The four fundamental fundamental equations of electromagnetism.

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Electric field from current without Maxwell's law of induction

A long, straight wire carries a current that decreases linearly with time. What is the direction of the induced electric field outside the wire? I would interpret this as follows: a current ...
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19 views

$\vec{E}$-and $\vec{B}$-fields in RCL circuit from Maxwell equations

Consider a basic RCL-Circuit consisting of an ideal resistor, an ideal capacitor and an ideal inductor in series. How do the $\vec{E}$- and $\vec{B}$-fields look like in dependence of the time? I ...
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1answer
238 views

Reaction-at-a-distance: Do charged plates immediately repel each other?

Imagine that we have a pair of parallel plates, $A$ and $B$, separated by some distance as in Fig. $1$ above. At time $t_1$ we simultaneously charge both the plates. This could be done by ...
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2answers
2k views

Does displacement current exist after the capacitor gets fully charged?

The displacement current is due to changing electric field. Since, after the capacitor gets fully charged there is no changing electric field there is no displacement current.(capacitor connected to a ...
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1answer
230 views

Electromagnetic inertia due to advanced radiation?

The scalar potential $\phi$ and vector potential $A$ at a distance $r$ from a charge $q$ are given approximately by $$\phi = \frac{q}{r}$$ $$\mathbf{A} = \frac{q\mathbf v}{r}$$ where the constants ...
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3answers
825 views

Curl of an electromagnetic wave

I can't understand the concept of the curl of an electromagnetic wave. $$ \nabla \times E = -\frac{\partial \textbf{B}}{\partial t} $$ All of the examples I find show a current through a conductor, ...
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1answer
106 views

How can electric field representation be obtained from Enge representation using Maxwell's equations?

Suppose we have a long electric capacitor. Let $L$ be its length ($z$ coordinate), $W$ its width ($y$ coordinate), and $D$ its full height (full aperture; $x$ coordinate). Let $L\gg W\gg D$. The ...
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1answer
212 views

Surely force on shell can't be balanced by field momentum?

Imagine a particle with charge $q$ at rest at the origin. It is surrounded by a concentric spherical insulating shell, also at rest, with charge $Q$ and radius $R$. At time $t=0$ I apply a constant ...
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41 views

Boundary conditions for Maxwell's equations at the interface between two media

Consider the following simple Maxwell's equations: $$ \nabla\cdot\mathrm{D}=\rho $$ $$ \nabla\times\mathrm{E}+i\omega\mathrm{B}=0 $$ $$ \nabla\cdot\mathrm{B}=0 $$ $$ ...
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1answer
240 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 ...
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1answer
17 views

In magnetostatics, is there any relation between flux and current?

I have noted while trying to find analogy between electrostatics and magnetostatics, for the equation, flux = charge/epsilon, is there any corresponding equation in magnetostatics, relating magnetic ...
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11 views

In electrostatics, what is the actual relation between flux density and flux

I know, in magnetostatics, unit of flux in webers. And unit of flux density B is webs per metre square. its clear. Now in electrostatics, unit of flux is volts metre. And unit of flux density D is ...
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2answers
44 views

Does Biot-Savart law apply in changing electric field or it needs a modification just like Ampere's law, to become as true as Maxwell's 4th equation?

Does Biot-Savart law apply in changing electric field or it needs a modification just like Ampere's law, to become as true as Maxwell's 4th equation? In the update to Ampere's circuital law, the ...
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0answers
50 views

Would a super conductive insulation completely prevent the propagation of a magnetic field from a wire where it is wrapped around?

I have limited understanding about super conductors and see them as expelling magnetic fields purely due to eddy currents produced without resistance opposite the magnetic field. I have read that ...
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2answers
118 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 ...
2
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2answers
644 views

Neither Biot-savart nor Ampere Law can solve this problem?

I'm confused about the use of the Ampere's Law and the Biot-Savart Law due the inconvenience of each law. I want to calculate the magnetic field due to current carrying a circular loop over itself, ...
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1answer
62 views

Would Michelson-Morkey experiment measure wind in non-vacuum?

If we derive the speed of light from the Maxwell equations we will find it's a function of the permittivity and permeability of the medium. Now let's play with the thought that we are living in a ...
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What was Feynman's “much better way of presenting the electrodynamics” — which did **not** appear in the Feynman lectures?

Does anyone know what Feynman was referring to in this interview which appears at the beginning of The Feynman Tips on Physics? Note that he is referring to something that did not appear in the ...
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0answers
65 views

What unit system puts a bunch of powers of ten in Maxwell's equations?

In what unit system can we get the Maxwell equation in the following form (section 1.2 from Lewin's book Advanced Theory of Waveguide) $$\nabla\times \vec E = -10^8\mu \frac{\partial \vec H} ...
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Is it possible to generalize the Maxwell equations to higher dimensions?

The usual Maxwell equations are for 3 spatial dimensions, right? Is it possible to generalize them to 2 spatial dimensions or 4 spatial dimensions?
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3answers
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Maxwell in multiple dimensions: What happens to curl?

I read this answer a while ago, and while thinking about $\nabla$, I realized something. Since the cross product can be written as a determinant, in higher dimensions we require extra vector inputs. ...
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1answer
82 views

Maxwell's equations in integral form using differential geometry

So I've been trying to convert from Maxwell's equations in terms of differential forms to the integral versions of Maxwell's equations that we know from vector calculus. We have, in vector calculus ...
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4answers
252 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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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 ...
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20 views

Single slit diffraction treated as a differential equation

I want to find the values of electromagnetic fields that result from single slit diffraction. This should be possible by solving maxwell's equations for appropriate boundary conditions. But I'm not ...
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2answers
210 views

How to use Ampere's Law for a semi-infinite wire with current?

Suppose that there is a semi-infinite wire which extends to infinity only in one direction. There are no other circuit elements at the other end(finite end) of the wire and the current does not loop. ...
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1answer
71 views

The truest/most general Maxwell's equations in isotropic, linear, inhomogeneous media with sources

Sources use $\mu H=B$ and $\epsilon E= D$, assuming homogeneous media. Obviously if $\mu$ is space varying, $\nabla . (\mu H)$ need not be equal to $\nabla . B$ What is the most general form for ...
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31 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 ...
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0answers
15 views

Pefectly electrically conducting Neumann boundary conditions

I have a rather subtle question regarding necessary boundary conditions. To solve Maxwell's source-free equations as an initial boundary value problem in a volume $\Omega$ bounded by a perfectly ...
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1answer
65 views

Time-harmonic Maxwell's equations

My question is about the time-harmonic or frequency domain (differential) form of Maxwell's equations. If one solves these and obtain the complex vector field $E$, are the real and imaginary parts ...
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2answers
96 views

Is magnetic reconnection reconcilable with magnetic field lines neither starting nor ending?

According to Maxwell's equations, magnetic fields are divergence-free: $\nabla \cdot \mathbf{B} = 0$. If I understand this correctly, this means that magnetic field lines do not start or end. How can ...
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43 views

Electric field from time varying charge density

Inside a cylinder of infinite length in $z$ axis, there is charge density $ ρ = cos(βz -ωt)$. I want to find the electric field and as far as i can understand we will get a radial component of $E$. ...
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57 views

$E$-field from changing current in straight wire

A very long insulated wire oriented along the $z$ axis of a cylindrical coordinate system is carrying current that is defined by the following function: $$I(t) =Io + k⋅t$$ (current increases linearly ...
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51 views

Spectroscopy from a classical light wave or photon only?

In chemistry we mostly regard light/electromagnetic radiation as a beam of particles or photons. This is a very useful model to explain molecular excitations and ionisations from quantum interactions. ...
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1answer
43 views

Apparent discrepancy between Lagrange field equation and Maxwell equation [closed]

I am deriving Maxwell's equations from a Lagrange field equation and have come across something I can not figure out no matter how hard I try. The problem is in the signs. If we take the Lagrange ...
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1answer
2k views

What is the meaning of this “let there be light” joke?

Someone across the restaurant is wearing this shirt, and I certainly don't get it. Update Related: What does this quote about the four dimensional divergence of an antisymmetric tensor mean?
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2answers
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Where do Maxwell's equations come from?

I recently started learning the basic forms (integrals) of the Maxwell's equations, and everything that is related to electromagnetism seems to be derived from these fundamental equations. Now my ...
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1answer
57 views

Books on Faraday, Maxwell

Can you recommend a/some good book(s) on Faraday for the lay person? In particular, in relation to his 'Experimental Researches in Electricity'. Also, any books explaining how Maxwell explained ...
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1answer
28 views

Bobbin with $I=I_{0}\sin(\Omega t)$

If I have an infinite bobbin with $I=I_{0}\sin(\Omega t), \mu$ and $n=N/L$ using Ampère and supposing that $d\vec{D}/dt=\vec{0}$ I have found that $$\vec{B}=n\mu I_{0}\sin(\Omega t)\vec{e_{z}}$$ But ...
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Would magnetic charge (i.e., magnetic monopoles) be Lorentz invariant if it existed?

Would magnetic charge (i.e., magnetic monopoles) be Lorentz invariant if it existed? It is clear that Maxwell's equations in themselves permit magnetic charges but what would their relativistic ...
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30 views

Boundary conditions for vector wave equations

Assume the time-harmonic case of Maxwell's equations, one can obtain the following vector wave equations: $$ ...
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0answers
29 views

Calculating current on power line from induced voltage on nearby loop

The question I'm having trouble with is: A small circular loop of 5mm radius is placed 1 meter away from a 60Hz power line. The voltage induced on this loop is measured at 0.6 microvolts. What is the ...
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2answers
329 views

Are photon energies conserved in general relativity?

As I understand it, both Maxwell's wave equation and the null geodesics of general relativity are scale invariant. Thus an electromagnetic wave can be shifted along a null geodesic without changing ...
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2answers
222 views

Solution of simple problems using only Maxwell equations in differential form

Solve simple electrostatic or magnetostatic problems using only Maxwell equations. For example: In every book there is an excercise to find a magnetic field outside a thin wire of radius $a$ with ...
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43 views

Why wouldn't any Emission Theory work?

http://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/origins_pathway/#Emission Here, at the Emission theories of light, I loved the discussed theory. There seems to be a contradiction right ...
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1answer
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Constant charge density and magnetic field

Suppose we have an arbitrary number of point charges in a vacuum, described by a constant charge density $\rho$. Can they be the sources of a magnetic field $\mathbf{B}$? My intuition is that they ...
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Faraday's law - does the induced current's magnetic field affect the change in flux?

I've had this conceptual problem with Faraday's law and inductance for a while now. Take the example of a simple current loop with increasing area in a constant field (as in this answer). So ...
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4answers
7k views

Displacement current - how to think of it

What is a good way to think of the displacement current? Maxwell imagined it as being movements in the aether, small changed of electric field producing magnetic field. I don't even understand that ...
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0answers
43 views

How to apply voltage source in FEM when solve Maxwell equation?

I need to solve the Maxwell equation of electric field by finite element method. In this function, the right hand side is the current density. However, in my problem, the voltage source with 1 MHz ...
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1answer
66 views

Problem with the Ampere-Maxwell Law [closed]

We know that $$J=\sigma E$$ where $J=dI/dS$ is the current density, $\sigma$ the conductivity, and $E$ the electric field. So, if we put that into the Ampere-Maxwell law, then the law transforms ...