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 Maxwell-Boltzmann distribution, or the thermodynamical equations known as Maxwell's relations.

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Deducing the Heaviside-Feynman formulae from Jefimenko's equations

I've tried to deduce the one point charge Heaviside–Feynman formula from the Jefimenko's equations. This should be possible, by replacing the densities with Dirac deltas, somehow, but I failed. Could ...
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Intuition of Faraday's law at a boundary

I know that Faraday's law means that the tangential electric fields have to be equal at both sides of a boundary. I'm struggling to understand intuitively why this has to be the case. What would ...
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How do signals propagate down unballanced coaxial transmission lines?

I have previously asked a related question however it was closed, thus I have sorted out my thoughts into this revised question. This new question comes in two parts. I do not understand the concept ...
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Loop of wire in changing magnetic field, open circuit vs. short vs. intermediate

I've wondered about this for years. Assume you have a loop of wire in a time varying magnetic field. The loop has only one turn and you can either leave the ends disconnected (open circuit), short ...
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Energy density of a electromagnetic wave [duplicate]

The average energy density of a electromagnetic wave is given as $U_{average}$ =$\frac{e_0E^2}{2}$ My textbook also claims that "electromagnetic waves incident on a surface exert a force on the ...
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Coaxial Confusion, what really are unbalanced transmission lines? [closed]

Thanks for clicking on my question. I do not understand how an unbalanced transmission line works. Take for instance coaxial cable which is the subject of my confusion. This confusion arises from the ...
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Hamilton-Jacobi Equation for Motion in Coulomb Field

In the text Gravitation Foundations and Frontiers by Padmanabhan, the equation of motion for Coulomb field can be written (in Coulomb gauge) as $$-\left(\frac{\partial \mathcal{A}}{\partial t}+\frac{\...
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How to connect $x$, $y$ component of 2D electromagnetic wave equation?

I want to solve following Maxwell's equation. $$ \triangledown ^{2}E+\frac{\omega^{2}}{c^{2}}E=0 $$ But, Electric field has x, y component in 2D geometry. So, it will be $$ \frac{\partial^{2} E_x}{\...
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Maxwell Equations WITHOUT electric monopoles/charges

I was wondering if Maxwell equations in vacuum would also describe a universe without electric monopoles, but where dipoles etc. are allowed. \begin{align} \nabla \cdot \mathbf{E} &= 0 \quad &...
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Magnet falling in copper tube, radial force component

Consider a Dipole magnet falling through infinite copper pipe. If we displace a magnet a little bit so that the dipole isn't pointing to the same way as pipe (dipole isn't parallel to the pipe) we get ...
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How is $E×B$ zero? [closed]

I was reading Feynman lectures vol. 2 pg no. 291. There I found the general solution of one dimensional planar waves along $x$ direction. My question is the when I apply dot product on $E$ and $B$ ...
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What is "free charge" in the macroscopic maxwell equations?

Wikipedia states the macroscopic Gauss' law as $\nabla \cdot \overrightarrow{D} = \rho_f$, where $\rho_f$ is the charge density of free charge carriers. I understand that conducting electrons in a ...
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Proof that $\nabla \times E = 0$ using Stoke's theorem [closed]

One way that Jackson proves that $\nabla \times E = 0$ is the following: $$ F = q E $$ $$ W = - \int_A^B F \cdot dl = - q \int_A^B E \cdot dl = q \int_A^B \nabla \phi \cdot dl = q \int_A^B d \phi = ...
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Find the strongest point of the magnetic field from three long conducting wires

Consider three long power lines buried in the ocean, with (from left to right) current $\frac{I}{2}, I, \frac{I}{2}$, where the direction of the current in the edge cables are negative $z$ (in to the ...
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How Do I Know Whether Waveguides Support TE or TM Modes?

I'm working through the formalism of waveguides, and I've seen many different situations with various boundary conditions: hollow metal rectangular waveguide, dielectric slab, dielectric rectangular ...
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Form of time-harmonic electric and magnetic fields far from source

In Born and Wolf chapter 3, they discuss how one can derive geometrical optics from Maxwells equations. Their original argument relies on considering the forms of plane and spherical waves to say that ...
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Understanding the interaction of two inductors, e.g mutual inductance, transformers, without energy conservation

Is there a way to understand the interaction of two inductors, such as in transformers and in mutual induction, without using energy conservation? In the texts that I have read so far, whenever I have ...
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Maxwell equation in material media assuming periodic fields

In article https://aip.scitation.org/doi/10.1063/1.440709 authors use the following equation for treatment of electromagnetic waves in dielectric material with inhomogenous electric permitivity: $$(\...
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Superposition of two electromagnetic waves

If an electromagnetic wave in isolation with vector potential $A^1_{\alpha}$ satisfies the wave equation $\Box A^1_{\alpha}=0$, how do we construct the total electromagnetic wave that results from ...
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Finding the geometry of induced electric fields using Faraday's law

Thinking of a long straight wire carrying increasing or decreasing current, we know by using Faraday's law of induction that the magnetic field produced by this wire will induce an electric field. Now,...
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Derivation of the maxwell equation in its differential form [duplicate]

I was going through the derivation of the differential form of maxwell equation and I ended up getting arrested at that part where it is used the gauss theorem to establish the follow relation The ...
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Satisfying and puzzling phenomenon about magnetic dipole

I just found a cool video of magnet falling through cooper pipe. So I naturally have a couple of questions about this physics phenomenon. I even tried to derive the equations of motion... During my ...
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Suspicious EMF equation

Some context: I am trying to get the equation of motion for a dipole magnet falling through copper pipe. To proceed I need to calculate the EMF. We can do this by using Faraday's law, $$\oint_{\...
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Does Coulomb gauge imply constant density?

Say we have $$\Box A = J$$ and $$\nabla \cdot A = 0\;.$$ Then $$0 = \Box (\nabla \cdot A) = \nabla \cdot J\;.$$ But, $$\nabla \cdot J - \partial_t \rho = 0\;.$$ So $$ \partial_t \rho = 0\;.$$ Thus, $$\...
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Equations of motion of $\mathcal{L}= - \frac{1}{4}F^{2}_{\mu \nu} - A_{\mu}J_{\mu}$ in momentum space

I'm reading the Matthew D. Schwartz, Quantum field theory and the standard model, p.128 and some question arises. Consider a lagrangian $\mathcal{L}= - \frac{1}{4}F^{2}_{\mu \nu} - A_{\mu}J_{\mu}$ ($...
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Do we need two different classical limits to go from QED to classical electrodynamics? [duplicate]

QED describes the interaction of two operator fields. Classical electrodynamics describes the interaction of a classical field with a point charged particle. My question is, what limits do you apply ...
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Curl of a vector field at a single point

I have always imagined the magnetic field of wires, as the superposition of infinitely many curl elements. I, naturally, wanted to see what a function with a single point of curl would look like. The ...
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Why is a photon's energy described by $E^2=(pc)^2$ if a photon field is described by $A^\mu$?

We can use Einstein's famous energy equation: $$E^2=(mc^2)^2+(pc)^2 \tag{1}$$ To find the relativistic energy. I can turn this into quantum mechanics and I'll have the Klein-Gordon Equation: $$\...
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Coulomb gauge choice: Does $A_0=0$ imply that we also need to choose $\nabla \cdot \vec{A} =0$ from the EOM of $A_0$?

How to justify the Coulomb gauge fixing condition choice with $$ A_0=0, \quad \nabla \cdot \vec{A} =0? $$ Below in the text image, I find a text explaining that imposing $A_0=0$ is always possible ...
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Is there a reflection when light destrucively interferes on a surface?

Imagine the following setup: I have a coherent single frequency electromagnetic wave (laser beam) that is imaged on a surface. It is reflected onto a detector (photodiode). I can easily take ...
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Having positive charge density, yet a particle experiences an attractive force [closed]

Before flagging this as a homework question, note that I'm not asking to solve something. I have the answer but cannot interpret it correctly. I have a conceptual problem that appeared in a specific ...
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Why does solution for magnetic field of moving charge from special relativity give $dq/dt=0$? [closed]

From electric field of a point charge: $$ \vec{E} = \frac{k Q \vec{r}}{\gamma^{2}r^3(1-\beta^2sin^2\theta)^{\frac{3}{2}}}, \vec{B} = \frac{\vec{u} \times \vec{E}}{c^2} $$ taking curl of B gives $$ \...
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If changing electric field induces magnetic field, how can steady current (therefore steady electric field) create magnetic field around it?

In the search for understanding electromagnetism on deeper level, one of the earliest observations was that magnetic field is created around a current carrying wire. Then it was noticed that changing ...
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How to find Weyl/temporal gauge fixing condition?

Transformations that leave the field invariant: $$\vec{A}' = \vec{A} + \nabla f$$ $$\phi' = \phi -\frac{\partial f}{\partial t}$$ I would like to solve for the weyl gauge, aka a gauge that leaves $$\...
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What are the Maxwell equations of motion in retarded Bondi coordinates?

I'm reading a paper about asymptotic symmetries at null infinity in electrodynamics. There, they had the following calculation: The Maxwell equations $\nabla^{\nu} F_{\mu\nu} = J_{\nu}$ written in ...
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What's making the scenario contradictory to Maxwell's theory of em waves?

I was imagining how an oscillating charge would produce an electromagnetic wave and I got stuck at a point. We know that the direction of propagation of em waves is perpendicular to both the ...
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Different ways to calculate magnetic field of a segment of current [duplicate]

Given a segment of current $I$ of length $L$, we want to calculate $\vec{B}$ on a plane that is perpendicular bisector of the segment. From the Biot-Savart law, $\vec{B}$ depends on $L$ and $R$ (the ...
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Could intensity be related to the flux of the electric field?

Imagine a cable in which an intensity $\mathbf I$, is passing through. This intensity is caused by the moving particles (for example electrons), going with a certain speed, and with some density of ...
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Relation between Area under $I$-$H$ hysteresis Loop and $B$-$H$ hysteresis Loop [closed]

If the area under the I-H hysteresis loop and B-H hysteresis loop are denoted by $A_1$and $A_2$ (The symbols have usual meaning as set in electromagnetics), then $A_2=\mu_oA_1$ $A_2=A_1$ $A_1=\...
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Electrodynamics - Faraday law in moving circuit (Jackson's ED)

I have had this issue with Jackson's derivation of Faraday law in a moving circuit for quite some time and have not been able to resolve it. The relevant parts of the book is p. 211-212 in 2nd edition,...
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Is my derivation of the electric field from a thin wire with changing current correct?

A quick look at my profile will show that I've spent that last couple of years trying to understand electromagnetism and more specifically, the creation and propagation of radio waves. Recently, I ...
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Maxwell's equations from conserved current

It's not clear to me how the determinant in equation (8) in this little paper (Space and Time) was calculated. My questions are: what are these $t_\nu, x_\nu, y_\nu, z_\nu$? Like does $t_\nu$ stand ...
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Lorentz Force law for charge density

I was going through chapter 8 of Griffiths' "Introduction to Electrodynamics", where he introduces the Maxwell Stress Tensor, by deriving it from the Lorentz law for some charge density $\...
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Lorentz's derivation of Lorentz force in 1892

I've found Lorentz's 1892 paper 'La théorie electromagnétique de Maxwell et son application aux corps mouvants' on Wikipedia (It's in French and I failed to find the English version.) https://ilorentz....
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Is curl of $J$ in steady-state zero?

I've been trying to follow this post on deriving the Biot-Savart law from Maxwell's Equations but am getting stuck on this step: $$-\frac{\mu_0}{4\pi}\iiint{\nabla\times\frac{J}{|r-r'|} d^3r'}.$$ ...
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What is the charge of an electric field created by an oscillating magnetic field? [closed]

An oscillating (or, even accelerating) magnetic field produces an electric field. What is the charge of that electric field?
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1 vote
2 answers
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Why is the electromagnetic wave equation derived from Maxwell's equations with no charges?

After having consulted numerous physics books, forums and videos, in all cases I found that the electromagnetic wave equation is derived from taking as a premise that the medium is a vacuum. This ...
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Maxwell Ampere law derivation

I have seen a proof on the internet regarding the derivation of the maxwell ampere law in this link: Deriving the Ampère-Maxwell law and even though I am pretty much satisfied in the way he derives ...
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Intrinsic impedance inside a good conductor

I am currently studying the textbook Microwave Engineering, fourth edition, by David Pozar. Chapter 1.4 THE WAVE EQUATION AND BASIC PLANE WAVE SOLUTIONS says the following: Plane Waves in a General ...
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Can we derive Ampere's Circuital Law from Gauss's Law or vice versa?

I was curious if it is possible to derive Ampere's Circuital Law from Gauss's Law as they are very similar and both can be applied for highly symmetrical problems $(Infinite\space wires,Rings..etc)$ ...

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