Questions tagged [maxwell-equations]

A set of four equations that define electrodynamics. They comprise the Gauss laws for the electric and magnetic fields, the Faraday law, and the Ampère law. Together, these equations uniquely determine the electric and magnetic fields of a physical system. Do not use this tag for the thermodynamical equations known as Maxwell's relations.

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Symmetry of Maxwell equations for electric-magnetic duality

According to Griffiths's book on electrodynamics, including magnetic charge the Maxwell equations become $$ \begin{align*} \nabla \cdot \vec{E} &= \frac{\rho_e}{\epsilon_0} &&& \nabla ...
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Why is FDTD derived directly from Maxwell's equations instead of the wave equation

I've been wondering why the Finite Difference Time Domain Method is derived directly from Maxwell's equations and not directly from the electromagnetic wave equation (that in theory is also derived ...
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Is the differential form of Faraday-Henry equation ( Curl(E)= - dB/dt) always valid?

My textbook suggests that the integral form of the law is evident from experiments, while the differential form can be obtained by considering a closed curve, constant in time, so that it is ...
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Why is the magnetic field of a spherically symmetric current zero?

We now ask about the magnetic field produced by the currents in this situation. Suppose we draw some loop $\Gamma$ on a sphere of radius $r,$ as shown in Fig. 18–1. There is some current through this ...
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Do the relations between E/B and D/H contain higher order multipole terms?

Jackson writes in section 1.4 (third edition) that \begin{align*} D_\alpha &= \epsilon_0 E_\alpha + \left(P_\alpha - \sum_\beta \frac{\partial Q'_{\alpha\beta}}{\partial x_\beta} + \ldots \right) ...
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How can Maxwell theory be viewed in terms of two-layer structure?

I'm trying to learn more about Maxwell equations and stumbled upon an essay by professor Freeman J. Dyson from Princeton. He explained Maxwell theory in a very interesting way. The modem view of ...
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Did Maxwell invent the math to describe the ideas of electromagnetism?

Did he invent surface and line integrals, or did they already exist when he formulated his equations. If they did, already exist, how did they come about in pure math?
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Is my simulation result for unpolarized light correct?

This is a follow-up of this question. After that, I picked up some knowledge of FDTD (an algorithm for solving Maxwell's equations) and simulated following scene: Pic 1 As the picture shows, a ...
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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, i....
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Electromagnetism - Why electric and magnetic fields are manifestations of the same phenomenon [closed]

Maxwell's equations reveal an interdependency between electric and magnetic fields, inasmuch as a time varying magnetic field generates a rotating electric field and vice versa. Furthermore, the ...
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How varying length of loop affects induced emf

What is happening when delta x of this loop increases? Give me a theoretical idea and how is emf increasing? I know that flux is changing but I think that the rails on which conductor rod is moving is ...
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Lagrangian of classical electromagnetism without $A_{\mu}$ field [duplicate]

Is there a Lagrangian reproducing Maxwell's equations without the use of the scalar and vector potential? Obviously $\mathcal{L} = -\frac14F_{\mu \nu}F^{\mu \nu}$ doesn't work since in terms of $E$ ...
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Maxwell's Equations and Special Relativity [closed]

A doubt has arisen regarding the following question: Are Maxwell's Equations necessary to prove the postulates of special relativity? What I mean to say is, Einstein assumed two postulates, namely ...
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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 rule)...
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Why Is Abelian Gauge Theory So Special?

I have a perhaps stupid question about Maxwell equations. Let $G$ be a generic Lie group. We consider a $G$-gauge theory. Let $A$ be the associated connection $1$-form, and $F=dA+A\wedge A$ be the ...
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How to understand holography and hologram

I've spent some time reading wiki etc. What I get now is that apart from the normal light amplitude information, holograms also record the phase information of light. But this is so difficult for me ...
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What electric field vector should I use for modeling unpolarized light?

Regardless of computational cost, light is a kind of electromagnetic wave, so it can be simulated with Maxwell's equations. If we want to simulate light with Maxwell's equations, we need to express ...
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Special Relativity: Transforming Maxwell's equations

I'm working through Einstein's original 1905 paper*, and I'm having trouble with the section on the transformation of Maxwell's equations from rest to moving frame. The paper proceeds as follows: ...
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“And God said…and there was light.” What does these equations mean? [duplicate]

Today while I was on the Internet I came across an interesting picture, that caught my eye. It's : I don't have to explain why this picture seems interesting to someone who knows the meaning and ...
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Does a homogeneous oscillating electric field produce a magnetic field?

I am working on a homework problem that says an electron in a continuous laser field can be modeled as experiencing a homogeneous oscillating electric field $\vec{E}(\vec{r},t)=\cos \omega t \ \hat {z}...
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Different predictions from differential vs integral form of the Maxwell–Faraday equation?

Assume a toroidal solenoid with a variable magnetic field inside (and zero outside) and a circular wire around one of the sides. Because there is no magnetic field outside the solenoid, we have $$\...
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Magnetic B Field of Point Charge Not at Constant Velocity

I'm working on an N-body simulator for charged particles. I know that moving charged particles generate a magnetic field, and another moving charged particle could be effected by this magnetic field. ...
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Intuition of Maxwell's Equations [duplicate]

Is there an intuitive explanation for Maxwell's equations? I know they are axioms but is there a logical understanding of why instead of mathematical. Both forms don't explicate the scientific ...
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Could magnetic fields really be completely substituted by relativity and electric fields?

In many textbooks (especially those for undergraduate level), magnetic fields are described merely as a relativistic side product of electric fields when considering frames in motion relative to ...
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Integration constants in Maxwell's equations (ambiguousness?)

In classical electrodynamics, if the electric field (or magnetic field, either of the two) is fully known (for simplicity: in a vacuum with $\rho = 0, \vec{j} = 0$), is it possible to unambiguously ...
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Do Maxwell equeations change somehow after Higg's boson finding?

When I was in some physics -lesson, probably something to do with Quantum Physics -- the teacher said that certain Maxwell equations would change if the Higg's boson is found. It is also possible that ...
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How is this classical “paradox” resolved in electromagnetism?

A magnet and a coil move relative to each other. In the frame of reference of the magnet, there is a magnetic field and consequently a force acting on the charges in the coil according to the Lorentz ...
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Does the Meissner effect preclude currents from the bulk of superconductors?

The Meissner effect means that superconductors will spontaneously set up currents that expel magnetic fields from them. The Ampere-Maxwell law, $$\nabla \times \mathbf{B} = \mu_0 \mathbf{J} + \mu_0 \...
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What was the improvement that Maxwell did to the electromagnetic field equations and why?

What was the improvement that Maxwell did to the electromagnetic field equations and why? I understand that he combined the main equations so that you could get a wave equation for the vectors of $\...
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Why is the displacement current term needed in the Maxwell's equations?

Why did Maxwell believe that a displacement current term needed to be added to Ampere's circuital law? I have found loads of answers online about the plates acting as capacitors but i don't ...
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Covariant Maxwell equations invariant under parity transformation

I tried to proof that the Maxwell equations are invariant under parity transformations. Therefore I used the covariant formulation of the Maxwell equations \begin{align} \partial_{\nu}F^{\nu\mu} &...
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Why do we assume simply connected domains and continuously differentiable fields in electromagnetism theory?

In many textbooks, including Griffiths', they erroneously claim that a field is irrotational if and only if it is conservative (there exists a scalar potential). This is true only if the domain of ...
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Proof that Maxwell equations are Lorentz invariant

In Peskin and Schroeder page 37, it is written that Using vector and tensor fields, we can write a variety of Lorentz-invariant equations. Criteria for Lorentz invariance: In general, any equation in ...
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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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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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Invariance of Maxwell's Equations under inverting variables - Reference and use

Some months ago, an ArXiv paper mentioned in passing that Maxwell's Equations were invariant under reciprocating the variables, or at least this results in a dual set of Maxwell Equations. (Actually I ...
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Is there a more elementary example of the holographic principle?

Someone was telling me about the holographic principle, basically he said that the state of a system is determined entirely by the values of various physical quantities on its boundary. This is not ...
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How to derive $c=1/\sqrt{\varepsilon_0\,\mu_0}$ from integral form of Maxwell equations? [closed]

I've read similar questions and answers given thereto but find them unsatisfactory. So please don't mark my question as "duplicate". The question may as well be a duplicate, but it's still waiting for ...
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Factor of 4 (or 2) in the gravitoelectromagnetic (GEM) Lorentz-force law. Which is correct? Why is it there?

I realize that the Gravitoelectromagnetic equations (GEM) are derived from the Einstein field equation (EFE) in the degenerate case of reasonably flat spacetime, which is the case for the propagation ...
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Lorentz transformation of the dual tensor

I am trying to lorentz-transform the dual electromagnetic tensor $G^{\mu \nu}:= \frac{1}{2} \epsilon ^{\mu \nu \alpha \beta} F_{\alpha \beta}$ and also show (perhaps by using that last result) that $G^...
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Is Gauss law still true in dielectric material?

In vacuum we have $$\nabla \cdot \mathbf{E} = \frac {\rho}{\varepsilon_0}.$$ Can we still use this formula when there's dielectric material in space? Where $\rho$ is total charge density.
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How is Biot-Savart law verification of Maxwell's 4th equation for steady current?

Please provide some theoretical procedure which equates Biot-Savart law with the Maxwell's 4th equation for steady current, which is Ampere's law $$\quad \nabla\times{\bf B} = \mu_0{\bf J}.$$
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Why does a function $\psi(v)$ appear when a Lorentz transformation is applied on Maxwell's equations?

In his 1905 paper, Einstein applies Lorentz transformation on Maxwell's equations, and relates the electric force $(X,Y,Z)$ and magnetic force $(L,M,N)$ in an inertial frame $K$ with spectime ...
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Plane wave complex notation

As far as I know, the function: $$ \vec{E}(\vec{r},t)=\vec{E_0}\cdot e^{i(\vec{k}\cdot \vec{r}-\omega t)} \hspace{2cm}(1) $$ is a mathematical solution of the wave equation: $$ \nabla^2 \vec{E}=\mu\...
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Electrodynamics and the Lagrangian density

Could anyone tell me what equations can I obtain from the Lagrangian density $${\cal L}(\phi,\,\,\phi_{,i},\,\,A_i, \dot A_i,\,\,A_{i,j})~=~\frac{1}{2}|\dot A+\nabla\phi|^2-\frac{1}{2}|\nabla \times ...
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Applying $\nabla\times\mathbf{B} = \mu_0\mathbf{J}$ in the presence of magnetic shielding

2012-06-13 - Revised question in experimental format (This is a thought experiment for which RF experts may have an immediate answer.) I'll assume (I could be wrong) the possibility of creating a ...
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Are Maxwell's equations unique?

The Einstein equation can be derived from the idea that energy causes the curvature of spacetime. Hence we have on the right-hand side of our equation the energy-momentum tensor $T_{\mu\nu}$ and need ...
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What makes the disturbance in Electromagnetic waves move.?

I get that changing electric field will have a curly changing magnetic field and changing magnetic field will have curly changing electric field. So when we move a charge up and down, electric field ...
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Questions about deriving Maxwell equation in the Newman-Penrose formalism

I had some questions while reading the Chandrasekhar textbook "The Mathematical Theory of Black Holes", in particular about the scalars introduced to reformulate the Maxwell equations ($g^{ik} F_{ij;k}...
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Why doesn't the acceleration of an electron along the line of sight from the observer contribute to the electric field?

In Feynman Lectures on Physics, Volume 2, Feynman gives the general solution of the Maxwell's equations as following: \begin{gather*} \begin{aligned} \...