

I'm looking for good online course for an introduction into theoretical electrodynamics. However, it seems that the MIT opencourseware only contains partial lectures for this topic. Has anyone got a ...
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1answer
75 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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1answer
213 views

Lorentz transformation for electric and magnetic fields

How do derive the following transformation rule (J.D. Jackson third Edition 11.10) for electric and magnetic field? $$\vec E' = \gamma \left( \vec E + \vec \beta \times \vec B\right) - ...
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1answer
58 views

Objects made up of electrons?

Say you have a neutral rod, and you bring a positively charged rod beside it (call the side the charged rod is brought near side A and the other side side B). The electrons from the side B will start ...
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1answer
55 views

What are the properties of the Electromagnetic wave $E=E_0e^{-i\omega t}$

My question is, whether this definition $E=E_0e^{-i\omega t}$ includes that it is a plane wave, since I am confused by the fact that we do not have any dependence on the position. So about what kind ...
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1answer
78 views

Electromagnetic tensor in CGS units

To write the electromagnetic field tensor in CGS units I just have to kick off the c-s from the SI tensor right? I know this is a stupid question but I need a reliable answer.
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0answers
24 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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1answer
22 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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1answer
19 views

Determine stationary angular velocity of wheel with circuit in magnetic field

I have a wheel (free to spin around the $z-$axis) with four spokes that is connected by sliding contacts to a circuit with $U_0 = 0,72V$. Also, there is a B-Field parallel to the $z-$axis For the ...