The four fundamental fundamental equations of electromagnetism.

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Do Maxwell's Equations overdetermine the electric and magnetic fields?

Maxwell's equations specify two vector and two scalar (differential) equations. That implies 8 components in the equations. But between vector fields $\vec{E}=(E_x,E_y,E_z)$ and ...
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9answers
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Can Maxwell's equations be derived from Coulomb's Law and Special Relativity?

As an exercise I sat down and derived the magnetic field produced by moving charges for a few contrived situations. I started out with Coulomb's Law and Special Relativity. For example, I derived the ...
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4answers
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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? If I am not mistaken, due to ...
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4answers
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Displacement Current - How to think of it?

What is a good way to think of the displacement current? Maxwell imagined it as being movements in the aether, small changed of electric field producing magnetic field. I don't even understand that ...
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Why did Feynman's thesis almost work?

A bit of background helps frame this question. The question itself is in the last sentence. For his PhD thesis, Richard Feynman and his thesis adviser John Archibald Wheeler devised an astonishingly ...
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4answers
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Can the Lorentz force expression be derived from Maxwell's equations?

The electromagnetic force on a charge $e$ is $$F=e(E+v\times B),$$ the Lorentz force. But, is this a separate assumption added to the full Maxwell's equations? (the result of some empirical ...
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2answers
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What is the physical significance of the Dipole Transformation of Maxwell's Equations?

The Question Given Maxwell's equations of the form \begin{align} \bar{\nabla}\times \bar{B} = \dfrac{4\pi}{c} \bar{J} + \partial_0 \bar{E} \\ \bar{\nabla}\times \bar{E} = -\partial_0 \bar{B} \\ ...
3
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2answers
761 views

Does existence of magnetic monopole break covariant form of Maxwell’s equations for potentials?

Absence of magnetic charges is reflected in one of Maxwell's fundamental equations: $$\operatorname{div} \vec B = 0 \text{ (1).}$$ This equation allows us to introducte concept of vector potential: ...
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1answer
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Physical meaning of Maxwell's equations and origin of EM waves

Is it possible to describe the physical meaning of Maxwell's equations and show how they lead to electromagnetic wave, with little involvement of mathematics ?
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Maxwells Equation from Electromagnetic Lagrangian

In Heaviside-Lorentz units the Maxwell's equations are: $$\nabla \cdot \vec{E} = \rho $$ $$ \nabla \times \vec{B} - \frac{\partial \vec{E}}{\partial t} = \vec{J}$$ $$ \nabla \times \vec{E} + ...
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How to understand holography and hologram

I've spent some time reading wiki etc. What I get now is that apart from the normal light amplitude information, holograms also record the phase information of light. But this is so difficult for me ...
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2answers
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Special Relativity: Transforming Maxwell's equations

I'm working through Einstein's original 1905 paper*, and I'm having trouble with the section on the transformation of Maxwell's equations from rest to moving frame. The paper proceeds as follows: ...
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Do We Need Maxwell's Equations Since They Fail to Account for An Experimental Fact at Least in One Occasion?

This question is an outgrowth of regarding voltage and emf where @sb1 mentioned Faraday's law. However, Faraday's law as part of Maxwell's equations cannot account for the voltage measured between the ...
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4answers
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Why do Maxwell's equations contain each of a scalar, vector, pseudovector and pseudoscalar equation?

Maxwell's equations, in differential form, are $$\left\{\begin{align} \vec\nabla\cdot\vec{E}&=~\rho/\epsilon_0,\\ \vec\nabla\times\vec B~&=~\mu_0\vec J+\epsilon_0\mu_0\frac{\partial\vec ...
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3answers
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Maxwell in multiple dimensions: What happens to curl?

I read this answer a while ago, and while thinking about $\nabla$, I realized something. Since the cross product can be written as a determinant, in higher dimensions we require extra vector inputs. ...
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4answers
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Derivation of Maxwell's equations from field tensor lagrangian

I've started reading Peskin and Schroeder on my own time, and I'm a bit confused about how to obtain Maxwell's equations from the (source-free) lagrangian density $L = ...
18
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3answers
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Can light exists in $2+1$ or $1+1$ spacetime dimensions?

Spacetime of special relativity is frequently illustrated with its spatial part reduced to one or two spatial dimension (with light sector or cone, respectively). Taken literally, is it possible for ...
6
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1answer
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Recovering all of Maxwell's equations from the variational principle

Whether you can get the first couple of Maxwell equations from a variational principle? In the second volume of the Landau theoretical physics said that it is impossible.
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Why is glass much more transparent than water?

There is a related question (Why glass is transparent?) but I am coming at it only from Maxwell's equations. One can determine the skin depth $δ$ for poor conductors like (pure) water and glass using ...
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1answer
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why is advanced radiation absent?

the Lienard-Wiechert green functions have future and past null cones of radiation. Maxwell equations allow for a continuous range of mixtures between the retarded and advanced components, but we have ...
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1answer
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Maxwell's Equations in curved spacetime

I know that we can write Maxwell's equations in the covariant form, and this covariant form can be considered as a generalization of these equations in curved spacetime if we replace ordinary ...
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3answers
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Faraday's law - does the induced current's magnetic field affect the change in flux?

I've had this conceptual problem with Faraday's law and inductance for a while now. Take the example of a simple current loop with increasing area in a constant field (as in this answer). So ...
5
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1answer
578 views

How can the Huygens-Fresnel principle be derived from the Maxwell equations?

The Huygens-Fresnel principle states that every point to which a luminous disturbance reaches becomes a source of a spherical wave. I have been trying to understand this considering a infinite screen ...
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4answers
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can one introduce magnetic monopoles without Dirac strings?

To introduce magnetic monopoles in Maxwell equations, Dirac uses special strings, that are singularities in space, allowing potentials to be gauge potentials. A consequence of this is the quantization ...
2
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1answer
388 views

Electrodynamics and the Lagrangian density

Could anyone tell me what equations can I obtain from the Lagrangian density $${\cal L}(\phi,\,\,\phi_{,i},\,\,A_i, \dot A_i,\,\,A_{i,j})~=~\frac{1}{2}|\dot A+\nabla\phi|^2-\frac{1}{2}|\nabla \times ...
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0answers
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Electromagnetism - Proof of the Uniqueness theorem for an external problem

In the electromagnetic Uniqueness theorem, we consider a volume $V$ enclosed by a surface $S$. It is initially assumed that two different fields are valid solutions for the Maxwell's equations with ...
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3answers
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Maxwell's Equations using Differential Forms

Maxwell's Equations written with usual vector calculus are $$\nabla \cdot E=\rho/\epsilon_0 \qquad \nabla \cdot B=0$$ $$\nabla\times E=-\dfrac{\partial B}{\partial t} \qquad\nabla\times ...
4
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2answers
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When studying electrodynamics do we assume Maxwell's Equations or derive them?

This question is because something made me confused. I always thought that the idea behind electrodynamics was to postulate some things, like Coulomb's law in electrostatics and so on, and then ...
4
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4answers
642 views

How to interpret the continuity conditions in the PDEs (for example, Maxwell equations) originated in physics?

I am currently working on PDEs in physics, mostly Maxwell equations. I am a mathematics graduate student, and this question has been haunting me for years. In PDE theory, or more specifically the ...
4
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3answers
396 views

Exactly how is the constant measured velocity of light deduced from Maxwell's equation?

For electromagnetic radiation the velocity of propagation is $c = 1/\sqrt{\mu_0 \epsilon_0}$. Since both $\mu_0$ and $\epsilon_0$ do not vary in any inertial frame, then $c$ must be constant in any ...
3
votes
3answers
200 views

What electric field vector should I use for modeling unpolarized light?

Regardless of computational cost, light is a kind of electromagnetic wave, so it can be simulated with Maxwell's equations. If we want to simulate light with Maxwell's equations, we need to express ...
3
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2answers
145 views

Derivatives of delta function and equation of continuity for a single charge…

For a single charge $e$ with position vector $\textbf R$, the charge density $\rho$ and and current density $\textbf{j}$ are fiven by: \begin{equation} \rho(\textbf{r},t)= ...
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3answers
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Question about units of mass, $M = (L^{3})(T^{-2})$?

In section 5 of the "Preliminary: On the measurement of quantities" chapter (page 3) in "A treatise on electricity and magnetism" Maxwell uses, total length, $s=mt^{2}/{2r^{2}}$to show that ...
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2answers
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Electron model under Maxwell's theory

I was not able to recall my memories, so: What is the formula that states the frequency of electrons revolving around nucleus is equal to the frequency of light (or photon) emitted (or radiated)? (I ...
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1answer
150 views

Determine the flow and amplitude equation for thermal energy (with Del operator)

It is a question vector calculus and Maxwell's laws. I put it this way. Let's say, we are working in a $3$-Dimensional space ( e.g $x\cdot y\cdot z = 4\cdot3\cdot2$, a certain room/class of that size ...
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0answers
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Obtain the same Maxwell's equation after a change of coordinates

In the usual $(x,y,z)$ system of coordinates, if we expand the Maxwell's curls equations for phasors $$\nabla \times \mathbf{E} = - \mathbf{J}_m - j \omega \mu \mathbf{H}$$ $$\nabla \times \mathbf{H} ...