New answers tagged maxwell-equations
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According to Maxwell Equations, how does the light travel straight line?
The electromagnetic wave equation allows for plane wave solutions in the form of
$$ \vec{u}=\vec{u_0}\exp(i\vec{k}\cdot\vec{r}-\omega t), $$
and since the wave vector can always be chosen to travel in ...
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According to Maxwell Equations, how does the light travel straight line?
From the Maxwell's equation you can derive the wave equation, whose solutions are a propagating wave. Next, we need to define what is meant by propagation direction of the wave, and then look to see ...
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Reasoning behind the Lorenz gauge
Everything you said is correct. To set the potential $A_μ$ to satisfy the Lorenz condition, you choose a $χ$ such that $∂_μ∂^μχ = -∂_μA^μ$, and $A^\prime_μ = A_μ + ∂_μχ$ will satisfy the Lorenz ...
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Reasoning behind the Lorenz gauge
If you start out with a potential that does not obey the Lorenz condition you can fix that with a gauge transformation as you correctly state. Then you still have the remaining freedom of a gauge ...
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Radiative and Longitudinal degrees of freedom of EM field
Okay, reading the answer of @my2cts I've come up with a reasoning that allows me to sleep at night. The 2nd and 3rd equation are indeed the same equation, say
$$\nabla^2 \phi + \frac{1}{c} \vec{\nabla}...
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Reasoning behind the Lorenz gauge
Your are confusing two things
The condition on $\chi$ such that the gauge transformed field
$$A'_\mu := A_\mu +\partial_\mu \chi$$
is in Lorenz gauge. This is indeed $\Box \chi = -\partial^\mu A_\mu$...
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Radiative and Longitudinal degrees of freedom of EM field
The time derivative of the second equation is identical to the divergence of the third one.
Edit. So the two field components are dependent and are one degree of freedom.
In fact the charge-current ...
- 26.6k
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Is the magnetic field in an ideal coaxial cable carrying a TEM wave solely defined by the Ampere/Maxwell displacement current?
To answer my own question 😺 ... I think it comes down to the different direction of the curl of the magnetic fields caused by the conduction current density (μJ) and the displacement current from (-$\...
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Unconvinced by a standard step in deriving Maxwell-Ampère's law from Biot and Savart's law
Not sure if this is relevant to your question, so let me know if I'm on the wrong track.
If we assume that $\nabla\cdot j = 0$ everywhere in $\mathbb R^3$ say, differential topology (e.g. the Poincar'...
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How did Maxwell combine Faraday's equation with the Lorentz force law?
The reference is wrong and Maxwell never came up with any Lorentz force law. That's a widespread myth that's been propagated on the net. It was Lorentz who came up with it (as I explain in more detail ...
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Unconvinced by a standard step in deriving Maxwell-Ampère's law from Biot and Savart's law
First off, I don't see why you think integrating over all currents is artificial. Ampere's law is a statement about the total magnetic field, and the total magnetic field depends on all the currents. ...
- 105k
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Is the magnetic field in an ideal coaxial cable carrying a TEM wave solely defined by the Ampere/Maxwell displacement current?
It turns out that there are vacuum (or linear-dielectric bound-charge) solutions to the Maxwell equations for a coaxial cable (c.f. Griffiths chapter 9), and the associated coupled equations aren't ...
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