Electromagnetic waves from Maxwell's equations

Using Maxwell's equations in free space to demonstrate the existence of electromagnetic wave solutions, and investigating the properties of the oscillating electric and magnetic fields. For example, we show that the fields oscillate in phase with each other, but are perpendicular to each other and to the wavevector.

About me: I studied Physics at the University of Cambridge, then stayed on to get a PhD in Astronomy. During my PhD, I also spent four years teaching Physics undergraduates at the university. Now, I'm working as a private tutor, teaching Physics & Maths up to A Level standard.

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[richardwilliams]

Very well presented mathematics, thanks.

[abdurrahmanlabib]

Great video!!. It would be really helpful if you could make a video for reflection and transmission coefficients. Thanks

[milessodejana]

isnt the first maxwell equation the gauss law and is not equal to 0? And the reason why del(del \cdot E) is 0 is because del \cdot E is constant?

[sonusangeeths]

sir one doubt we know that
E0/B0 = C (1)
Meaning that magnitude of B0 is very much smaller compared to E0.
So when we are taking
(K x E0)/w = B0
By comparing (1) wrt (2) to make B0 a small value we should take a higher value of omega(w).
w >> (K x E0).

if w(2πf) is greater meaning we have a higher frequency. So no of oscilations of magnetic field at a time interval ΔT will be higher than EF. ?

[SurprisedDivingBoard-vurz]

Why we use cross product dot products. Because of trigonometry of material structure. The shape of an electron is a tetrahedron structure with a packing effect. I mean if you write the field equations for electrons. Probability and statistics is about study of structures.

[philoso]

Nice video and presentation.
Vacuum is empty of anything?
Yes to mechanical engineer and some mathematicians, and no to RF radio engineers.

This video just confirms that light speed in vacuum is dictated by e0 and u0 in vacuum. Also that vacuum is a medium of light.

The logic and mathematics in the Michelson and Morley Experiment are correct except the concept.

Concept? To proof that Aether, a light medium, is like wind can blow through all matter and not dragged by it.

If that is correct, we’d expect that electromagnetic and light waves riding on a medium of Aether can also blow through any matter, and as a result, light becomes undetectable.

[williamwalker]

What is presented here is a very simple approximation. Setting the wave equation to zero is a boundary condition valid at infinity, which does not exist in reality. The correct way to analyse this problem is to set the wave equation to a source and then analyse the propagation of the resultant electromagnetic fields. When this is done a lot of detail overlooked here is revealed. The fields propagate instantaneously when they are created by the source in the nearfield, and they reduce to about the speed of light at about one wavelength from the source, and never becomes exactly c even at extreme astronomical distances from the source. This corresponds to the phase speed, group speed, and information speed. Another important detail that is revealed is that there is a circulation of the electric field in the nearfield. The longitudinal electric field that is launched from the source, curves toward the opposite pole and creates the transverse electric field at about 1/4 wavelength, and launches transverse electric fields back toward the source and also away from the source. These propagating fields in the nearfield completely violates Relativity, which says nothing goes faster than speed c.

So the speed of light is not a constant as once thought. Inserting c=infinity into the Lorentz Transformation yields Galilean transformations, where time and space are absolute. These results indicate that if a moving body is observed with nearfield light, then no Relativistic effects will be observed, but if farfield light is used then Relativistic effects will be observed. Since time and space can not depend on the frequency of the light used to observe effects on time and space, then one must conclude the effects of Relativity are just an optical illusion. Any theory based on Relativity such as General Relativity, and Quantum electrodynamics are wrong. See the following short YouTube presentation for details, as well as the paper it is based on:

[JaganJagan-tr]

I wana mathematics proof of coulomb law in classical mechanics and how epsilon=8.85×10^-12 and not use proportional term