What is Maxwell's equations: Definition and 245 Discussions
Maxwell's equations are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits.
The equations provide a mathematical model for electric, optical, and radio technologies, such as power generation, electric motors, wireless communication, lenses, radar etc. They describe how electric and magnetic fields are generated by charges, currents, and changes of the fields. The equations are named after the physicist and mathematician James Clerk Maxwell, who, in 1861 and 1862, published an early form of the equations that included the Lorentz force law. Maxwell first used the equations to propose that light is an electromagnetic phenomenon.
An important consequence of Maxwell's equations is that they demonstrate how fluctuating electric and magnetic fields propagate at a constant speed (c) in a vacuum. Known as electromagnetic radiation, these waves may occur at various wavelengths to produce a spectrum of light from radio waves to gamma rays.
The equations have two major variants. The microscopic equations have universal applicability but are unwieldy for common calculations. They relate the electric and magnetic fields to total charge and total current, including the complicated charges and currents in materials at the atomic scale. The macroscopic equations define two new auxiliary fields that describe the large-scale behaviour of matter without having to consider atomic scale charges and quantum phenomena like spins. However, their use requires experimentally determined parameters for a phenomenological description of the electromagnetic response of materials.
The term "Maxwell's equations" is often also used for equivalent alternative formulations. Versions of Maxwell's equations based on the electric and magnetic scalar potentials are preferred for explicitly solving the equations as a boundary value problem, analytical mechanics, or for use in quantum mechanics. The covariant formulation (on spacetime rather than space and time separately) makes the compatibility of Maxwell's equations with special relativity manifest. Maxwell's equations in curved spacetime, commonly used in high energy and gravitational physics, are compatible with general relativity. In fact, Albert Einstein developed special and general relativity to accommodate the invariant speed of light, a consequence of Maxwell's equations, with the principle that only relative movement has physical consequences.
The publication of the equations marked the unification of a theory for previously separately described phenomena: magnetism, electricity, light and associated radiation.
Since the mid-20th century, it has been understood that Maxwell's equations do not give an exact description of electromagnetic phenomena, but are instead a classical limit of the more precise theory of quantum electrodynamics.
Homework Statement
# Everyone knows that a time varying magnetic field produces an electric field and vice versa. But are the fields produced, static or dynamic? From Maxwell's equations(Faradays and Ampere's law), it seems like they are static. Moreover, Faraday's law of electromagnetic...
I'm new to these equations but let's see if I have the talk down.
1. The electric field surrounding a charge will go thru a surface and not come back into the surface. It's strength is proportional to the charge and inversely proportional to the perm of free space.
2. The magnetic field...
Could someone point me in the direction of the derviation of each of Maxwell's equations? I'm working on a presentation and can't find a good one that starts with primitive assumptions (i.e. to help explain to a non physics audience).
I was reading Michio Kaku's book Prallel Worlds recently and I believe I saw it say that Maxwell's equations for electricity and magnetism become the same for electricity and magnetism when monopoles are introduced.
My question is, if the equations become the same then why don't we say that...
Homework Statement
The question is simple, I want to obtain Eq.5 from Eq.2 using Eq.1.
Homework Equationshttp://img150.imageshack.us/img150/1108/question.png
The Attempt at a Solution
Can anybody explain how Eq.4 becomes Eq.5, what does happen to Re (Real part)?
Homework Statement
Show that any charge distribution in a conductor of conductivity σ and relative
permittivity κ vanishes in time as ρ = ρ0exp(−t/ζ) where ζ = κǫ0
σ
Homework Equations
Maxwell's equation
∇ · D = ρfree
equation of continuity for a free charge density
∇ · Jfree =...
In Feyman's lectures on physics, he said Maxwell's first 2 equations in electrostatics, namely curl E =0 and div E=rho/epsilon, is equivalent to Coulomb's law and superposition principle,
But for a particular charge distribution, we can always use Coulomb's law and superposition principle to...
Hello,
I was tempted to put this in the math section but it is more of a visualization problem though it is most likley due to my lack of understanding the divergence and curl operators fully.
I am comfortable with the closed loop integral of E dot dA and can visualize it as a solid closed...
Let respectively b = (b1, b2, b3) and e = (e1, e2, e3) denote the magnetic
and electric field in some medium. They are governed by Maxwell’s equations which look as follows:
(0.1) \partialte = curl b
(0.2) \partialtb = − curl e
(0.3) div e = 0
(0.4) div b = 0.
Show that each bi and each ei...
Homework Statement
What conditions need to be imposed on \vec{E}0, \vec{B}0, \vec{k} and ω to ensure the following equations solve Maxwell's equations in a region with permittivity ε and permeability µ, where the charge density and the current density vanish:
\vec{E} = Re{ \vec{E}0...
Maxwell's Equations say about the velocity of electromagnetic wave..Does Maxwell's equations also say about path of the electromagnetic wave i.e. light?
I want to know how to find the path of light from Maxwell's equations? Or it says only about velocity?
One more question, what is the path...
I was reading "understanding light'' on this forum.
If one wants to know what a photon is one first must ask, does one want to know what the physics is or does one want to know what the mathematics says.
A physicist might ask a the question, "Are Maxwell's equations (the E,B fields) a...
Basic electrostatics (as I've seen it presented) usually starts off with an implicit \mathbf{F} = q q_2 \hat{\mathbf{r}}/r^2 = q \mathbf{E} definition of the electric field. Then with a limiting volume argument, you can then show that this can be expressed div \mathbf{E} = \rho. Eventually one...
Easy question for those who know, I expect. It would help me understand though.
Generally, wherever I look for information the equation
curl E = - dB/dt
is given, but in some areas I see the equation
curl E(r,t) = j*omega*u0*H(r,t)
where j is the imaginary unit, omega is angular...
One author states that "the usual Maxwell field is the quantum wave function for a single photon" - see http://arxiv.org/ftp/quant-ph/papers/0604/0604169.pdf
Is it correct that a single photon can be described using Maxwell's equations - or do the Maxwell equations only describe the behaviour...
I've seen two references to magnetic charge density as something that Dirac said would explain charge quantization. The first is in Schwartz's "Principles of Electrodyanamics" (Dover) where the author comments how it is unaesthetic that the two maxwell's equations aren't symmetric in form...
Let's say you're in a very fast car that can accelerate from zero to, eventually, 0.7c. I understand that as the car moves faster and faster, the driver will observe the light that hits him in the face to be of higher and higher frequency. This seems consistent with things becoming narrower in...
Homework Statement
It is often said that Maxwell's equations in differential form hold in special relativity while Maxwell's equations in integral form don't hold. Consider one of equations:
\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}} {\partial t}
\oint_{\partial S} \mathbf{E}...
It is often said that Maxwell's equations in differential form hold in special relativity while Maxwell's equations in integral form don't hold. Consider one of equations:
\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}} {\partial t}
\oint_{\partial S} \mathbf{E} \cdot...
Maxwell's equations give that the electric and magnetic fields in E-M radiation are orthogonal. This is a classic equation, but can it be related to the orthogonality of, for example, the momentum and position operators which lead to non-commutivity?
[SOLVED] invariance of maxwell's equations under Gauge transformation
Homework Statement
Show that the source-free Maxwell equations \partial_{\mu} F^{\mu\nu}=0 are left invariant under the local gauge transformation
A_{\mu}(x^{\nu})\rightarrow...
Homework Statement
http://en.wikipedia.org/wiki/Maxwell_relations
I am confused about the subscripts next to the partial derivatives.
\left(\frac{\partial T}{\partial V}\right)_S =
-\left(\frac{\partial p}{\partial S}\right)_V\qquad=
\frac{\partial^2 U }{\partial S \partial V}
What does the...
I am having trouble going about proving the Lorentz invariance and non-Galilean invariance of Maxwell's equations. Can someone help me find a simple way to do it? I've looked online and in textbooks, but they hardly give any explicit examples.
I'm not sure if this should go here, or in electrodynamics, or in relativity, but never mind. I'm given to understand that Maxwell's equations are completely compatible with the theory of relativity, and apply over all distance scales. I've also heard of Kaluza-Klein theories in which adding a...
I've put quick intros to these subjects on my web site, and I'd like to invite readers to comment. The goal of the tutorials is to give as quick an introduction as possible with the miminum of unnecessary technicalities, and yet to get to the essence of the matter . No doubt improvment is...
Hi,
I'm just someone trying to learn a bit more about quantum. I was wondering
what the relationship between maxwell's equations and quantum electrodynamics is? Are they compatible? Are maxwell's equations for solving macroscopic problems only? How
do you determine the E field...
I have a question regarding two electric lines running parallel to each other with their current running in opposite direction. Under this set up the electric field points up vertically on the page and the magnetic field points out from the page. I am to show that Maxwell's equations reduce to...
Is it possible to derive Faraday's Law from the other three Maxwell equations plus the conservation of charge? If so, how?
Any help would be greatly appreciated.
Thank You in Advance.
The skepticism thread reminded me of a question I had for the professionals here.
A lot of Electrodynamics (especially the idea of displacement current) was developed by Maxwell with the idea of Ether in mind.
I'm not trying to argue that the ether-as-we-know-it actually exists, but the...
Is the fact that there could be no E-field inside a conductor purely experimental? I don't see any way to apply Maxwell's equations to prove this fact.
maxwells third equations states that the curl(electric field)=-rate of change of magnetic field intensity... does it have any other physical significance other than being derived from faradays laws of electromagnetic induction... does curl(electric field) indicate the curling or rotational...
Folks,
I believe the direction of the circulation in the curl equations must always be considered counterclockwise (positive), because of Stokes' theorem and the right-hand rule. Right? (I'm asking because my books do not have a direction specified in the circulation integral) Thanks.
Maxwell's Equations:
\nabla \cdot D= \rho
\nabla \cdot B=0
\nabla \times E=- \partial B/ \partial t
\nabla \times H=J+ \partial D/ \partial t
Together with the continuity eq:
\nabla \cdot J=- \partial \rho / \partial t
There are 9 scalar equations and 16 scalar unknowns (B, E, D, H, J...
Here are some thoughts; if you have a different opinion, I'd be glad to hear it.
In the real world, on a small enough scale, linear charge distribution and surface charge distributions do not exist. It all comes down to \rho. Same for the currents; there are only current densities \vec{J}. So...
Right or wrong? Specifically, an equation is said to be Galilean invariant if a substitution
x \rightarrow x \pm v_x t
y \rightarrow y \pm v_y t
z \rightarrow z \pm v_z t
t \rightarrow t
doesn't change the equation.
If right, would simply showing that
x \rightarrow x \pm vt
y...
Are Maxwell's equations deterministic in the sense that e.g. if given free space with H and E defined for any point at time t0, then Maxwell's equations are sufficient to determine H and E for any t>t0?
I'm trying to understand the physical meaning of Maxwell's Equation, but I'm confused about what generates what. According to Gauss's Law, electric charge placed somewhere generates electric flux, whereas Gauss's Law for Magnetism says that charge itself doesn't generate magnetic field...
hey i need help explaining this... I am really lost...
What is the further condition on the charges and the currents, which is necessary for the Maxwell Equations? Explain how it relates to the existence of the displacement current.
I want to make sure that I understand this good.
Given E and B are possible in a region of free space (J=0) only if \triangledown \times E=0 and \triangledown \cdot B = 0
I've never understood how the aether was dispensed with. It is said that Maxwell's equations don't require it. If that is the case, then where do the x, y and z axes come from if not from an aether.
Having some problems with my Electromag Unit again.
Heres the questions I'm having problems with, any help would be appreciated
1
For plane electromagnetic waves in a homogeneous, linear, uncharged non conductor
Formulate the Maxwell equations for the electromagnetic fields E and B...
the final equation
∇XB(x) = μ0j(x)
But this means that the curl of the magnetic field at any point is proportional to the current density at that point.
But take the case of a long straight wire carrying current.
The magnetic field surrounding the wire is circular and...