3.3 Solutions to Maxwell's Equations

[@redaabakhti768]

just a little notation error, at 1:45 the second memeber of the third Integral equation the derivative wIth respect to time of the flux of b over an open surface so there should be no ring in the double integral . I really love thIs lecture oterwIse and I'm Impressed by the sImplIcIty of your methods

[@scottmoerschbacher8664]

Physicist guess more often than you think. We even have a name for it: Ansatz :) Nice vid

[@El650Jefe]

at what point did we assume the electric field lies on the xy-plane? At 17:09 this is mentioned but it was neve mentioned prior.

[@otissumnerbrown]

Mr. Oliver Heavyside - helped re-write Maxwell's equations.

[@chaaotiic]

My book says that you should assume the permittivity e and permeability u should be assume as homogenous (not isotropic as you mentioned).

[@matusfrisik3887]

They should be homogeneous (have same values at all points) and isotropic (do not depend on the direction of propagation) at the same time.

[@omega7377]

Doesn't homogeneity imply isotropicity?

[@NeedOsrsHelp]

No, permittivity is actually a tensor quantity which relates the electric field en the electric displacement. Isotropicity means that for each point in space the permittivity is independent of the direction which reduces the tensor to a scalar but this doesn't mean that it has to be identical for each point in space. On the other hand homogeneity makes it identical for each point in space but it can still be dependent on the direction in which the quantity is measured. To give you an counter example, I will use Young's modulus (relates stress and strain) as quantity which is more intuitive. Assume you have a glass fiber reforged composite which is completely homogeneous. It will be tougher to pull it apart along the direction of the fibers than along a direction normal to this.

[@CalebDiT]

Michiel, I think you're accidentally equivocating in your example. Material homogeneity is different than homogeneous wrt permittivity, permeability, and even Young's modulus. The Young's modulus for a glass fiber is certainly not homogeneous despite the material's being reasonably homogeneous, which is precisely why it is anisotropic wrt strain. Whenever homogeneity is being mentioned, one must always define the scope: it is limited to electrical properties, mechanical properties, and so on, and only very carefully should you use one to imply another. So within this scope, yes, homogeneity implies isotropicity. The tensor may be reduced to a scalar since all values of the tensor are equal (say, epsilon_0). Still, the professor should have said homogeneous since that was the term he implied.

[@yasserel-azab7033]

Brilliant Prof. !

[@simonblue56]

You know what, I was stuck into the deviation you showed for about 2 hours. Your video is just like a can of Coca Cola for me when I finish a kilometer in summer.

[@srishtikumar3444]

Really helpful! Thanks a lot

[@mohamedesamelbeltagy9794]

Is there video for modes and general solution !

[@lukamadrid1428]

could you help me please i have a question how i can contact you?

[@williamwalker39]

Electromagnetic waves are only created by sources. So it is not valid to set the sources to zero. When the source is included, this results in the wave equation equal to a source. Solving this inhomogeneous PDE yields a nonlinear phase vs distance dispersion curve. Apply phase speed and group speed operators on this curve shows that the both the phase speed and group speed are instantaneous in the nearfield and reduces to the speed c in the farfield, starting at about 1 wavelength from the source. After that the speed decays asymptotically toward speed c, but never becomes exactly c, even at astronomical 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 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. *KZbin presentation of above arguments: kzbin.info/www/bejne/qZazlX1tq7iErLM *More extensive paper for the above arguments: William D. Walker and Dag Stranneby, A New Interpretation of Relativity, 2023: vixra.org/abs/2309.0145 *Electromagnetic pulse experiment paper: www.techrxiv.org/doi/full/10.36227/techrxiv.170862178.82175798/v1 Dr. William Walker - PhD in physics from ETH Zurich, 1997

[@goku5591]

really helpful

[@ashenone5774]

Thank you so much!

[@robert9219]

Excelent! Thanks!

[@ahmedismail1018]

beautiful you are my master in wave

[@adelsalam9735]

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[@spmanc]

very nice