Speed of light from Maxwell's equations (derivation)

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a)Write the Maxwell’s equations and explain the significance of each
equation.
(b) Deduce the Maxwell equations for free space and determine speed of light in free space.

#maxwell'sequations #emwaves #speedoflight #maxwellandspeedoflight #gradiant #gusseslaw #divergence #curl #electricfield #magneticfield
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Thank you! It was outstanding how precisely and transparently you explained the subject! Thanks again

NickN
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Excellent video.

I remember seeing this in a lecture years ago and forgot how to do it from Maxwell's equations.

Thanks for bringing this all back to me.

craigfowler
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Finally understood it thanks to this video! Thank you so much!!

ighia
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How do you determine mu naught and epsilon naught?

rudyberkvens-be
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Sir,
I am 12 th science student...I have studied in the simple form
the maxwell's law in the integration
I can't understand DEL...."and Curl...."

underratedPie
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Just reading the equations, please explain it also from student's understanding point of view

neerajbhardwaj
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So since the permeability of free space contains pi as a constant, does this mean that if the speed of light was a different number, pi would be different too?

barthvapour
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thanks for the great explanation, sir!

fidelazuara
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where did you get the general wave equation with at 1:39?

Zghost
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There were some errors in the slides.

But apart from it, it was all good.

createvideo
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This is like magic without any big instrument or machines ...Only by just pen and a paper we can calculate the speed of light 😄

soikatmaji
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This derivation is wrong! Maxwell equations have source terms and you can not set them to zero if the fields are emitted by a source. Instead the wave equation must be set equal to a source term, and when this inhomogeneous PDE is solved, one sees that the phase vs distance relation from the source is nonlinear in the nearfield and only approximately linear in the farfield. Applying well known relations for the phase and group speed which are proportional to the imverse of the slope of the phase curve, shows that the phase speed, and group speed are instantaneous in the nearfield and reduce to about speed c in the farfield, .starting about 1 wavelength from the source, and never becomes exactly c even at astonaumical distances from the source.

So, the speed of light is not a constant as once thought, and this has now been proved by Electrodynamic theory and has also bewn proved by Experiments done by many independent researchers. The results clearly show that light propagates instantaneously when it is created by a source, and reduces to approximately the speed of light in the farfield, about one wavelength from the source, and never becomes equal to exactly c. This corresponds the phase speed, group speed, and information speed. Any theory assuming the speed of light is a constant, such as Special Relativity and General Relativity are wrong, and it has implications to Quantum theories as well. So this fact about the speed of light affects all of Modern Physics. Often it is stated that Relativity has been verified by so many experiments, how can it be wrong. Well no experiment can prove a theory, and can only provide evidence that a theory is correct. But one experiment can absolutely disprove a theory,   and the new speed of light experiments proving the speed of light is not a constant is such a proof. So what does it mean? Well a derivation of Relativity using instantaneous nearfield light yields Galilean Relativity. This can easily seen by inserting c=infinity into the Lorentz Transform, yielding the GalileanTransform, where time is the same in all inertial frames. So a moving object observed with instantaneous nearfield light will yield no Relativistic effects, whereas by changing the frequency of the light such that farfield light is used will observe Relativistic effects. But since time and space are real and independent of the frequency of light used to measure its effects, then one must conclude the effects of Relativity are just an optical illusion.

Since General Relativity is based on Special Relativity, then it has the same problem. A better theory of Gravity is Gravitoelectromagnetism which assumes gravity can be mathematically described by 4 Maxwell equations, similar to to those of electromagnetic theory. It is well known that General Relativity reduces to Gravitoelectromagnetism for weak fields, which is all that we observe. Using this theory, analysis of an oscillating mass yields a wave equation set equal to a source term. Analysis of this equation shows that the phase speed, group speed, and information speed are instantaneous in the nearfield and reduce to the speed of light in the farfield. This theory then accounts for all the observed gravitational effects including instantaneous nearfield and the speed of light farfield. The main difference is that this theory is a field theory, and not a geometrical theory like General Relativity. Because it is a field theory, Gravity can be then be quantized as the Graviton.

Lastly it should be mentioned that this research shows that the Pilot Wave interpretation of Quantum Mechanics can no longer be criticized for requiring instantaneous interaction of the pilot wave, thereby violating Relativity.  It should also be noted that nearfield electromagnetic fields can be explained by quantum mechanics using the Pilot Wave interpretation of quantum mechanics and the Heisenberg uncertainty principle (HUP), where Δx and Δp are interpreted as averages, and not the uncertainty in the values as in other interpretations of quantum mechanics. So in HUP: Δx Δp = h, where Δp=mΔv, and m is an effective mass due to momentum, thus HUP becomes: Δx Δv = h/m.  In the nearfield where the field is created, Δx=0, therefore Δv=infinity. In the farfield, HUP: Δx Δp = h, where p = h/λ. HUP then becomes: Δx  h/λ = h, or Δx=λ. Also in the farfield HUP becomes: λmΔv=h, thus Δv=h/(mλ). Since p=h/λ, then Δv=p/m. Also since p=mc, then Δv=c. So in summary, in the nearfield Δv=infinity, and in the farfield  Δv=c, where Δv is the average velocity of the photon according to Pilot Wave theory. Consequently the Pilot wave interpretation should become the preferred interpretation of Quantum Mechanics. It should also be noted that this argument can be applied to all fields, including the graviton. Hence all fields should exhibit instantaneous nearfield and speed c farfield behavior, and this can explain the non-local effects observed in quantum entangled particles.




Dr. William Walker - PhD in physics from ETH Zurich, 1997

williamwalker
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"gusses law" (!!) is just Gauss' law! Ever heard of a guy named Gauss?

ascaniosobrero