Gauss law logical proof (any closed surface) | Electric charges & fields | Physics | Khan Academy
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- Опубликовано: 12 сен 2024
- Using geometry let's prove that the Gauss law of electricity holds true for not just spheres, but any random closed surface.
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Created by Mahesh Shenoy
I'm so glad I found you, it has always bugged me how the flux had to be the same for any closed surface, and I was never able to find a convincing proof online
i have been hovering on internet for hours to find a correct explanation. I am so greatful to find your video , it completely solve my problem. thanks for helping us.😊😊😊😊
great explanation, as always!
It was actually amazing, sir.
Wow, I have to admit when you said logical proof and stuff I was really skeptical, felt like it barely even involve math totally caught me off guard with how detailed this was, great work.
But just to make sure I got this part right, at the start you basically divided the whole sphere into many tiny circles and same with the blob all to sum it up later much like how we can divide anything into tiny squares in calculus but transferred into spherical coordinates, or something like that right?
yeah
Thanks for explaining this so easily 🤝
thank you for this amazing proof.
I have never been this happy while learning physics😅, but this one blowed my mind❤
theres a really weird implication of this though. Because now if we have a flat board and some charge outside of it(that lets say creates a uniform field), the flux is simply the field strength times the area (assuming the board is facing the field ). However,if the board is even slightly not flat, making it a closed surface, then the flux is suddenly 0.
To me this seems intuitively paradoxical, because the flat board has field lines entering and exiting it as well, but for some reason the idea that the flux is negative when entering and positive when exiting only applies to closed (3d surfaces).
What do you think about this?
For a charge outside the gausian surface, every electric field line (originated from charge) IF goes inside the surface must also come outside the surface.
Field line inwards the surface denotes negative charge and outwards denotes positive. So net enclosed charge (assume two equal and opposite charges cause the entering & exiting field line) cancel out.
By gauss law
Flux * e = net charge enclosed
(Net charge =0) Implies flux =0
Hence field lines by charges outside the surface don't change the results
My head hurts. My mind is blown. My heart beating.
Thank you!
your work is truly amazing
Fantastic, thank you!
gauss is truly a genius he went from proving the flux for only a sphere to proving its the same as long as it's a closed surface using only high school geometry truly magnificent
Make such videos on on other maxwell's equations also
You're literally the best. I seriously love you from the bottom of my heart
FloatHead Physics ? Mahesh is that your voice ?❤
Got amazed by this explanation. Love it .
What is the book of Richard Feynman he is talking about?
Your best at explaing a boring topic in an exiting way and easy way
Thanks sir !!Great Explanantion!!❤❤❤
Nice explanation!
So much helpful 💕
Great proof and explanation! Most people argue using the electric field lines when introducing Gauss's Law and its independence of the closed surface, but I always found that argument a bit unsatisfying. I find electric field lines are merely a simplification of the electric field for visualization purposes (they are artificial in a sense the other concepts aren't), and using them to "prove" E&M laws always seemed unrigorous to me, at least not as rigorous as a limiting process as this one. But then again, I'm still a student, so maybe I'll change my opinion. Nevertheless, great video =))
this is a proof for spherical charge but is there any proof gauss law also holds for a plane charge
Here, the tiny portion of the irregular closed surface was approximated as a circle, how is that?
The area of the outer area on the random surface is finite because n*r is finite . But then also , why do we use gauss law for extended infinite distributions ?
Thank you very much!😊 I am so happy today. I was searching for it from so long time.
Nicely explained sir ❤
make more videos i enjoyed it sir
Beautiful and elegant proof!
Just ,.....WOW. Thank you so much
maan this is really great. it kinda surprised me
This is so clear. Thank you!
This guy seriously need a raise.
I'm in love with this writing dude
Thank you!!!
Love from Bangladesh
amazing...love from heart
Very informative... appreciated
Thanks!
very intuitive thankss
thanks for this excellent video sir
My new favorite channel
Beautiful trickery !
great explanation!
Thank you soooo much ❤
Thank you a hundred times.
9:16 If diameter of smaller circle is rθ then shouldn't the diameter of bigger circle be nrθ?
yeah, So?
Great explanation ....👍👊
💓
Awesome 😎
Why do you take the area perpendicular to E at the outer surface. You need to take the area A of the outer surface and normal vector n to that area.
it's the same thing
Endlich eine zufriedenstellende Erklärung, wo die 1. Maxwell-Gleichung herkommt.
SO fcking amazing explanation, I now love richard feyman.
This is so cool!
Sir, please make awesome video more fastly
Thank you sir
Is it true that the radius is nr, is it not n+r...
I LOVE THIS CHANNEL
beautiful!
amazing explanation. oof finally, my sch is nth compared to this...
You always rock
Great 👌👌👌
thanks
2:30
9:50
beautiful
Fantastic
I've got a doubt bugging my head.... If the flux due to the charges outside do cancel out then why consider the field due them in the E.S surface integral ? Why don't we just ignore them altogether?
That's a great question. You are absolutely right. So, then why do that?
It's accurate to say flux through a closed surface also equals E (only due to charges inside). S.
But that's not a very useful thing for me?
Because, my goal is most often is to calculate the electric field at some point in space.
And that field is due to all the charges in the universe.
So, the idea is to first find the flux - which is E (due to all charges).S - using Gauss's law and then use it to find the E(due to all charges).
Does that make sense?
@@KhanAcademyIndiaEnglish Ohh yeahh.. I get it now !! Thank you so much for replying sir... These lectures are on a whole different level and it feels so great when the logic is known :)
❤❤❤❤❤❤
i love you sir
Tku mesh keep on
It seemed cool bro
hell awsome
Love from Pakistan
It kinda looks electric flux follows equation of continuity!
Rivhard Feynman!!!
Let me explain...
E = kq / r^2
kq = E * r^2 (flip variables)
E' = kq / (nr)^2
E' = E * r^2 / (nr)^2 (substitution)
E' = E / n^2
A = pi * r^2 = pi * (d/2)^2
A' = pi * (nd/2)^2
A' = A * n^2
E' * A' = E * A
You're welcome ❤
dude what a beautiful explanation !!mind blowing
Thank you sir