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.

Filter by
Sorted by
Tagged with
0
votes
1answer
78 views

Why visible light satisfies Maxwell equations? [duplicate]

As it is described in standard textbooks I looked at, the Maxwell equations were first established for electromagnetic fields created by electric currents. Then it is stated that it was discovered ...
1
vote
2answers
147 views

Colors of the Earth from space, an “average” of particular emitters?

When we're say about 100 km above Earth's ground and look down to it and see the Amazonian region as green, is this green color a sort of "average" of greens from trees from that forest or is the "...
0
votes
1answer
18 views

Magnetic induction by changing permeability of a uniform magnetic field?

As far as I know, magnetic fields are created by either magnet or running current, which both can be changed by changing the permeability of the medium and thus change the magnetic flux through the ...
2
votes
1answer
49 views

How to remember Maxwell equation in Gaussian units?

I know Maxwell relation in MKS unit $$\begin{cases}\nabla\times E=-\frac{\partial B}{\partial t},\\ \nabla \times B = \mu_0 \epsilon_0 \frac{\partial E}{\partial t} + \mu_0J,\\ \nabla\cdot E = \frac{\...
1
vote
1answer
41 views

Help on electromagnetic tensor equations in Einstein's original General Relativity papers

Studying Einstein's original Die Grundlage der allgemeinen Relativitätstheorie published in 1916's Annalen Der Physik, I came across Equations 66) and 66a) regarding the electromagnetic contribution ...
0
votes
4answers
49 views

Maxwell Equation: Definition of Invariance

Knowing Lorentz Transformation and knowing the differential formulation of Maxwell Equations: Precisely, what is the meaning of the statement: "Maxwell equation are invariant under Lorentz ...
3
votes
1answer
238 views

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 ...
0
votes
0answers
32 views

When all does Ampere's circuital law FAIL to work? What are the inconsistencies that arise when considering conducting wires of finite length?

Does Ampere's law hold when trying to compute the line integral around a closed-loop; if the current-carrying wire is of finite length? It is obvious that the integral values change with changing the ...
2
votes
1answer
41 views

Maxwell equations for Transverse Electro-Magnetic (TEM) modes

I'm confused after reading of a book in which the author proves mathematically that electric and magnetic fields are orthogonal to each other (for TEM mode). I'm calculating it in the same way, ...
0
votes
1answer
47 views

Energy conservation and magnetic field around wire

A current-carrying wire has a magnetic field around it according to the Maxwell equations (Oersted's law/Biot–Savart law). When this is AC current, then also the magnetic field oscillates. The energy ...
2
votes
1answer
58 views

How to be sure that a law is invariant under Lorentz's Transformation?

For starters let's talk about Maxwell's Equations; we know that Maxwell's Equations are invariant under Lorentz's Transformation, after all this is why all the relativity business got started. To ...
0
votes
2answers
44 views

Divergence of the magnetic field $H$

it is known (although I have not found much information about it on books and websites) that, while the divergence of $B$ is always zero ($\nabla\cdot B = 0$), we cannot say the same about $H$: the ...
0
votes
0answers
28 views

Radiated power from a straight conducting wire

Consider an infinite long straight conducting wire with an oscillating current inside. The current is assumed to be uniform over the cross-section of the wire. The resistance per unit length is given ...
3
votes
3answers
126 views

Simple derivation of the Maxwell's equations from the Electromagnetic Tensor

Lets start by considering the electromagnetic tensor $F^{\mu \nu}$: $$F^{\mu \nu}=\begin{bmatrix}0 & -E_x/c & -E_y/c & -E_z/c \\ E_x/c & 0 & -B_z & B_y \\ E_y/c & B_z & ...
2
votes
2answers
73 views

What would Maxwell's equations look like if photons had only a single helicity?

There are two types of photons, positive and negative helicity photons. What would Maxwell's equations look like say if there were only negative helicity photons? It would be interesting to see this ...
0
votes
1answer
78 views

Electromagnetic field confined inside a closed optical resonator

I am currently studying Maxwell's equations. Out of interest, I was reading the introduction to the textbook The Quantum Theory of Light, third edition, by Louden. When discussing the photon, the ...
1
vote
2answers
64 views

Magnetic Vector Potential and Ampere's law

If I can set the divergence of $A$ as whatever I want, won't it affect Ampere's law: $$\nabla ^{2}A=-\mu_0J$$ I could set it to zero and that would mean $\nabla 0=0=J$ I have understood the proof ...
0
votes
1answer
13 views

Why is the value of volume charge density $ρ$ zero in lossy medium?

Given is the page of a book which I was studying. I was trying to study the derivation of the wave equation in a lossy medium. As I have underlined a sentence that says, "most of the case in ...
29
votes
6answers
3k views

How can we conclude from Maxwell's wave equation that the speed of light is the same regardless of the state of motion of the observers?

I am reading a book titled "Relativity Demystified --- A self-teaching guide by David McMahon". He explains the derivation of electromagnetic wave equation. $$ \nabla^2 \, \begin{cases}\vec{...
25
votes
6answers
5k views

What is the complete proof that the speed of light in vacuum is constant in relativistic mechanics?

I study maths in uni and we have a course about relativity. In the main principles I've read that the speed of light is invariant since we can calculate it from the Maxwell equations. My problem ...
3
votes
1answer
633 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. ...
0
votes
1answer
38 views

Do the electric field and magnetic field derived from the Lienard-Wiechert potentials satisfy Gauss's law?

I've already got the electric fields and magnetic fields derived from the Lienard-Wiechert potentials: $${\bf E}=\frac{q}{4\pi\epsilon_0}\frac{R}{(\bf R\cdot u)^3}[(c^2-v^2){\bf u}+\bf R\times(u\...
12
votes
2answers
295 views

How to prove that both $\mu_0$ and $\epsilon_0$ don't depend on any frame of references? [duplicate]

Based on my previous question here, lets us step back a little bit. The speed of light $c=1/\sqrt{\mu_0\epsilon_0}$ is assumed as a value that does not depend on the observer because it is just a ...
1
vote
2answers
47 views

Interpretation of Gauss's theorem applied to Maxwell's equations: $\dfrac{d}{dt} \int \rho \ dV + \int \mathbf{j} \cdot \mathbf{n} \ dS = 0$

Using Maxwell's equations and Gauss's theorem, we get $$\dfrac{d}{dt} \int \rho \ dV + \int \mathbf{j} \cdot \mathbf{n} \ dS = 0,$$ where $\rho$ is the electric charge density and $\mathbf{j}$ is the ...
0
votes
1answer
289 views

Does displacement current occur in an inductor?

We have learned in school that displacement current comes about due to a change in electric field flux per time in a capacitor (Ampere-Maxwell Law). Does the same displacement current come about in an ...
5
votes
1answer
171 views

Electric Field in a uniform time-varying Magnetic field

Suppose a homogenous Magnetic Field $\vec{B}$ in vacuum that varies with time, but always points in the z-direction. This induces a curl in the Electric Field $\vec{\nabla} \times \vec{E} = -\frac{\...
0
votes
1answer
82 views

What is the value of $\vec{\nabla}\cdot\vec{E}$ inside a conductor?

I thought that since a conductor as a whole, an electrically neutral medium, $\vec{\nabla}\cdot\vec{E}=0$ inside a conductor. But while reading Ashcroft and Mermin's Solid state physics, I found out ...
1
vote
0answers
24 views

Deriving solenoid inductance using Faraday's Law

The inductance $L$ of a long solenoid of length $\ell$, cross-section area $A$, and turns per length $n$ is given by: $$ L = \mu_0 n^2 \ell A $$ where $\mu_0$ is the magnetic constant. I am currently ...
0
votes
0answers
51 views

The Lagrangian density of electromagnetism, expressed in geometric algebra such that $\nabla \mathbf{F}=0$ is the equation of motion?

Geometric algebra admits a very short and sweet definition of Maxwell's laws of electromagnetism: $$ \nabla \mathbf{F}=0 $$ where $$ \mathbf{F}=\mathbf{E}+i\mathbf{B} $$ and where $$ \nabla \mathbf{F}=...
-3
votes
1answer
22 views

Current flowing through a closed conducting loop in a time-dependent magnetic field

Consider a closed conducting loop (e.g., a circular wire) in a time-dependent magnetic field. Assume that the resistance per unit length of the wire is $r$ and that its total length is $L$. If the ...
0
votes
3answers
61 views

Are two interacting electrons in an isolated system?

From your point of view, two electrons are initially at rest. In time, they repel one another, leading to an increase in both of their kinetic energies. If they are isolated from the rest of the ...
0
votes
0answers
27 views

How do the time reversed retarded solutions to Maxwell's equations maintain T-symmetry?

Maxwell's equations are T-symmetrical in that they remain invariant to a change in the sign of $dt$ if the sign of $B$ and $J$ are also reversed. Hence the corresponding time reversed solution is ...
1
vote
1answer
210 views

Accelerating charges giving rise to electromagnetic waves from Maxwell's laws?

For a long time I have been wondering how accelerating charges give rise to electromagnetic radiation. I have now seen 'graphical' reasoning in terms of requiring continuity of electric field lines, ...
0
votes
1answer
45 views

Covariant formulation of electrodynamics homogenous Maxwell eq

It is know that $$\epsilon{^\mu} {^\nu} {^\rho} {^\sigma} \partial_{\nu} F_{\rho} {_\sigma} = 0$$ How can one deduce from this equation that $$ \partial_{\mu}F_{\nu} {_\lambda} + \partial_{\lambda}F_{\...
0
votes
2answers
81 views

A consideration on the last Maxwell equations: doubt

If I consider the last equation of Maxwell, $$\oint_\gamma \mathbf{B}\cdot d\boldsymbol{\ell}=\mu_0\left(I_C+\epsilon_0\frac{d\Phi(\mathbf{E})}{dt}\right) \tag 1$$ where $I_C$ indicates the conduction ...
0
votes
1answer
38 views

Ohm's Law and induced fields

Consider a simple circuit: A battery and a resistor, where the resistor is connected between points A and B. We then have: $$\int_{a}^{b}-\vec{E}.\vec{dl}= iR$$ Will the same expression hold if $\vec{...
0
votes
0answers
25 views

Can stable magnetic field induce current?

I read about a experiment conducted in 1933 by W.Meissner that follows: Metal was put in constant magnetic field then been cooled down in order to enter superconductivity state. Then researchers ...
-1
votes
0answers
27 views

Continuity equation derivation from Lorenz Gauge

How can deduce the Electromagnetic Continuity Equation from the Lorenz gauge condition?
1
vote
1answer
68 views

Covariant form of Maxwell Equations in curved spacetime

The real world doesn't care about our choice of coordinate to describe nature. Maxwell equations in vectorial form are written with respect to an Inertial frame of reference as: \begin{align} \vec\...
1
vote
0answers
47 views

Formal definition of charge density and current sources in classical electromagnetism

Charge density and current sources are fundamental to classical electromagnetism and appear in Maxwell's equations and everything that comes after. They are intuitive, charge density is a scalar field ...
0
votes
0answers
17 views

Is there a Gaussian Beam Solution to Maxwell's Equations in 2 dimensions?

I know the typical treatment of "Gaussian beams" defines the beam to be radially Gaussian (or if the beam is propagating in the z-direction, Gaussian in both x and y). I believe this comes ...
15
votes
4answers
11k views

Are the Maxwell's equations enough to derive the law of Coulomb?

Are the 8 Maxwell's equations enough to derive the formula for the electromagnetic field created by a stationary point charge, which is the same as the law of Coulomb $$ F~=~k_e \frac{q_1q_2}{r^2}~? ...
2
votes
1answer
191 views

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?
5
votes
0answers
195 views

Solving Maxwell equations on curved spacetime

I have difficulties to understand how to solve the Maxwell equations on curved spacetime. I want to solve the equations in the weak regime $g_{\mu\nu}=\eta_{\mu\nu}+h{\mu\nu},~ h_{\mu\nu}\ll 1$ ...
1
vote
2answers
43 views

Ampére-Maxwell's law in the absence of sources

My question: If I have the Ampére-Maxwell law $$\oint_\gamma \mathbf{B}\cdot d\mathbf{l}=\mu_0\left(I_{\text{enc.}}+\epsilon_0\frac{d\Phi_S(\mathbf{E})}{dt}\right) \tag 1$$ where $I_{\text{enc.}}$ is ...
8
votes
4answers
2k views

Misunderstanding of the magnetic field

We know that any field can be constructed using its divergence and rotational. The divergence of the magnetic field is always zero. However its rotational is proportional to the current density. ...
1
vote
0answers
60 views

Conceptual Question on Maxwell's 3rd Equation in Integral Form

$$ \oint_C \vec{E} \cdot d \vec{l} = -\frac{d}{dt} \oint_S \vec{B} \cdot d \vec{A} $$ where $S$ is a surface and $C$ is its boundary. Why is there no negative sign in front of the left-hand side? I ...
0
votes
2answers
565 views

Why will a magnetic field cause a ring to hover?

I was attempting a homework question which went like this: Where the crosses indicate a magnetic field in that rectangular region pointed into the screen, and we're asked which of the rings would ...
1
vote
1answer
62 views

if an oscilating LC circuit without antenna could produce electromagnetic waves since there is changing electromagnetic field?

Just shown as the above picture, if the right part removed, would electromagnetic waves still be produced near the inductor and what the changing electromanetic field are in this situation? I used to ...
0
votes
1answer
14 views

Regarding Faraday's law as written in Pozar's Microwave Engineering

We can clearly see in page $6$ of Pozar's Microwave Engineering Faraday's law written under this form $$\nabla \times \bar{\mathcal{E}}= \frac{\partial \bar{\mathcal{B}}}{\partial t}-\bar{\mathcal{...

1
2 3 4 5
20