# 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.

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### Maxwell's equations UPML in FDTD with inhomogeneous media

I'm looking at matching the UPML (uniaxial perfectly matched layer) defined in Taflove&Hagness' Computational electrodynamics to an inhomogeneous media (inhomogeneous w.r.t. both $\varepsilon$ and ...
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### $* d *$ operator — Digest the (differential/geometry) meaning

I like to digest better: the $* d *$ operator in Maxwell differential form equation the $* D *$ operator in Yang-Mills differential form equation We already knew that in Maxwell differential ...
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### Is the speed of Magnetic field infinite?

My real question is: From Amperes law we know that there is no magnetic field outside of the coaxial cable because the magnetic field generated by the inner wire and outer shell are equal but in ...
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### What is the formula that gives the EMF

I have been recently studying Maxwell Equations, and I wasn't able to understand properly the EMF $\zeta$. Mathematically we have $\zeta=-\dfrac{d\Phi_B}{dt}$ where $\Phi_B$ is the magnetic flux of a ...
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### Variational formulation of Maxwell equations with interface/boundary conditions

Consider $\Omega = \Omega_1 \cup \Omega_2$, where $\Omega _1$ and $\Omega_2$ are two different media with conductivity and permeability \sigma= \begin{cases} \sigma _1 & \text{in ...
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### Differentiability of electric field due to bounded volume charge distribution

In books on electromagnetism, one often sees expressions of Maxwell's equations like $\nabla \cdot \mathbf{E}$ and $\nabla \times \mathbf{E}$. These expressions make sense if $\mathbf{E}$ (which is ...
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### Prove that the electric field produce by a punctual charge is isotropic and radial

I would like to prove mathematically that the electric field produced by a punctual charge is isotropic and radial, i.e. $$\vec{E}(r,\phi,\theta)=E(r)\vec{e}_r\tag{1}$$ I think that this statement ...
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### Simple explanation to the induction from the slowly changing $\vec B$ of a solenoid in the region of $0$ magnetic field

I would like to get some elementary intuition into the problem a solenoid fed with a time-dependent current, and the resulting current that such the solenoid field would induce in a loop completely ...
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### How to derive $c=1/\sqrt{\varepsilon_0\,\mu_0}$ from integral form of Maxwell equations? [closed]

I've read similar questions and answers given thereto but find them unsatisfactory. So please don't mark my question as "duplicate". The question may as well be a duplicate, but it's still waiting for ...
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### How to choose the boundary condition for Maxwell's equations in the vacuum?

I need to solve the Maxwell's equations with sources in the vacuum numerically. The simplified problem is as following. A charged particle moving along the $z$ direction with speed $v_z$. Then, it ...
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### How are the differential forms for Maxwell's Equations used?

I am currently reading up on Maxwell's Equations (specifically Ampere's Circuital Law- with Maxwell's Addition) for a presentation on differential equations. I chose the topic ignorant of how the ...
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### Does superposition of all possible plane waves represent complete solution of Maxwell's equations in free space?

Consider the set of all possible superpositions of all possible "plane waves that satisfy Maxwell's equations in free space". Does this set represent all possible solutions of Maxwell's equations in ...
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### Polarization on a spherical electromagnetic wave in free space using classical electromagnetism

The polarization of a plane wave traveling in free space is well defined and traverse to the direction of propagation from classical electromagnetic theory. Spherical waves are another type of ...
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### Solution to Maxwell's equations in free space that are not plane waves [closed]

Are there solution to Maxwell's equations in free space that are not plane waves? I think there aren't. (Save trivial ones, i.e. E=const , B=const ) But i am not able to prove it. Please help. I would ...
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### Derivations of Maxwell equations

In my book of electrodynamics, the Maxwell equations are always used for specific conditions (electrostatics, magnetostatics, …). But nowhere I see a complete derivation of the equations. Maybe it ...
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### How to extract all information regarding electric and magnetic fields from Maxwell's equations in free space? [closed]

Is it possible to obtain some set of equations in E and B that have decoupled E and B , but are exactly equivalent to Maxwell's equations in free space? Exactly equivalent in the sense that the any ...
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### Maxwell's equation in free space from wave equations of electric and magnetic field

How to go from the wave equations of electric and magnetic field and $$\boldsymbol{\nabla}\cdot \mathbf E = 0 \quad \text{ and } \quad \ 0 = \boldsymbol{\nabla}\cdot\mathbf B,$$ to the remaining ...
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### Flux of Electric field non-zero through a surface for light in free space?

Consider an electromagnetic wave propagating through free space.The Electric and magnetic components of the fields, vary as sinusoids. If I construct a sphere of radius $\lambda/4$ at any location; i ...
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### Are wave equations equivalent to Maxwell's equations in free space?

In free space, do Maxwell's equations contain the same amount of information regarding electric and magnetic fields as is contained in the wave equations derived from them? If so, how?
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### How do we get a expression for speed of light $\frac{1}{\sqrt{\mu\epsilon}}$ using Maxwell's equation? [duplicate]

I am a $12^{th}$ class student in India. I am quite new to these interesting concepts. And, I think I've learnt about electrostatics, magnetism, Maxwell's equations very thoroughly. But, my books ...
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### Maxwell stress tensor for electromagnetic wave

Sorry if this is a naive question but I've been struggling in trying to proof this for a week. Consider an electromagnetic wave with wave vector $\vec{k}=k\hat{n}$, the Maxwell stress tensor can be ...
### How can we prove the law of Ohm $V=I*R$ from Maxwell's equations [duplicate]
$$∇⋅E=ρϵ0$$ $$∇⋅B=0$$ $$∇×E=−∂B/∂t$$ $$∇×B=μ0(J+ϵ0 ∂E/∂t)$$
I was wondering if the Feynman-Heaviside formula for the electric field of a moving charge could be used to write down the force/reaction force between charges $q_1$ and $q_2$ in a Machian purely ...