Transforming four Maxwell's equations into two

[Correction]
at 11:24, it should be "Ey/c" not " - Ey/c".
I've explained how Four Maxwell equations can be shown with just two Maxwell's equations in tensor notation. Electromagnetic field tensor is present. Gauss law, Ampere law and Faraday law are present.
At the end, I also showed "continuity equation" in tensor notation as a bonus info !

[@ReumiChannel]

I've put quite an effort into making this video, but I'm not getting that many subscribers 😢 If this video helped you, pleaseeeee subscribe to my channel. It really motivates me ! :)

[@arslonbeknaimjonov8035]

don't lose motivation. I'm sure over time the number of subscribers will grow.

[@ReumiChannel]

@@arslonbeknaimjonov8035 Thank you so much ! 😢

[@matthijsgeerlings]

It definitely helped me, thanks

[@wealllovelain]

Subscribed, thank you so much!

[@tommasodavi5394]

I'm a mathematics student, with an interest in physics. Don't just look at the number of subscribers; instead, think about how you manage to explain such complex topics in a simple and clear way to each person who watches your videos. I love them, be proud of what you have done!

[@qissorpz]

If i had seen this 1 year ago, this would have saved me in special relativity classes 😅 great explanation!

[@heyn1785]

Great video, great visuals, perfectly explained, thank you👏🏼👏🏼🙏🏼

[@ReumiChannel]

Thanks ! plz help me by recommending this to your friends, too! :)

[@pizzapineapple2425]

thanks from south korea ! it is very simple and i think it is a better form of maxwell eqn!

[@ReumiChannel]

감사합니다!

[@MojiWord]

I truly appreciate great teaching...thank God for you🙏🏽

[@danielzorrer1388]

Thanks for the great explanation, helped me a lot!

[@gevodem]

This video is wonderful! Job well done and thank you!

[@anandbavkar8572]

Really appreciate your hard work, Thanks you very much. Hope you will come up with more enlightening videos like this... Best wishes for your channel.... Just one thing though... At 4.24 You were saying "The left hand side of the Eqn will be expanded like this .................. and Nu is varied and All terms are added because this is just a partial derivative Right!! " I think all the terms were added not because it's a partial derivative but because of Einstein Summation Convention.

[@ReumiChannel]

Thank you! Yes you are right. Its from the summation convention. I just told people in a comprehensive way :p. I mentioned the summation convention in "tensor contraction with indices".

[@amlanpatra6365]

Thank you very much ❤️ Indeed a nice video and hope you will continue to upload more videos on tensors and Electrodynamics soon

[@ReumiChannel]

Thanks !

[@sebrady951]

Best explanation you have a new subscriber

[@ReumiChannel]

yayyy thanks !

[@Flaystray]

Good Lord this channel is good

[@ReumiChannel]

Haha, satisfying?

[@erickordunahernandez3579]

This is the best explanation I've ever seen, thank you very much for sharing it! What books do you recommend to find this topic?

[@ReumiChannel]

Griffiths "Introduction to electrodynamics" , and Zwiebach "A first course in String Theory". These are the good ones :) Thanks for such a compliment ! Subscription helps me a lot !

[@AvivKaveh]

Amazing video! great explanations!

[@nilhanozceylan2838]

I understood, thank you🙏🏻

[@bendeguzbanfalvi706]

hello, Isn"t there an einstein summation around 6:00 ? i mean, why you break apart the equation to different \mu values? if we make a sum to \mu as well, we'll have the same resoult, but we'll need the assumption of the non-existance of magnetic monopoles to get 2 equations.

[@declandougan7243]

Einstein summation is assumed in the notation, yes.

[@declandougan7243]

It is also forced by the equations, however, since there have to be only four resultant vector components.

[@MrFlappslap]

Really good content you should make more physics vids

[@ReumiChannel]

Thanks a lot ! You could suggest me :)

[@ambiscreativetips1264]

Great explanation.....😄👍

[@cutekitten719]

Nice video!

[@shubhamshahi.]

bro thanks so much it helped and I guess I understood it . But can you please reply that why Lenny used contra variant instead of covariant in his book . theoretical minimum ( special relativity ). like he used randomly any of covariant and contravarint and that get me confused . or we are free to use any indices we want but dosent that reverses the sing ?

[@ReumiChannel]

Mathematicians will say "There is a clear mathematical difference between covariant and contravariant". But to be honest, it shouldn't really matter as long as everything is consistent. It's like, 3m[Right]+2m[Left]=1m[Right]. But Lenny (I don't know about this book) probably did something like 3m-2m = 1m[Right]. Not being careful about the notation and stuff. This is just my guess. I did also talk about the difference between covariant and contravariant using vectors/dual vectors. kzbin.info/www/bejne/bovQon-Vo7GpoK8 So check it out (especially 5:35)

[@x_vald]

Hey, great video!!! Could you answer me a question? Why do we need to use the dual tensor for the other two Maxwell equations?

[@ReumiChannel]

That is.. quite a deep question. You would need to understand general relativity :)

[@vedantdandage97]

Bro do you have a pdf of this proof? Loved the video btw

[@ReumiChannel]

Thanks bro! The closest one you can refer to is "Griffith's electrodynamics"

[@Shining-lz9se]

Nice explanation ✨

[@bidyutsarkar256]

Good.. explanation

[@ReumiChannel]

Thank you !

[@miguelaphan58]

..a most useful exposition

[@andykoh-z8s]

nice video, Actually i am trying to understand why a moving electric charge creates a magetic field according to special relativity. So many videos tried to explain about length contractions and time dilations. But i cannot get the idea. I think that electric and magnetic field are 2 fields which cannot be transformed between one another. It will be great if you can do a video to help me understand this mystery. Thanks ... subscribed

[@ReumiChannel]

That's a great question. I will make a video that covers your question in the future. But to give you a quick short answer, if electron starts moving, the electric field that was spreading outward symmetrically in 2D will start changing its shape. Imagine you are picking up a spider net (electric field) from the surface. The net will curl. It will curl up. When it's not moving, curl of E is zero (electrostatic). But when it's moving, curl of E starts having non-zero matrix elements. The third Maxwell's equation tells, if the curl of E has a value, dB/dt starts appearing. I've actually been keeping this topic until our channel makes a sufficient amount of income so that I can hire someone for graphic designing haha. So it might take some time to make such a video.

[@andykoh-z8s]

@@ReumiChannel Great, Thanks for the reply ...i will wait for your new videos. :) I think we cannot derived ampere's law from special relativity. A few video's on youtube that said that they can do that are just bs.. :)...

[@AbdUllah-gh3qp]

impressive sir

[@rudypieplenbosch6752]

Thank you for the very clear explanation. I have 1 question, how do you get the values that are filled into the 2 field tensor matrices (shown at 3") ? I understand the main diagonal is zero and the remaining matrix values are antisymmetric around the diagonal to represent the circular electric field (generated by a point charge) and the circular magnetic B field that the tensor needs to represent. But how do you get those specific E and B values at their positions in the two tensor matrices ? Because I can see how the table lookup works but I don't see how you got the table. Update: found it, this guy shows it around 16" how to calculate the individual matrix entries kzbin.info/www/bejne/mHqtioebjNSlrJo it seems he calculates the contravariants so his signs are all inverted.

[@ReumiChannel]

You are right. I should make a video (in my style) about how to make those tensors. Good that you found another video cuz im on a vacation right now. Thanks for the compliment ! It motivates me !

[@rudypieplenbosch6752]

@Reumi's world Thanks fir your answer, it will be interesting to see your video, it does belong in your series.

[@aabidmushtaq3243]

Subscribed u deserve it. ❤❤

[@ReumiChannel]

Thank you so much !

[@aabidmushtaq3243]

@@ReumiChannel ❣️❣️It's ok

[@Trust_4G_Leaders]

Bro u not from NUS right?

[@ReumiChannel]

No. I live in Canada :)

[@deneshk353]

Just take a minute and adore the fact that how beautiful physics is! 🙏How it unfolds 🥲

[@AntonioTiagoNunes-kf6ml]

The best.

[@marisolvelez9027]

Yes! But ...

[@KingG924]

Ich küss dein Herz

[@joposepeph]

The video it's ok, but you haven't demostrated the transformation, you just verified that it works...

[@ReumiChannel]

Sorry that I didn't satisfy you. It was in fact backward verifications. I hope you at least feel better after watching this : kzbin.info/www/bejne/gmS0hmaHnLaAnsk&ab_channel=Reumi%27sworld