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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Stokes Theorem with Ampere's Law

Whilst researching Maxwell's Equations (here), I found (effectively) the following pieces of logic: $$\int_S \left(\nabla \times \boldsymbol{H}\right) \cdot d\boldsymbol{S} = \oint \boldsymbol{H} \...
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Dipole Receive Antenna: Derivation of circuit representation

Many textbooks cover generation of electromagnetic radiation via transmit antenna and then invoke a reciprocity theorem for the antenna acting as a receiver. I'm wondering, can you derive the ...
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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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Confusion on Maxwells equations and Gauge Transformations

I know a little bit about electrodynamics but I don't understand the validity of Gauge Transformations. In particular I am confused on how the theory can be consistent among different gauges, in ...
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188 views

Use of Ampere's law in case of a finite wire

I myself tried computing magnetic field due to a finite current carrying wire using Ampere's law and I found the expression comes similar to the case of infinite wire. Obviously, there must be ...
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Derivation of maxwell's equations - how to make it mathematically correct?

So, we started from $$\oint \vec{E}d\vec{A}=\frac{Q}{\epsilon_0}$$ And used an electric dipole setup with $\vec{p}=q\vec{l}$ and $\vec{P}=\frac{\sum\vec{p}}{V}$, and reached the desired result: $$\...
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Do the Maxwell equations definitively rule out the existence of magnetic monopoles?

Gauss's law for magnetism, $\nabla \cdot \mathbf {B} =0$, is most directly interpreted as a sort of Kirchhoff's current law for magnetism, stating that while magnetic fields can be drawn between ...
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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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Maxwell's equations and Lorentz force

In a previous question I was told that the Lorentz force can compute the force on charges in one system A from electric and magnetic fields from another system B, but A cannot be the same system as B ...
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Solving Third Maxwell Equation [closed]

Suppose I want to solve the third Maxwell equation: $$\nabla\cdot\mathbf{B} = 0$$ The first assumption is that we could write the magnetic field as: $$\mathbf{B} \equiv B(x,y,z) \equiv b(x)\beta(y)Z(z)...
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Inteference and energy conservation

I have this equation given in my lecture notes about interference between electromagnetic waves. I have searched the internet and cannot find it anywhere, I do not understand how you would come to ...
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Derivative of the electromagnetic tensor invariant $F_{\mu\nu}F^{\mu\nu}$

The electromagnetic field tensor is $F_{\mu\nu}=\partial_\mu A_\nu - \partial_\nu A_\mu$. I am trying to calculate the quantity $$ \frac{\partial(F_{\alpha\beta}F^{\alpha\beta})}{\partial(\partial_{\...
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Non radiation charge density

For all $l,m$ but $l=0,m=0$, can we find $r_0,w_0$ such that the following charge distributions can represent a charge field that does not radiate: $$ \rho(r,\theta,\phi) = \Re(c_{l,m} Y_{l,m}(\theta,...
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Maxwell Equations and magnetic field?

One of the maxwell equations state that the magnetic field induced around a closed loop is proportional to the electric current plus displacement current (rate of change of electric field) it encloses....
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If the photon were massive how do the electric and magnetic field change?

According to electrodynamics the photon is massless. That is due to gauge invariance. But if the photon were massive what would be the change in the electric and magnetic field? Is the massive nature ...
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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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Has anyone ever tried to derive gravitoelectromagnetic waves equation?

Has anyone ever tried to derive gravitoelectromagnetic waves equation? As we know, there is Maxwell-like equation in gravity. Has anyone here ever formulated gravito electromagnetic waves equation ...
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Induced current and Maxwell's equations [closed]

A thin cylindrical shell is made of a perfect conductor (PEC) with radius $b$ and length $L$. There is a cylindrical current source with a surface current density with radius a, so that $a<b$, and ...
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Radiation Pattern for a Dipole Antenna with non-sinusodial forcing voltage

I was wondering, how does one derive the radiation pattern for a dipole antenna if you don't assume a sinusoidal forcing function? It seems this assumption kind of ignores the most important question ...
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which surface to use in Faraday's law?

To find the emf (voltage) generated for a changing magnetic field around a conducting loop, we use faraday's law with flux defined across the surface of the disk which the loop encloses. This tells ...
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Two field form of the Maxwell equations: Why are effects due to polarisation ignored.

I have a couple of questions regarding the following section in my notes and would like some help in resolving some confusions. 1)why is εr = 1 in the plasma? 2) If µr = 1 it means we switched off ...
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Displacement current in charging capacitor [duplicate]

In the classic example of a charging capacitor I can see how an Amperian loop with a surface going between the capacitor's plates would feel a changing electric flux, as the electric field between the ...
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Maxwell's equation. E and H. Two homogeneous but different media [closed]

I need your help in explanation/understanding the following question: The electric and magnetic fields have at an interface between two homogeneous media the continuity conditions. How can it be ...
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Why are the $\mathbf E$ and $\mathbf B$ fields of an electromagnetic wave mutually perpendicular?

Why are the wave number $\mathbf k$ and the electric and magnetic fields $\mathbf E$ and $\mathbf B$ are perpendicular to each other? I know it but I haven't thought about it deeply. How can I prove ...
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Spreading resistance of a microelectrode in a bath

I have a question regarding the spreading resistance, or series resistance, around a glass microelectrode in a bath (a conducting fluid with uniform resistivity $\rho$). The bath is grounded at a far ...
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Factor of two for inductance of parallel plates

Studying transmission lines I am confused about a "missing" factor of two in the formula $L = \mu_0 a/b$ for the inductance per unit length of two "infinite" parallel sheets. Say we have two parallel ...
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How is it possible to shield eletomagnetic waves?

I've learned the Maxwell equations and how light is described as an electromagnetic field. But then the teacher just jumped to geometric optics. I'm trying to understand light in terms of ...
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My attempt to implement linear memristor

Memristor, which makes relationship between charge and flux, has not been discovered, according to Wikipedia. So I tried to implement it, here linear. As it both stores charges and induces magnetic ...
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Covariant Formulation of E&M

Can anybody explain me what does mean the "covariant formulation of electrodynamics"? What does the covariant here mean? Invariance of Maxwell equations under Lorentz Transformations? In what way? ...
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What would happen to the transverse nature of EM field if photon had a mass?

If the photon had mass, will Maxwell's equations in free space $\vec{\nabla}\cdot\vec{E}=\vec{\nabla}\cdot\vec{B}=0$ still be satisfied? If not, will the transverse nature of EM waves (which follows ...
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Simplification of Maxwell equations assuming that the induced fields are much weaker than the applied fields

In cases where induced fields are much smaller than the applied fields, are there any terms in the Maxwell equations that can be neglected? I tried to do a simple scaling analysis to come up with a ...
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398 views

Why is magnetic field zero for open circuit and electric field zero for short circuit?

I read this statement in a book for a simple circuit (1 resistor connected to a voltage source). If we short out the resistor, the E field is said to be zero and if the circuit is broken (open circuit)...
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Does a conducting rod moving in a magnetic field itself generate another magnetic field?

A standard problem in elementary EM goes something like this: An infinite straight wire conducts a stationary current $I$. A conducting rod, perpendicular to the wire, moves with constant velocity ...
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Physical implication of $\textbf{E}\rightarrow\textbf{B},~~\textbf{B}\rightarrow -\textbf{E}$ invariance of the Maxwell's equations

An interesting observation to consider about the Maxwell's equation is that in absence of the sources, the equations are symmetric under the interchange $$\textbf{E}\rightarrow\textbf{B},~~\textbf{B}\...
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What is needed to determine the Faraday tensor?

What data is needed to determine the Faraday tensor and how is it done? The Maxwell equation seems coupled to the Faraday tensor and the four-current (which seems coupled to either the charge ...
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About Homogeneous Maxwell equation from EM Lagrangian

I have studied some of the relevant Q&A here. Everything is quite satisfactory. But is there any way to prove homogeneous part of 4 Maxwell equation from Lagrangian formalism, i.e constructing the ...
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What conserved charge follows from the dual field strength tensor?

The homogenous Maxwell equations $$ \partial_\mu \tilde{F}^{\mu \nu} =0 $$ follow "trivially" from the definition of the dual field strength tensor $\tilde{F}^{\mu \nu} = \epsilon^{\mu \nu \sigma \...
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The wave function of the photon and electron are probability waves, does this mean the Maxwell are some time correct some time wrong? [closed]

The wave is probability wave, it is seams that the wave function some time is correct, the energy is sent out. Some time it is wrong the energy is not sent out. Hence we can obtained the conclusion ...
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The electric field is still there if the test charge is removed?

The test charge is used to measure the electric field. The problem is that if we measured some value of the field, then the test charge is removed, what will happen? The measured field is still there?...
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Does Feynman's derivation of Maxwell's equations have a physical interpretation?

There are so many times that something leaves you stumped. I was recently reading the paper "Feynman's derivation of Maxwell's equations and extra dimensions" and the derivation of the Maxwell's ...
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Does an accelerating electric dipole radiate?

For such a simple question I'm finding it remarkably hard to get a definitive answer. Googling has not helped me. Consider an ideal electric dipole that is constant i.e. neither its magnitude nor ...
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Do we fix divergence of the vector potential $A$, because $\nabla \cdot \nabla \psi \ne 0$?

Because $\nabla \times \nabla \psi = 0$, we can transform the vector potential $A \longmapsto A + \nabla \psi$, without changing the magnetic field. Is the reason we specify $\nabla \cdot A$ in the ...
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Maxwell's equations from continuum limit

In appendix A.6 of Schroeder's Thermal Physics, he mentions (in regards to classical fields): The usual approach is to first pretend that the continuous object is really a bunch of point particles ...
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Relationship between the magnetic and electric component of an EM field

I am studying Maxwell's equations and their use to derive a wave equation to derive the behaviour of electromagnetic waves in vacuum. In the case of plane waves, EM fields can be described by: $\vec ...
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Maxwell's equations and nonlinear media

Are there analytical methods to analyze electromagnetic fields or magnetic diffusion in materials which are not linear using (or starting from) Maxwell’s equations? Nonlinear material could be ...
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Why is induced electric field (due to a changing magnetic field) in the form of concentric circles?

What can't it be any other shape, like concentric squares, or rectangles, etc? Also, where is the common centre of the electric field lines?
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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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What does the charge density signify in the differential form of Gauss law?

Let us say that I have uniformly charged sphere of total charge Q and radius R. The electric field due to this charge distribution at r=R/2 is given by, $$E = \frac{kQ}{2R^2}\hat{r}$$(This was derived ...
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Physical difference between retarded and advanced green's function in Electrodynamics

I do not fully understand the difference physically between a retarded solution and an advanced green's function solution to the wave equation with an arbitary source in electrodynamics. Can someone ...
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Are the electromagnetic waves transverse?

The em waves are said to be the oscillations o electric and magnetic field perpendicular to each other and to the direction of propagation of wave and hence transverse. However consider a charged ...