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.

Filter by
Sorted by
Tagged with
0
votes
0answers
60 views

Why must we reapply 0-divergence constraints in extracting valid solutions of free-space Maxwell's equations from solutions to Helmholtz equations?

--------Definitions---------- For reference: Maxwell's equations as I understand them plus definitions of $\vec{B}$ and $\vec{D}$ \begin{align} \textrm{Maxwell's curl of }\vec{E} &: \nabla\times\...
1
vote
0answers
19 views

Observing Electric and Magnetic Field Lines Around a Current Carrying Wire

Referring to the idea of using grass seeds for observing electric field near current carrying wires from the following article, https://www.ifi.unicamp.br/~assis/Found-Phys-V29-p729-753(1999).pdf I ...
1
vote
1answer
75 views

Changing Electric Field in a Capacitor

A capacitor has circular plates with radius $R$ and is being charged by a constant current $I$. The electric field $E$ between the plates is increasing, so the energy density is also increasing. This ...
0
votes
3answers
222 views

Missing Lenz's Law in Maxwell's Equation?

I am wondering if the Lenz's law is missing in the fourth equation of the Maxwell's equation with regards to the negative sign that exists in the Faraday's law (3rd equation). $$\begin{align} \nabla\...
0
votes
1answer
53 views

Magnetic field of a thick conductor

as explained here, the magnetix field generated by a thick conductor is equal to: Inside the wire: $$B = \frac{\mu\cdot I}{2 \cdot \pi \cdot R^2} r$$ It grows linearly with the radius $r$ because ...
0
votes
1answer
117 views

How to choose the surface for the magnetic flux in case of an open circuit (Faraday Law)?

I have a doubt about a topic about which I did not found many informations. Each time I've applied Faraday Law ($EMF = -\frac{d\phi(B)}{dt}$), such magnetic field crossed a loop conductor (for ...
4
votes
3answers
185 views

Line Integral of electric field through the nucleus

In the case of electrostatics, We know that for electric field $\mathbf{E}$, $$\nabla \times \mathbf{E}=0$$ which in the line with the integral form $$\oint \mathbf{E}\cdot d\mathbf{l}=0$$ Now Can I ...
0
votes
3answers
72 views

Can you have electric current without a circuit?

I'm trying to understand Maxwell's 4th equation, which is $$ \bigtriangledown \times B = \mu_0j + \mu_0\epsilon_0\frac{\partial E}{\partial t} $$ I understand that $\bigtriangledown \times B$ ...
17
votes
1answer
524 views

Was Maxwell's displacement current the only way to fix up Ampère's Law?

It is well-known that Maxwell added the displacement current term to Ampère's Law to make electrodynamics whole. As it is taught in the modern context (I am currently reading Griffiths's text, ...
0
votes
2answers
136 views

Why is the magnetic field dot producted in the integral version of Ampere's circuital law?

you know amperes circuital law? Well in that equation there's a dot product between the magnetic field B and a length element dl...why is that? I mean its not like the magnetic field can be at an ...
1
vote
1answer
104 views

Is there a more satisfactory answer than just saying that the manifold of special relativity is the $\mathbb R^4$/some set of "events"?

I'm an undergraduate who visited a course on differential manifolds and now I have the task to reformulate the maxwell equations in terms of differential forms. The most obvious question that arises ...
1
vote
0answers
46 views

How to apply Maxwell's equations to electromagnetic waves? [closed]

You know how antennas work and create EM waves...They oscillate charges which create EM waves Well I'm not satisfied with that explanation so it would be great if you could use maxwells equation to ...
1
vote
1answer
160 views

Faraday's law, Lorentz force law and $3^{\rm rd}$ Maxwell Equation

I see a very serious conceptual problem in the way these three equations are related to one another, as it is usually shown in electrodynamics textbooks. Usually one starts with experimental evidence: ...
0
votes
1answer
62 views

Validity of Ampere circuital law

I read that the line integral in Ampere circuital law is applicable for a piece-wise continuous curve (loop). My question is whether the law is valid only for planar loops or does it hold good even ...
0
votes
1answer
81 views

Curl is invariant PARADOX

1 charge $Q$ is moving with velocity $v$, to a lab observer is has a magnetic field, and an electric field with curl due to the changing magnetic field around it But from the charges perspective, ...
0
votes
1answer
84 views

Raising and lowering indices

I read multiple sources about raising and lowering indices and Einstein summary notation but am having problems doing it. Here is an example. I am trying to derive Maxwell's inhomogeneous equations in ...
1
vote
1answer
21 views

Maxwell equations in non-transparent media

There are many examples of media non-transparent for the light of visible spectrum. What does it mean in terms of the Maxwell equations in such media? More precisely what does it mean for dielectric ...
0
votes
1answer
323 views

What does it mean to decouple Maxwell's equations with the curl operator?

I'm reading Introduction to Electrodynamics 4th Edition by D.J. Griffiths where after listing the Maxwell equations in empty space (i.e. $\rho = 0, \mathbf{J} = 0, \mu = \mu_0, \epsilon = \epsilon_o$) ...
1
vote
0answers
77 views

Paradox of radiation of charged particles in a gravitational field

"Paradox of radiation of charged particles in a gravitational field" - Wikipedia ( Paper by a guy I forget the same of) On wikipedia (reliable ikr), there is a paradox occuring between ...
1
vote
0answers
108 views

Physical interpretation for Helmholtz's theorem

Maxwell's four equations are enough to specify the fields (electric and magnetic) in a region, once you specified the charge density and current density. Maxwell's four equations basically give you ...
1
vote
1answer
41 views

Magnetic vector potential from harmonic electric field [closed]

Let's say I have a spatially constant but time-varying electric field in vacuum of the form $$\textbf{E} = E_0 e^{i \, \omega t} \, \hat{x}$$ that describes some E-M wave. What is the magnetic vector ...
2
votes
1answer
84 views

Poynting vector for a whole spectrum

Considering an electric and magnetic plane wave, $E(t)=E_p(\omega)e^{i\omega t}$ and $H(t)=H_p(\omega)e^{i\omega t}$, where $E_p(\omega)$ and $H_p(\omega)$ represent the frequency dependent peak ...
1
vote
1answer
74 views

Misunderstanding about induced $\mathbf{E}$ field direction

Imagine a region in space that has a changing magnetic field through it. Two imaginary closed loops are "placed" in that region such that the two loops intersect with each other at different ...
0
votes
1answer
56 views

Simplified forms of Maxwell's curl equations for special case of $\vec{J}$

From Maxwell's curl equations, obtain the particular differential equations for the case of $\vec{J} = J_z(y,t)\hat{z}$. The solution provided for this question shows something like this: $\begin{...
0
votes
4answers
144 views

Finiteness of speed of light

The postulates of the special theory of relativity say that there is a limiting speed - the speed of light. But this is a postulate. There are experiments confirming that the speed of light is ...
0
votes
4answers
165 views

Time varying Ampère's law

Ampère's law is stated as $$\nabla\times\vec{B}=\mu_0\vec{J}.$$ I am told this only works in steady currents and not with time varying ones. However Maxwell's addition of $+ \mu_0\varepsilon_0 \frac{\...
0
votes
0answers
120 views

What is the magnetic field of a uniform steady volume current?

Consider a slab of a material of finite, non-zero conductivity, infinite in the $y$ and $z$ directions but sandwiched by two metal plates at $x=x_{1}$ and $x=x_{2}$, say i.e. we are essentially ...
0
votes
1answer
60 views

If a cosine wave satisfies Maxwell's equations then how does a sine satisfy the equations as well?

Say the real part of $$\tilde{\mathbf{E}}(z, t)=\tilde{\mathbf{E}}_{0} e^{i(k z-\omega t)}$$ satisfies all Maxwell's equations. Then how can we say the imaginary part satisfies the equations as well? ...
13
votes
6answers
454 views

Is the Green function of electromagnetism a scalar or a tensor?

When I check classical electromagnetism books Maxwell equations \begin{equation} \Box A^\nu (x)=\frac{4\pi}{c}j^\nu (x) \end{equation} can be solved using a scalar Green function $G(x,x')$ \begin{...
0
votes
0answers
21 views

Condition on 4-potential to give left-circular polarized light?

To get a collection of left-circularly polarised photons, do we put a condition on the 4-potential $A_\mu$? Or is it a condition on the wavefunction $\Psi[A]$ to say that the amplitude for right-...
1
vote
1answer
85 views

Induced EMF in open loop

Take a wire that doesn't form a closed loop, moving at velocity $v$ perpendicular to a constant magnetic field. In the frame of reference to a stationary person the induced emf caused by the magnetic ...
1
vote
0answers
19 views

Can an induced EMF be generated from a loop kept in an constant electric field?

I am wondering whether the following set-up can be used to generate an induced EMF. Since the electric field between the parallel-plates is in such a direction that the positive charge accumulate at ...
1
vote
1answer
115 views

Full capacitance matrix symmetry property - how to derive it?

In this excellent article, the author, in sec. 1.4 describes the full capacitance matrix properties. He writes: The capacitance matrix is symmetric: $C_{ij} = C_{ji}$. This is related to the fact ...
0
votes
1answer
99 views

Gauss law for moving charges

since gauss law for electricity is derived from the divergence theorem and couloumbs law. why can it be assumed it is valid for moving charges as coulombs law is only valid for static charges since it ...
1
vote
1answer
115 views

Why does $\epsilon_{\mu\nu\rho\sigma}\partial^{\rho}\partial^\mu A^\nu-\epsilon_{\mu\nu\rho\sigma}\partial^{\rho}\partial^\nu A^\mu=0$?

The tensor $F^{\mu\nu}$ is defined as $\partial^\mu A^\nu-\partial^\nu A^\mu$. Why is the equation $$\epsilon_{\mu\nu\rho\sigma}\partial^{\rho} F^{\mu\nu} = 0$$ identically satisfied by $F^{\mu\nu}=\...
0
votes
0answers
29 views

Magnetic flux as a function of distance experiment

For my electrical engineering senior design I created an experiment to test magnetic flux (more voltage) increase from a material in a coil of wire. There is a large sending coil with A.C. voltage and ...
2
votes
3answers
156 views

How electromagnetic wave was related to visible light? [closed]

The presentation I see in the textbooks goes something like this, Maxwell realized changing electric fields produce changing magnetic field and vice versa. Therefore, at least intuitively, one can ...
1
vote
1answer
53 views

Can we use the method of image charges when the source is time dependent?

Let's say we have a grounded conducting plane at $z=0$ and a charge moving above it with some position $\vec{r}_q(t)$ and velocity $\vec{v}_q(t)$. I know that in the particular case when the velocity ...
1
vote
1answer
148 views

Is it possible to find potential difference between two point in case of induced EMF created by a time-varying magnetic field?

Q: There is a uniform time varying magnetic field in a circular region as shown in the figure. find out the potential difference across 2 point along an elliptical path as shown in figure. As far as ...
0
votes
1answer
110 views

How to find potential difference between two points in a loop in case of motional emf? [closed]

Given below is a question in my physics textbook. A rectangular frame of wire abcd has dimensions 32 cm×8.0 cm and a total resistance of 2.0 Ω. It is pulled out of a magnetic field B=0.02 T by ...
2
votes
0answers
38 views

Lossy electromagnetic wave and reactive power

Consider an electromagnetic wave in a lossy medium. This medium has a complex permittivity $\varepsilon_r=\varepsilon_r' +j \varepsilon_r''$ and a wave impedance given by $$Z=\frac{E}{H}=\sqrt{\frac{\...
1
vote
0answers
69 views

From geodesic motion of photons to Maxwell equations in curved spacetime

In curved spacetime, 1.) a photon is supposed to move along a null-geodesic, i.e., a trajectory $x^{\mu} = x^{\mu}(\lambda)$ satisfying $$\frac{d^{2}x^{\rho}}{d\lambda^2} + \Gamma^{\rho}{}_{\mu\nu}\...
1
vote
1answer
301 views

How does one take the Divergence of a Tensor?

I’m trying to understand the derivation of the Maxwell stress tensor in Heald and Marion. Im confused how they go from 4.101 to 4.102 in the image above. I can't seem to see how 4.101 is the ...
1
vote
0answers
64 views

Maxwell solution in differential forms

Maxwell equation's in differential form: $dE = 0 \ and\ \ (\ast d \ast)E = p$ in static situation. Where $E \in \Omega^1(U)$, $p \in \Omega^0(U)$, $\ast$ is hodge star operator, $U= \mathbb{R}^3$ ...
1
vote
1answer
116 views

General covariance of the Maxwell equations in 4-tensor form

Are the Maxwell equations written with the derivatives of the EM field strength tensor not generally covariant? I can't seem to prove that is. The Maxwell equations in 4-tensor form: $\partial_{\mu}F_{...
1
vote
1answer
64 views

Interaction of charges in gauge

Let's consider Maxwell theory: $$ \mathcal{L} = -F_{\mu\nu}F^{\mu\nu} = 2 A_\mu (\Box \eta^{\mu\nu} - \partial^\mu \partial^\nu) A_\nu $$ Is it possible to fix gauge $A_0 = 0 $ and concider ...
2
votes
1answer
108 views

Wilson line and external source

Let's consider free Maxwell theory: $$ L = -\frac{1}{4g^2} F^{\mu\nu}F_{\mu\nu} $$ As I understand, one can describe external particles with help of Wilson lines: $$ W(q,l) = e^{iq\int_l dx^\mu A_\mu} ...
1
vote
0answers
76 views

Using the electromagnetic field tensor to derive Maxwell-Faraday equation

I'm currently going through Byron and Fuller, and problem 1.13 is a problem about deriving the electromagnetic field tensor. The field tensor we derive is the complex version: $$F = \begin{bmatrix} 0 ...
0
votes
1answer
20 views

Electric lines of force: direction

fairly simple question here: how do we know that the lines of electric force move into a negative charge and out of a positive charge? Does this have physical significance, is it detectable in an ...
0
votes
2answers
85 views

How exactly do electromagnetic fields interact with matter?

The four equations of Maxwell tell us how electromagnetic fields evolve in time. Suppose we wanted to describe bulk phenomena... say resistivity for instance, then could we derive them starting from ...

1 2 3
4
5
24