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0answers
45 views

Finding the dipole moment of a continous charge distribution [closed]

I am looking for the dipole moment given by the charge density \begin{equation}\rho = -e_0\frac{1}{\pi a^3}e^{\frac{-2r}{a}}+e_0\delta(\vec{r})\end{equation} where $e_0$ and $a$ are positive ...
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2answers
43 views

Flow from higher potential region to lower potential region

In Thermodynamics, it is said that heat transfer takes place from higher temperature to lower temperature. Things having higher temperature have higher potential energy because of more vibratory ...
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0answers
44 views

Trapping force in optical tweezer

I am reading a paper on theory of optical tweezers in ray optics regime by A. Ashkin. For reference "click here". It is given that Gradient force $F_g$ is directed perpendicular to the light ray and ...
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1answer
98 views

How can I prove that the axial gauge is a valid Gauge fixing condition?

I am studying classical electrodynamics and I have been introduced to the concept of gauge transformations and gauge fixing conditions. Right know I am trying to prove that some conditions are valid ...
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1answer
55 views

What is the physical explanation of Fresnel's equation?

When EM radiation is travelling between the media of different refractive indices, parts of it are reflected and transmitted according to Fresnel's equations. The amount of reflectivity and ...
1
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1answer
99 views

Does a laser beam converge and diverge without lens?

In the case of $TEM_{00}$ mode laser produces gaussian beam. I read in wikipedia that it converges till some point called 'beam waist'and then it diverges to infinity. If there is a lens placed along ...
1
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0answers
38 views

Is the Dirac string continuous?

Is the Dirac string continuous? Suppose I have a point magnetic charge. Do the necessary singularities of the vector potential lie on a continuous curve in 3D space?
0
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1answer
45 views

Demonstration for the existence of longitudinal electrostatic oscillations

How could I demonstrate that in a linear, homogeneous and isotropic medium without losses but electrically charged, Maxwell's equation admit as solutions longitudinal electromagnetic waves, beyond ...
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1answer
28 views

Relaxation time for moving charges in a medium

This will be a short question: How could I show that the quotient between permittivity and conductivity $\left(\frac{\varepsilon}{\sigma_c}\right)$ is the relaxation time for moving charges in a ...
0
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1answer
54 views

What is the effect of circularly polarized light on a charged particle?

The force on an electron due to electric field is given by $F=qE$. For a circularly polarized light, $E=E_x+iE_y$. So $F=q(E_x+iE_y)$ which means particle travels in a circle. As there is magnetic ...
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1answer
50 views

Determining the phase delay between H and E fields

I want to determine the phase delay between H and E fields in a medium with losses and not electrically charged. In this medium we also have $\sigma_c\approx \varepsilon \omega$. The enunciation of ...
0
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0answers
41 views

Induced dipole moment of an atom

Assume that we have a neutral atom that consists of a $+Q$ particle in its center surrounded by a uniform charge density $\rho$ such that $-Q = (4/3)\pi R^3 \rho$, where $R$ is the radius of the atom. ...
0
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1answer
116 views

how do photons move with respect to EM (I'd like to picture wave magnitudes frame by frame) [duplicate]

(I'm aware treating photon as particle and talking about its position is not exactly, conceptually right but I think it makes sense, at least in the point of view of a beginner. Please just assume ...
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1answer
58 views

Can one make a propagating field along a waveguide only have longitudinal/transverse components?

We know that in free space, a propagating electromagnetic wave is always transverse. However, along a dielectric waveguide, the propagating wave can have longitudinal components. The exist of the ...
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4answers
82 views

the relation between frequancy and energy of EM waves

In quantum theory, $$E=\hbar w$$ In classical theory, we have the Poynting vector: $$\vec{S_\space}=\frac{1}{\mu_0}\vec{E_0}\times\vec{B_0}{\cos}^2(kr-wt)$$ given S is energy flux density (the ...
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0answers
41 views

The dipole moment P in a metallic sphere

A metallic sphere is in a homogenous field $\vec{E}=E \cdot \vec{e_z}$. Put a dipole moment P at the origin, so the total potential is constant on a surface of a sphere with radius $a$. Which $p$ is ...
1
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1answer
101 views

Bohr atomic model: does the electron fall?

I know this is a classical system, and thus not compliant with the quantum nature of real atoms. But please bare with me. I have heard this before: the orbiting electron should radiate in the ...
3
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1answer
65 views

Introductory literature on the multipole expansions including toroidal moments

I wish to understand the general idea of the multipole expansion in the context of classical electrodynamics and, especially, the concept of the toroidal moments. All the papers on the subject I've ...
3
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1answer
49 views

Problem - Demonstration of electromagnetic energy conservation

I want to solve the following problem from my Classical Electrodynamics' book: Consider a pontual mass body, $m$, with charge $q$, which moves with an uniform velocity $v$ in a region where an ...
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2answers
76 views

Particles radiating energy when accelerating?

Let us say we have a charged particle moving in the positive $X$ direction with velocity $v$. If we give the particle a nudge in the $-X$ direction causing it to decelerate. Then from the saying ...
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1answer
167 views

Method of image charge for cylindrical conductor

I am simply puzzled that only for spherical and planar conducting surfaces the method of images is applied. Is it (really) impossible to find image charge or charge distribution which can simulate the ...
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1answer
82 views

How can you use the Delta Function to find the Electric field inside of a Hydrogen Atom?

This is a problem from my homework, but I'm lost conceptually on how to do it. I'm not looking for someone to do the work for me, I'm looking for some guidance on how I can set it up/understand it ...
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4answers
274 views

When does the concept of electric field in classical electrodynamics fail, and QED is needed?

It is really hard to find reference to when the traditional concept of electric wave, especially TEM wave, fails, and needs to be replaced by quantum electrodynamics. So when does the concept fail? ...
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0answers
28 views

Change in magnetic field region reduces overall voltage due to change in resistance?

Consider the following diagrams: Diagram(1): A large conductive slab($C$) with resistance ($R$) and region with magnetic field($B$), the conductor moves to the right as indicated with ($v$). ...
2
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5answers
528 views

Euclidean geometry in non-inertial frame

Refer, "The classical theory of Fields" by Landau lifshitz (Chap 3). Consider a disk of radius R, then circumference is $2 \pi R$. Now, make this disk rotate at velocity of the order of c(speed of ...
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0answers
26 views

Local Gauge Invariance and Masslessness [duplicate]

I am wondering if the masslessness of photons is due to the local gauge invariance of $u(1)$-gauge fields. The reason why I consider about this question is that I remember that the Proca field is not ...
0
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2answers
146 views

Electromagnetic wave and quantum mechanics [duplicate]

I'm very new to physics. I studied and read about quantum mechanics and what the assumptions are (wave particle duality, uncertainty principle, observation, wave function collapse, etc.), but I also ...
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3answers
96 views

doubts regarding the classical electron radius

When estimating the classical electron radius, people normally equate the energy needed to assemble a charged sphere to $mc^2$, due to the so-called mass-energy relation. However, personally I don't ...
0
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0answers
54 views

Current flow direction, based off the equipotential line?

From the following diagram: Given the wires are only connected to a certain portion of the conductor, will current flow all around the conductor? Or only throughout the equipotential line(diagram ...
1
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1answer
84 views

Maxwell Stress Tensor at material boundaries

I am trying to grasp the meaning of the Maxwell Stress tensor $T_i^j$ at material boundaries. Concretely, I am trying to calculate the force between two waveguides. The results are given in an article ...
0
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1answer
118 views

Difference in induced current, when magnetic field “span” is reduced?

A conductor of known volume $(V)$ passes a uniform magnetic field$(B)$with a constant velocity $(v)$ the conductor is a source of induced EMF, a power source to a circuit. The induced EMF can be ...
0
votes
1answer
23 views

Show that the electric dipole term vanishes for a particular current

I'm interested to show that given a ring with radius a where there's a current $I_0 \cos \omega t$ ($I_0$ is a constant) there is no radiation due to the electric dipole term (appearing in the ...
3
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1answer
70 views

Eddy currents Vs. Inducing EMF in opposing the change?

In the following circuit there is a power supply applying a voltage(+$V$) to a circuit with resistance ($R$), current($I$) is now flowing in the circuit, and there is a movable part like so: The ...
2
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1answer
210 views

Will two opposing magnetic fields cancel out?

When a conductor induces eddy currents that creates a magnetic field opposing the change that created it, would the two fields at some point cancel out? Imagine the change to be so great, it ...
2
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4answers
401 views

Is Gauss' law valid for time-dependent electric fields?

The Maxwell's equation $\boldsymbol{\nabla}\cdot \textbf{E}(\textbf{r})=\frac{\rho(\textbf{r})}{\epsilon_0}$ is derived from the Gauss law in electrostatics (which is in turn derived from Coulomb's ...
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3answers
118 views

In terms of the Ampere-Maxwell law, why is $\vec {E}=0$ in a wire of a capacitor circuit?

I'm currently studying from "Introduction to Electromagnetics" by D.J. Griffiths. In the book the significance of the displacement current term is explained by looking a non-steady capacitor circuit ...
1
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1answer
75 views

Eddy currents on a conductors surface, and induced current flow in a circuit coexist?

The title seems confusing, because Eddy currents are induced currents... however, let me explain. Assume the following closed loop passing a uniform magnetic field like so: Now, this loop would ...
0
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0answers
69 views

Surface current density and infinite solenoid

I have an infinitely long cylinder with radius $R$ and axis lying on the $z-$axis, charged with volume density $\rho$ and surface density $\sigma$. The cylinder is spinning with angular velocity ...
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4answers
919 views

Method of calculating eddy currents of a conductor, is this correct?

I have a conductor with volume $V$, passing a magnetic field($B$) with velocity($v$): I'm trying to calculate the Eddy currents to figure out the magnitude of the drag force($F_d$) generated the ...
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0answers
37 views

Two equal charges accelerating parallel to each other

Let's say constant acceleration for simplicity. Ignore possible logistic concerns, such as what is accelerating them or how they stay in path. Lets just assume they are in a conduit made of a solid ...
0
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0answers
94 views

Magnetic field due to current carrying sheet

I have 2 infinite plates (x direction) with the width of A (y direction) and the distance between them is d (z direction). The current density is J on the first plate and -J on the second (the ...
0
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0answers
74 views

Is this a good explanation of electron mobility to the layman?

I'm writing an informative paper on graphene for my writing class (layman-oriented), and was describing electron mobility in very simplified terms. Let me know if anything is mistaken, badly ...
3
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2answers
345 views

Why do high voltage transmission line workers need a Faraday cage suit?

In this video the high voltage transmission line workers are wearing a Faraday cage suit. Why is this needed? Without the Faraday cage, the resistance of the human would be very high compared to the ...
0
votes
1answer
240 views

How is polarization vector in QFT related to polarization in classical electrodynamics?

As i know in classical electrodynamics polarization shows the orientation of the electric vector in a plane perpendicular to the direction of propagation of light. But in quantum field theory ...
0
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1answer
86 views

How do you take the derivative with respect to a rank two tensor?

I am learning classical field theory and am trying to find the momentum density of the electromagnetic lagrangian as part of an example of Noether's Theorem. The derivative I am encountering is: $$ ...
0
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0answers
46 views

What is the form of the skin effect in exponentially decreasing (or exponentially increasing) voltages?

I tried to replicate the standard derivation of the skin effect for exponentially shrinking or growing voltages (idealize the surface of the wire as a half-infinite volume of conductor) but I'm not ...
6
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1answer
143 views

Why can the Lorenz gauge condition always be fullfilled?

Why is the Lorenz gauge condition always possible for classical electromagnetic fields? So far I can only understand the following: If we perform a gauge transformation $A\mapsto ...
0
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1answer
38 views

Induced current in a loop due to varying flux

Suppose you have a loop of wire beside a infinite long wire carrying a current I. The current in the infinite wire is given by: $$I(t) = I_0(1-e^{(-\alpha t)})$$ Where $\alpha$ is a constant and $I_0$ ...
2
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0answers
79 views

Torque on a wire loop from straight wire [closed]

I need to show that the torque on this wire loop is $$N = \frac{\mu_0}{\pi} 2abdII' \frac{(b^2+d^2)\sin(\theta)}{b^4+d^4-2b^2d^2\cos(2\theta)}$$ The where $\theta$, is the angle between the loop ...
0
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3answers
470 views

Tricks for evaluating tensor contractions with Levi-Civita symbol

I am trying to evaluate the Lorentz invariant $\epsilon^{\alpha\beta\gamma\delta}F_{\alpha\beta}F_{\gamma\delta}$, where $F_{\mu\nu}$ is the electromagnetic field tensor, $$ F_{\mu\nu} = ...