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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How does the electric field instantly reflect the divergence in a system?
Suppose I have a decreasing charge ρ at the center of a sphere being carried away by a wire out of the sphere at a uniform rate. By Gauss law, the surface integral of the electric field normal to the ...
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Topological current in (2+1)D spinorial electrodynamics
Giving the coupled Dirac equations for $\psi$ and its conjugate $\bar{\psi}$ in 2+1:
\begin{align}
(i\gamma^\mu\partial_\mu-m)\psi&=qA_\mu\gamma^\mu\psi,\\
\bar{\psi}(i\gamma^\mu\partial_\mu+m)&...
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Hertzian Dipole: Why is there no longer a phase shift at $\frac\lambda2$? [closed]
Today we learned about the Hertzian Dipole. Out teacher told us that the length of the wire connecting the two capacitor plates is $l=\frac\lambda2$. He also stated that there is a no more phase shift ...
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Infinite/recursive solution for magnetic field due to a long straight wire?
I'm trying to use Maxwell-Ampere's law to find the field due to a long straight wire, but I keep running into some circular reasoning...
Maxwell-Ampere's law states that $\oint_c \vec{B} \cdot \vec{dl}...
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Integrating current density for cylindrical symmetry
Considering a constant current density, $\vec{J}=\frac{I}{A}\hat{k}$, and also assuming there is no displacement current in the situation, how would one apply Maxwell-Ampere's law? I keep running into ...
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Confusion with displacement current
I'm currently studying maxwell's equations in class, and my professor has explained the concept of displacement currents. The idea makes sense to me -- I mean, after all, isn't that entirely how a ...
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Is the magnetic field generated by a surface current always a vacuum field?
I am wondering about this since usually if there are no current distributions then we would obtain a vacuum field since $\nabla \times \mathbf{B} = \mu_0 \mathbf{j} = 0$ from Ampere's Law.
For the ...
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What is the intuitive reason why Ampere's law is incorrect?
I don't understand why Ampere's Law for magnetic fields is wrong. So initially, we got taught it as the following:
$$\vec\nabla\times\vec{B}=\mu_0\vec{J}$$
and this turns out to be wrong. I also ...
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Phase Difference between Electric and Magnetic Field in EM waves?
Is it possible to get a phase difference between an Electric Field ($E$) and a Magnetic Field ($M$) in an electromagnetic wave and why are they in phase?
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Can two different electric field exist for the same potential?
Take the electric field due to a electric dipole. If i do the line integral of this field from infinity to a point 'r' radially then \theta component of field has no role in this integral. So can two ...
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What is the solution of wave equation for a moving charge?
The electric field of a point charge at rest in an inertial frame is static in the frame. Any location outside the charge follows the Maxwell equations in the vacuum, and as a consequence the wave ...
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Confusion about transformers
let’s suppose we have an ideal transformer with 500 windings on the primary side and 5 windings on the secondary side.
The primary voltage is 230 V and the primary current 16 A.
So the equations tell ...
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Magnetic field outside a toroidal surface with a sheet current
The integral from of Ampere's law is $\int \mathbf{B}\cdot d\mathbf{l} = \mu_0 I$. Let's say our contour of integration $\mathbf{l}$ is a contour on the surface of a toroidal surface. Also, let the ...
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Understanding Maxwell's equations as opposed to high-school physics [closed]
I am currently learning university-level electromagnetism and have a problem arranging that with pre-existing school-knowledge. Unfortunately, the books I looked into so far simply introduce the ...
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Waveguide allowed modes | Transverse resonance condition
Consider a planar waveguide for example. The guiding index is $n_f$, and the cover and substrate indices are $n_c$ and $n_s$ respectively. Let the waveguide propagate along z, and have a height $h$ in ...
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Coupling of scattered TE mode to TM mode using vector Helmholtz equation
I solve a scattered field computation problem using the frequency domain Maxwell's/Helmholtz PDEs. Particularly, I'm studying the behavior of light, which is essentially a plane wave propagating in a ...
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Are Maxwell's equations ideal approximations? [closed]
So, I'm revising Maxwell's equations to understand how they work a little better, but Faraday's law seemed a little tricky to me for some reasons, so I came to the conclusion that Maxwell's equations ...
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Trying to understand how to apply Maxwell stress tensor to calculate forces
I'm struggling to understand how to use Maxwell's stress tensor to compute electromagnetic forces acting on surfaces. I'll take problem 8.7 from Griffths Introduction to Electrodynamics as an example.
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$B$ vs $H$, Ampere's Law, $\mu \ne \mu_0$, why is the field weaker outside a high permeability core?
Apologies in advance for the basic question - I haven't taken physics in a while.
In trying to understand an electromagnet from "first principles", I'm left wondering why magnetic field ...
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In the equation $B = ∇ \times A$. When $B =0$ it is said $A$ is not necessarily equal to zero. My question is how can $A$ exist without $B$?
How can one understand intuitively that without magnetic field, the potential can still exist?
Also $\nabla^2 \Phi=−\rho/\epsilon_0$. If charge density is $0$,$\Phi$ is non zero. How can potential ...
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Why does the surface integral over the $B$-field in a Stokesian loop tend to zero as the surface tends to zero (boundary conditions)?
I am confused by the standard argument used for deriving the boundary conditions at the interface of two media as told by Jackson, e.g. see here.
My question concerns the fact that Jackson says that ...
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Deriving macroscopic electromagnetic field energy density from microscopic field energy density
J.D.Jackson in his book classical electrodynamics derives macroscopic maxwell's equations by averaging microscopic maxwell's equations ,I wonder if something similar could be done to get the ...
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Problematic conversion of phasor form of field in electromagnetic wave equation
Edit (answer)
Although I do not have enough reputation to post a formal answer to the question, thanks to Mike Stone and Triatticus (see comments below), it became apparent that the issue was with ...
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Why should the shape of the surface affect the flux in Faraday's law?
Many 'proofs' of Faraday's law use the third of the Maxwell's equations $\nabla \times \bf {E} = -\dfrac {\partial B}{\partial \it t}$ to simplify the flux integral by first splitting it into two ...
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Faraday's law of induction: why there is no constant of proportionality?
I am learning the Maxwell's equations on my own, and I ran into some questions about Faraday's law $$\nabla \times \mathbf E = -\frac{\partial}{\partial t} \mathbf B.$$
As far as I know, Faraday ...
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Doubt regarding a possible mistake in Griffiths Electrodynamics
Griffiths, in section 7.3 Maxwell's Equations, says:
There’s another way to see that Ampère’s law is bound to fail for nonsteady
currents. Suppose we’re in the process of charging up a capacitor (Fig....
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Explanation of why Kinetic Energy Increases when Particle Reaches the End of the Magnetic Bottle?
I don't understand how to explain why kinetic energy increases using Faraday's Law as a charged particle reaches the end of a magnetic bottle.
I know that along the field line in the bottle, the ...
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What are the fundamental equations of quantum electrodynamics?
I hope this question hasn't already been asked, but I looked and couldn't find a question with a similar title.
It is my understanding that Maxwell's equations and the Lorentz force law form the ...
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Doubt regarding an assumption made in an example in Griffiths
In Griffiths' Introduction to Electrodynamics, example 14 in chapter 7, "Electrodynamics." He makes an assumption/claim that I don't understand the reason behind, or don't agree with.
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What is the magnetic field at the walls of a cavity with conducting walls and containing EM radiation?
If electromagnetic radiation is confined in a cavity with perfectly conducting walls, the total electric field at the walls (i.e., both its components tangential and normal to the walls) must vanish. ...
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Can an Electric and Magnetic fields be non-perpendicular? [duplicate]
Can an Electric field and a Magnetic field be non-perpendicular to each other$?$ If yes, can an electromagnetic wave pass through that region$?$
I think that yes, both can be non perpendicular to ...
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Why can't we "simply" quantize Maxwell's equations without a Lagrangian to create a quantum theory of electrodynamics?
Useful quantum field theories like quantum electrodynamics (QED) suffer from a litany of problems related to the fact that, at least in their usual Lagrangian formulation, interactions between the ...
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Infinite wire with alternating current and conducting half-plane
I'm kinda confused about the following. Suppose I have a harmonic current-density of
$$j=j_0 e^{i\omega t}=I_0 e^{i\omega t} \, \delta(x)\delta(y-h) \, e_z$$
parallel to the $z$-axis (at $x=0$ and $y=...
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What is the electric field around an inductor?
This question comes from this Walter Lewin video at 35:00 where he says "I'm going to confuse you even more" (and I suppose he somewhat succeeded). Walter Lewin claims there is an electric ...
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Electric field beyond its simple definition of force per unit charge
I read this from Div, Grad, Curl and All That:
The second reason for introducing the electrostatic field is more basic. It turns out that all classical electromagnetic theory can be codified in terms ...
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Magnetic field around a current carrying wire with changing magnitude of current
The magnetic field around a long, straight current carrying wire is given by $B = \frac{\mu i}{2\pi r}$ which comes from Maxwell's fourth equation,assuming that there is no changing electric flux as ...
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Why Euler equation in Ideal MHD is not identically zero?
In Ideal MHD, we assume the plasma to be force-free:
$$\vec{E} = - \frac{1}{c}\left(\vec{v}\times \vec{B}\right)$$
But the Euler equation of motion is written as:
$$\rho \frac{d\vec{u}}{dt} = \vec{j}\...
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Electrical and Electronic circuits simulation using Maxwell's equations
How can the Maxwell equations be used for developing exact mathematical model of electrical and electronic circuits?
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Choice of origin for Induced Electric Field due to Magnetic Field
Consider a region of a magnetic field varying uniformly with space such that change of magnetic field is along z-axis of a cylindrical coordinate system. Now, this will obviously induce an electric ...
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EMF Generated according to Faraday's Law
According to Faraday's Law, due to a relative movement between the current carrying loop and the magnetic field, an EMF is induced in the loop causing a current flow. However, according to Maxwell-...
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In Maxwell's equations concerning dielectric materials , does the electric field represent the external electric field or the net electric field?
Let's assume we have dielectric material and we apply an external electric field that acts on it (let's call it Ex ) . As a resault we get dipoles who in turn create another electric field (let's call ...
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How would you calculate (numerically) the shape of the electromagnetic waves emitted by an accelerating charge?
I am interested in trying to create an animation showing an accelerating charge emitting electromagnetic waves that is physically accurate. Writing the code is not what I am worried about, however, I ...
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Inconsistency with Bio-Savart Law and Ampere's law
In David J Griffiths textbook "Introduction to Electrodynamics", he states that the strength of the magnetic field a distance $s$ away from a steady current along a long wire is $$ B = μ_0(...
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Asking about a clarification of a rather strange notation of a Yee Grid used for discretizing Maxwell's Equations
The thesis I am following requires me to discuss a rather strange formulation of a Yee grid used to discretize Maxwell's equations in order to solve them numerically mentioned in a research paper. The ...
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Why are the electric and magnetic fields not determined by the first two Maxwell equations (understanding the Landau volume 2 book explanation)?
(The question is short but the context is long)
In Chapter 3 of Volume 2, Landau derives the equation of motion of a charged particle in an electromagnetic field as follows. Consider a charged ...
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How does displacement current relates to capacitive coupling?
Im reading make: electronics, and I have investigated a little bit about displacement current and how a change in electric flux can create a magnetic field in a vacuum. A can understand that, however ...
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Doubt regarding microscopic averaging of current density
We know that when averaging the velocity vector field of a current distribution over a particular volume, we get velocity fields that are slow varying over macroscopically small / infinitesimal ...
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Why is current density proportional to electric field strength, and why does this relation seem contradictory to Maxwell (and others)?
I've got three physics equations in mind which seem (to me) to contradict eachother, using a simple case of charge(s) in a static electric field. If someone can give an explanation as to what I'm ...
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A strange formulation of the Maxwell's equations
I am working on a project that involves Maxwell's equations, and the research paper that I am working on has formulated the equations in a strange and unfamiliar way. Here are the four equations (1)-(...
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Maxwell's divergence of electric fields
According to Maxwell's equations, if we take a circle close to a positive charge (such that the charge is not inside the circle), the divergence of the circle should be $0$ (because there is no ...
