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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147 views

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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176 views

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} \...
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144 views

EM waves in terms of differential forms

I know you can write Maxwell's equations in terms of the four-potential $A = A_{\mu}\mathrm{d}x^{\mu}$, the four-current $j = j_{\mu}\mathrm{d}x^{\mu}$, the exterior derivative $\mathrm{d}$, and the ...
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228 views

Why only gauge transformations in electromagnetism?

first of all, I need to say that I'm a mathematician, so this question may sound a little stupid. Keeping this is mind, please, try to use coordinate-free notations. Along this question, I will use ...
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Boundary conditions for Maxwell's equations at the interface between two media

Consider the following simple Maxwell's equations: $$ \nabla\cdot\mathrm{D}=\rho $$ $$ \nabla\times\mathrm{E}+i\omega\mathrm{B}=0 $$ $$ \nabla\cdot\mathrm{B}=0 $$ $$ \nabla\times\mathrm{H}=\mathrm{J}+...
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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 ...
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Magnetic field in materials with non-constant magnetic susceptibility

I'm quite lost what $B$ and $H$ is. It seams to me that most of the texts I read do quite poor job in explaining them properly. They are explained only in cases when magnetic susceptibility is ...
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741 views

Information content of the electrostatic Maxwell equations vs Coulomb's Law vs Poisson's Equation

In electrostatics, we have Maxwell's equations: $\nabla \cdot E = \rho$ $\nabla \times E = 0$ These four equations (the second line standing for three equations) can also be written in terms of the ...
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Divergence of non conservative electric field

I'm looking for the proof that the 1st Maxwell equation is valid also on non conservative electric field. When we are talking about a electrostatic field, the equation is ok. We can apply the Gauss (...
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Electron model under Maxwell's theory

I was not able to recall my memories, so: What is the formula that states the frequency of electrons revolving around nucleus is equal to the frequency of light (or photon) emitted (or radiated)? (I ...
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Understanding Dynamic light scattering

I'd like to understand the physics of dynamic light scattering experiment. In particular I want to understand the basic relation between relaxation time $\tau_q$ and the diffusion coefficient $D$: $\...
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Why using an imaginary surface is allowed when applying Faraday's law?

In a lot of problems, like a rod rotating in a constant magnetic field $B$, we find the EMF induced by the movement by defining an imaginary surface in which the rod is a part of it. Then we apply ...
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Does superposition of all possible plane waves represent complete solution of Maxwell's equations in free space?

Consider the set of all possible superpositions of all possible "plane waves that satisfy Maxwell's equations in free space". Does this set represent all possible solutions of Maxwell's equations in ...
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120 views

Flattening Electrodynamics in a curved space

It is possible, apparently, to describe gravitational lensing as if gravitational potential induces an effective refractive index change in the vacuum, and spacetime is flat. As pointed out by @...
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What is the potential inside a hollow conducting sphere with multipoles uniformly surrounding it?

If considering a hollow conducting sphere with a surrounding uniform charge distribution, for example, it will have a constant and uniform potential throughout the inside of the hollow sphere because $...
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Once introduced will an electric and/or magnetic field live for ever?

So if generate an electric field or magnteic field, will it live for ever? because whenever you get rid of that field for example getting rid of electric field by discharging a capacitor, it will ...
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Euler-Lagrange equations using $\vec{E}$ and $\vec{B}$ instead of $A^\mu$ [duplicate]

We all know that the lagrangian for the free electromagnetic field is given by $$ \mathscr{L} = -\frac{1}{4}F^{\mu \nu}F_{\mu \nu} $$ where $ F^{\mu \nu} = \partial^\mu A^\nu -\partial^\nu A^\mu $ is ...
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Magnitude of induced Electric field

Let us suppose there is a uniform magnetic field present in all space, pointed into the screen. If this magnetic field varies with time, Electric fields will be produced that in turn produce fields ...
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In Maxwell equations, why time derivatives only appear together with Curl?

In the four maxwell's equations, the time dependence only appear in curl of $E$ and $B$ but not divergence. My question was that: Why time dependence only appear in curl? what's the implication? (I ...
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349 views

Where is the energy and momentum of the electromagnetic field?

Using Lorentz force law and Maxwell's equations, one can derive the following relations: \begin{align} \dfrac{dW_{\text{mech}}}{dt}& =-\dfrac{\partial}{\partial t}\bigg(\dfrac{\epsilon_0 E^2}{2}+...
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Why can we use the 2D projection of a 3D gaussian surface to calculate electric flux?

In order to calculate the electric flux passing through one side of a cone with no net charge enclosed, I originally thought you needed to take infinitesimal areas and dot the normal vector with the ...
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What happens if you try to apply Maxwell's Equations to this quantum mechanical system?

In another post, we discussed the oscillating charge in a hydrogen atom and the weight of opinion seemed to be that there is indeed an oscillating charge when you consider the superposition of the 1s ...
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What can Maxwell's Equations tell us about permanent magnets/ how are permanent magnets and electromagnets related?

It makes sense that Maxwell's equations tell us that there are no monopoles, but can the equations tell us anything else about the magnetic fields of permanent magnets on their own, i.e. without ...
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DC current in a wire

I'm sure that this question was addressed here before, but I failed to find any other instances, so with your permission I ask the question myself. I'm experiencing a very disturbing glitch, there is ...
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459 views

Why does current follow a conductor above a ground plane

Suppose there is a conductor above a ground plane. Current flows from a source through the conductor to a load on the other side. Depending on the frequency of the current the return path through the ...
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312 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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225 views

Can Maxwell's Equations explain electromagnetic radiation emission in an atom?

Can Maxwell's equations be used to explain the process of spontaneous emission when an electron drops from a higher energy level to a lower energy level? According the Maxwell equations, a changing ...
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What does it physically mean to take the curl of the curl of a field (wave equation derivation)?

What does it physically mean to take the curl of the curl of a field in the derivation of the electromagnetic wave equation from Maxwell's equations, as presented here, on Wikipedia? Why was it a ...
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How did special relativity change physicists views on the two prominent inverse square laws (ie Newton grav and Coulomb's law)?

On page 107 in Hartle's Gravity -- An introduction to Einstein's General Relativity, he says the following With the success of special relativity it became apparent that the Newtonian theory of ...
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When to use which representation for an electric field

In class we covered three types of possibilities to evaluate the electric field for static problems. Unfortunately, most physics textbooks cover these ways without addressing the question of ...
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Assumptions when calculating $\vec{B}$ using Ampère's (circuital) law

When considering the same setup as in this question, i.e. a straight, infinitely long wire carrying the current $I$, Ampère's circuital law $$\oint_C \vec{B} \cdot \mathrm{d}\vec{r} = \mu_0 I_\text{...
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$D$ and $H$ in macroscopic Maxwell's equation: auxiliary or constitutive?

I'm not a physicist. I want to understand the macroscopic Maxwell's equations. But after reading Wikipedia and other Googled stuffs, I got very confused. In particular, $D$ and $H$ have two different ...
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Understanding the Ampere's Law

We want to study the magnetic field at point $P$. So, from the figure we take that: $\oint_{L_1} B\cdot dl=\mu_0 I_1$ $\oint_{L_2} B\cdot dl=\mu_0 I_2$ $\oint_{L_3} B\cdot dl=\mu_0 I_2$ The magnetic ...
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329 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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Magnetostatics of Current-Carrying wire

A question has been nagging at me about Faraday's Law as related to a wire with a constant current: If you have a circular loop of wire with some small resistivity, connected to a battery so that it ...
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why is advanced radiation absent?

the Lienard-Wiechert green functions have future and past null cones of radiation. Maxwell equations allow for a continuous range of mixtures between the retarded and advanced components, but we have ...
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What is knotted in EM and GR?

I found this paper with beautiful illustrations: Helicity, Topology and Kelvin Waves in reconnecting quantum knots, and this one which seems to describe something closely analogous: New knotted ...
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Maxwell theory : How to justify the potential gauge fields if there are magnetic monopoles?

Without magnetic monopoles, the Maxwell equations are these (I'm dropping vector notations and all constants, for simplicity): \begin{align} \nabla \cdot E &= \rho_{elec}, \tag{1} \\[12pt] \nabla \...
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$\mathcal{\underline{J}}(\underline{r},t)=\rho(\underline{r},t) \underline{v}(\underline{r},t)$ from Maxwell equations

In classical EM theory one can use the following equations as independent: $$\nabla \times \mathcal{\underline{E}}(\underline{r},t)=-\frac{\partial \mathcal{\underline{B}}(\underline{r},t)}{\partial ...
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Lateral momentum of Gaussian beam

A beam of light carries momentum. What fraction of this is lateral rather along the propagation direction if we assume something like a Gaussian beam? Wikipedia claims in the entry on Gaussian beams ...
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Lorentz transformation without constant speed of light in vacuum reasonable?

So there are many methods to teach the special relativity, such as Bondi's K-caculus, or the Minkowski diagrams from the viewpoint of geometry. But all these methods have two fundamental assumptions, ...
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Number of Independent postulates in Electrodynamics

We know that there are two ways to get charge conservation in electrodynamics by using the following action: $$S[A]~=~\int\! d^4x {\cal L},$$ $$ {\cal L} ~=~{\cal L}_{\rm Maxwell} + {\cal L}_{\rm ...
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533 views

Why must this boundary condition be met? (Electromagnetic wave at interface between two mediums)

My textbook says that The laws of Electromagnetic Theory (Section 3.1) lead to certain requirements that must be met by the fields, and they are referred to as the boundary conditions. ...
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Can a Set of “Maxwell's Equations” for Newtonian Gravitation be Derived from Newton's Force + Special Relativity?

When I learned about electromagnetism in my first year of undergraduate school, Maxwell's equations were derived roughly in the following way (see also here or in [1]): Gauss's law for a static ...
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Does a Static E-field Increase the Gauge Invariant Vector Potential Without Bound?

The gauge invariant formulation of Maxwell's Laws (7.13): Indicates that the transverse electric field is the time derivative of the transverse vector potential. This gauge invariant vector ...
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How to properly construct the electromagnetic tensor in curved space-time? (Part II)

In this question, I am testing what was previously discussed. I can't seem to get my results to match D'Inverno's electromagnetic tensor for a charged point (page 239 of his book - Introducing ...
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Electromagnetic duality

A key aspect of modern physics is the mapping of theories or different descriptions of a theory into a one-to-one correspondence. As I am trying to further understand the electromagnetic field tensor, ...
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769 views

Forms of Maxwell's equations

In my physics class, I was taught two forms of one of Maxwell's equations: Ampere's law $$\vec{\nabla} \times \vec{B} = \mu J$$ and Maxwell-Ampere's law $$c^2\vec{\nabla} \times \vec{B} = \dfrac{\...