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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Validity of Maxwell's laws

I know Lorentz's force changes, according to Wikipedia, when the charges are moving nearly light speed but what about Maxwell's laws? Are they still valid when particles move at light speed? I ask ...
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Were the original Maxwell quaternion equations different than Heaviside's vector equations in any of their predictions?

Gibbs vector calculus removed scalar quaternion parts of equations thus predicting no scalar waves that transfer energy. Did Maxwell have a different take on similar predictions.
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Maxwell equations and continuity equation

I want to show the following equation with the maxwell equations: $$\frac{\partial}{\partial t}W+\vec{\nabla} \cdot \vec{S} = 0 $$ The problem is that I'm not understanding why I can do the following ...
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Electric field for point charge in a smoothly-varying dielectric?

A classic textbook E&M problem is to calculate the electric field produced by a point charge $Q$ located at $(\mathbf{r}_0,z_0)$ inside a medium with two semi-infinite dielectric constants defined ...
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For a constant total charge arbitrarily distributed on a fixed closed surface boundary: is every internal and external field unique? [duplicate]

As an example: in free space, a constant total charge Q distributed uniformly on a fixed spherical surface gives rise to a zero internal and Coulombic external electric field. As far as I can see, ...
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Reduction of Maxwell's equations to classical circuit theory

Can classical circuit theory based on lumped element models be obtained from Maxwell's equations as a limiting case in an appropriate sense? If this is the case, what exactly are all the assumptions ...
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Boundary conditions of electrostatics

As we have seen that while deriving the boundary conditions in Griffith's electrodynamics he stated some conclusions, that were The Perpendicular components of Electric field and Gradient of ...
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Why does gauge invariance have physical consequences?

My understanding is that gauge invariance occurs when the description of a physical field as a mathematical field (i.e., function whose domain is space-time) contains a redundancy: there are ...
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Deriving the wave equation for electromagnetic waves

I'm currently referring to the wave equation derivation given in "Introduction to Electrodynamics" by David J. Griffiths. It follows something like this: The electromagnetic wave equations are given ...
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Is dispalcement current produced in inductor?

As we know in case of capacitor, changing electric field inside it produces a current which is called a displacement current (Amperes law modified by Maxwell). In case of inductor, is there any ...
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Eddy currents and diamagnetism

In this video showing magnetic melting of aluminum the metal piece levitates above the solenoid due to eddy currents: https://www.youtube.com/watch?v=8i2OVqWo9s0 So aluminum behaves as a diamagnet ...
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Writing an expression for the scalar value of the electric field $E$

I am currently studying Optics, fifth edition, by Hecht. In chapter 2.7 Plane Waves, the following example is given: An electromagnetic plane wave is described by its electric field $E$. The wave ...
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Does Maxwell's Equations on Magnetic Field holds good in year 2020? [duplicate]

Does "Maxwell's equations" on "Magnetic Field" still hold good in year 2020? Till now no parameters are changed or corrected? Why does speed of Magnetism always relate to Speed of Electromagnetic ...
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How does the physical meaning of curl is in agreement with these scenarios?

In the foundation chapters of Electrodynamics I was introduced to concept of curl of a vector field. It was defined as follows $$ \nabla \times \mathbf A = \begin{vmatrix} \hat{i} &...
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Where do induced electric fields originate from and end?

Electric fields originate from charges. But according to faraday's law $$\nabla \times E = - \dfrac{\partial B}{\partial t}$$ changing magnetic fields creates electric fields. How do these electric ...
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Why is the magnitude of the electric field dependent only on $x$ and $y$ coordinates?

So I am reading a book on electromagnetism and in it they are assuming that the magnitude of the electric field is dependent only on $x$ and $y$ coordinates in a waveguide and I wanted to know why ...
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Physical Justification of Retarded Potentials

How did physicists interpret the physical significance of retarded potential before the advent of special relativity? , Did it account for the time taken by electromagnetic forces to propagate through ...
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How to find the magnetic field of a current using the differential form of Maxwell's equations? [closed]

To find the magnetic field produced by a long straight wire, one would ise either Biot-Savart law or Ampere's Law in integral form. How do you find this simple result starting from $\nabla \cdot \vec{...
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Degrees of freedom of a photon/electromagnetic field, meaning of degrees of freedom [duplicate]

as I understand it a photon field $A^\mu$ has two physical degrees of freedom corresponding to the two polarisations. I was wondering why, for example, energy isn't considered a degree of freedom. I ...
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How can the Vector Magnetic Potential be defined in both the regions where current density is equal and non-equal to zero?

I am currently reading about the steady magnetic field, and when I came across the vector magnetic potential I came to know that it can be defined in both the regions where current density $\mathbf J =...
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Qualitative thought model for retarded potentials

I attempted to grasp the retarded potentials by staring at them and wanted to know if my thoughts seem to work out. Equation taken from wikipedia (replaced $t_r$ with its definition): $$ \mathrm\...
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Extending Maxwell's Equations from Flat Spacetime To Curved Spacetime

Assume we are working on a Minkowski (i.e. flat) spacetime. Let $A^{\mu} = ( \phi/c, \textbf{A})$ be the contravariant potential four-vector. Then, assuming a covariant Minkowski metric of $\eta_{\...
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Induced current at a metal disk

If i have a metal disk, and i apply a variable magnetic field perpendicular to the plane of the disk. The field changes with a constant rate $\frac{\partial B}{\partial t}$. How can i find the ...
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How can I actually use Maxwell's equations to solve an electromagnetism problem?

I studied Maxwell's equations, but when it comes to problem solving my teacher never actually used them, so I was wondering if and when do they come useful? For example, if I have an empty infinite ...
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Electric field boundary conditions in the radiation regime

In electrostatics, one obtains the boundary conditions on the tangential components of $\vec E$ across two boundaries by using a small closed circuit so that \begin{align} \oint \vec E\cdot d\vec\ell =...
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Derivation of KVL for AC circuits

AC circuits have periodically changing current, due to which there will be a change in the magnetic flux as a consequence of which an electric field will be produced and hence an emf; my question is, ...
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Compute forces on charged particles without fields in $v << c$ limit

For a set of particles with charges $q_i$ and positions and velocities $\vec{r}_i(t)$ and $\vec{v}_i(t)$, I'd like to calculate the electromagnetic forces on them in the limit that $v \ll c$, so that ...
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In plasma physics, why are the motional electric field and the frozen-in-flux condition represented by the same equation? ($E = -u \times B$)

I'm trying to refine my understanding of space plasmas, and feel like there's an intuitive understanding here that I'm just missing. We commonly refer to a motional electric field in the solar wind. ...
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Is the author of the article below right? To cast two (6) of the Maxwell equations into a QM wavefunction?

Look at this flow chart: It's taken from this article (from the archives of Cornell University), in which this is claimed: James Clerk Maxwell unknowingly discovered a correct relativistic, ...
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What's so different about divergence and curl in Maxwell's Equation?

The Four Maxwell's equation that are given by $$\nabla . \mathbf{E}=\frac{\rho}{\epsilon_0}$$ $$\nabla.\mathbf{B}=0$$ $$\nabla\times \mathbf{E}+\frac{\partial \mathbf{B}}{\partial t}=0$$ $$\nabla \...
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Differentiating Plasma Wave Modes Using Phase Difference

Graphically, the four plasma wave modes for 'cold' plasma overlap for various frequencies. According to Fundamentals of Plasma Physics by Bittencourt, the dispersion relations characterize an $\omega$-...
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Mathematics of phasor representations of sinusoidal variations of fields

In physics, we often use phasor representations of sinusoidal variations of fields, such as $$\mathbf{e}(\mathbf{r}, t) = Re[\mathbf{E}(\mathbf{r})e^{j \omega t}]$$ I have some questions about how ...
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What does adding a gauge fixing term $-\frac{1}{2\xi}(\partial_\mu A^\mu)^2$ really mean?

Given any electric and magnetic field (or $F_{\mu\nu}$), there is always some freedom in defining what $A_\mu(x)$ should be. In fact, there are infinite choices for $A_\mu(x)$. This is because for an ...
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Proof that $||\vec{E}|| = c||\vec{B}||$ for electromagnetic waves from maxwells equations in vacuum

Starting from Maxwell-equations in vacuum : $$ \nabla \cdot \vec{E} = 0 $$ $$ \nabla \times \vec{E} = - \frac{\partial \vec{B}}{\partial t} $$ $$ \nabla \cdot \vec{B} = 0 $$ $$ \nabla \times \vec{B} =...
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Free space Maxwell equation in frequency domain?

While reading the textbook "Classical Theory of Gauge Fields" by Valery Rubakov but I couldn't follow some of the steps in the 1.3 chapter. Firstly Fourier transform of 4-vector-potential is given as ...
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Doubt On Maxwell's Stress Tensor

I was reading Introduction to Electrodynamics By D.J. Griffiths Chapter 8 Conservation Laws , Maxwell's Stress Tensor.The starting lines are the following Let's calculate the total electromagnetic ...
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X-ray scattering: Mathematical description of a *fluctuating electric field* and *accelerating charged particle*

My textbook, Solid-State Physics, Fluidics, and Analytical Techniques in Micro- and Nanotechnology, by Madou, says the following in a section on x-ray diffraction: X-rays are scattered by the ...
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What is the relevance of Maxwell's equation being linear?

My prof in my intro to electrodynamics class briefly mentioned that the linearity of Maxwell's equations is related to the superposition of electric fields by point charges, but I don't see how. Would ...
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Problem with Faraday's law and Lorentz force

There are two forms of Faraday's law: The first one: $\nabla \times \vec{E}=-\frac{\partial \vec{B}}{\partial t}$ and the second one: $\oint \vec{E} \cdot d\vec{s}=-\frac{d\Phi_B}{dt}$. If we have a ...
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Is $F_{\mu\nu}F^{\mu\nu}$ the only possible gauge-invariant Lagrangian for the electromagnetic field?

Maxwell's equations can be derived from a Lagrangian formulation using the Lagrangian term (modulo some constants) $$\mathcal L=-\frac{1}{4}F^{\mu\nu}F_{\mu\nu}-A_\mu J^\mu.$$ Focusing on the free ...
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Can't figure out how Maxwell equation about divergence holds for Electric field of a very long cylinder

So, this is a formula for electric field of an infinitely (or very long) cylinder. $$\mathbf{E}= \frac{\lambda}{2\pi \varepsilon _{0}r}\mathbf{\hat{r}}$$ And this is the divergence law of E field ...
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Electromagnetic tensor in the Reissner Nordström metric

At scholarpedia.org/article/Kerr-Newman_metric it is stated that, I quote: but since $F_{\mu \nu}=\frac{\partial A_{\mu}}{\partial x^{\nu}}-\frac{\partial A_{\nu}}{\partial x^{\mu}}$, where does the $...
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What are the physics implications of a world with magnetic monopoles? [closed]

When I studied Electromagnetism, even though I was already used to the idea of always finding magnets with two poles, one thing that was really shocking for the first time was seeing one of Maxwell's ...
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Induced electric field from homogeneous magnetic field in free space points in all directions

If there is a homogeneous magnetic field varying with time, say $\vec{B} = B_0 \sin(t) \hat z$, then this should, from faradays law of induction, induce an electric field. Since the problem looks ...
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What it means for the wave equation of light in vacuum to be a solution of the maxwell equations? [closed]

I know how to get the wave equation of light from Maxwell's equation, but I never understood why it is called the solution of the Maxwell equations. If say we have a positive charge standing still ...
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Maxwell's Equations: Taking the real part of the product $\mathbf{E}\exp(j \omega t)$ in order to get the “complete field”

My textbook, Laser Electronics, Third Edition, by Verdeyen, says the following in a section on Maxwell's equations: To describe an electromagnetic wave, we need two field-intensity vectors, $\...
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About the formation of an electromagnetic wave

I was going through the derivation for the equation electromagnetic waves and got these equations $$\mu\epsilon \frac{\partial^2\mathbf{E}}{\partial t^2} = \mathbf{\nabla}\times\left(\frac{\partial\...
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How can one $E$-field formula be rewritten to another version [closed]

I will start with going through a rewriting of one E field to another that I understand which is that the total E field out of a sphere is derived as $$\pmb{r}=x\pmb{i}+y\pmb{j}+z\pmb{k}=r\cos\theta \...
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Quasi-classical model of an atom

This question does not have a close relationship to this or this Stack Exchange question. It's not about the Bohr atom model nor the Rutherford atom model, but is fairly closely related to this3 SE ...
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Electromagnetic fields and electromagnetic wave boundaries

I have first learnt the concept of plane electromagnetic waves as a solution to Maxwell's equations in vacuum recently and they are usually depicted them as follows: Here is my confusion: in the ...

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