Electromagnetic Wave Equation in Free Space

00:00 Maxwell's equations in vacuum
00:27 Derivation of the EM wave equation
02:13 Velocity of an electromagnetic wave
03:17 Structure of the electromagnetic wave equation
05:00 E- and B-field of plane waves are perpendicular to k-vector
07:24 E- and B-field of plane waves are perpendicular
08:15 Summary

Books by Alexander Fufaev:
1) Equations of Physics: Solve EVERY Physics Problem
2) Alexander Fufaev and His Never Ending Story:

[pyropulseIXXI]

I think it should be pointed out that the EM wave in vacuum isn't actually moving up and down in space. I've tutored many students, and this is what they commonly think. It is the strength of the electric and magnetic field that oscillates, so, if looking along a single propagation axis, the EM-wave is literally on a straight line that doesn't move up or down. The field strengths along this straight line merely oscillate between a maximum and minimum value.

I just wanted to point this out because from my experience of tutoring, many students thought the EM-wave looked like that in space, like it was a string or something.

[mariocaponnetto]

Trying to image the excitement when Maxwell realized that the speed found was the speed of light!

[finn]

Thank you so much, way better than my prof's derivation. so simple!

[stellarbrg]

I am studying the griffiths electrodynamics and i was stuck here. Beautifully explained, earned a subscriber:)

[williamrhopkins]

Very nice exposition. One thing to note is that the calculation of c does not depend on the frame of reference of the observer and this is the basis of special relativity. I don't think Maxwell gets enough credit in this regard.

[fufaev-alexander]

I re-uploaded the video to correct a mistake!

[mantikor-gp]

I really enjoy your calm explanations and the great animations

[plrc]

I don't know what's wrong with physics that it attacts a lot of "lunies" writing pseudo-science gibberish. Notice that everywhere where you hear/read about physics you will find such comments. On the other hand, there's no something like that about mathematics. Mathematics somehow doesn't attacts such lunies.

[jean-francoisbouchard]

I realy like the animations in the equations. It makes the maths really easier!

[helmutalexanderrubiowilson]

Oh what a nice discovery is this channel. Love every detail and the speed of your explanation. You are a gifted teacher

[UnaiGZ]

These explanations are GREAT. Many thanks

[JamBergMann]

Thanks for your explanation and for your effort.

[abdulbasir]

the best explanation sir. thanks a lot

[shikangliu]

Great Video! I am looking forward to the case in Dielectric medium!

[alejandrohc]

the best video with the best explanation!!!! thx

[Naomi_Boyd]

The B field and E field must be orthogonal to each other in an electromagnetic wave. That much makes sense. But if the change in the E field induces the B field and the change in the B field induces the E field, why are they not 90 degrees out of phase?

[wal]

Love the videos, how about a video on singular value decomposituon, and eigenvalue decomposition? I guess you could beautifully animate those :)

[primaryendo]

I don't understand this but i love it

[petershelton]

Thank you for demystifying the science I so long to comprehend 🎉

[plrc]

Great video. You're an excellent teacher. Please make video about how Maxwells Equations imply that there is momentum of light/electromagnetic wave. I asked at Quora how momentum of light is even DEFINED, because "school" definition p:=mv obviously doesn't make sense here. A lot of professors and doctors answered me but in fact they didn't know :P Only one person wrote an answer that makes sense i.e. that momentum is a very general notion that stems from the Noethers theorem and conservations principles. I'd like to hear about it in the context of classical electromagnetism.