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.😊😊😊😊
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
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?
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 =))
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
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 ?
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 :)
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 ❤
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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
great explanation, as always!
It was actually amazing, sir.
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.😊😊😊😊
thank you for this amazing proof.
My head hurts. My mind is blown. My heart beating.
Thank you!
Thanks for explaining this so easily 🤝
I have never been this happy while learning physics😅, but this one blowed my mind❤
Fantastic, thank you!
your work is truly amazing
U r a life saver bro ❤
Thanks sir !!Great Explanantion!!❤❤❤
Got amazed by this explanation. Love it .
Nice explanation!
Your best at explaing a boring topic in an exiting way and easy way
So much helpful 💕
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
This guy seriously need a raise.
My new favorite channel
I'm in love with this writing dude
Nicely explained sir ❤
You're literally the best. I seriously love you from the bottom of my heart
Thank you!!!
Thank you soooo much ❤
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
Just ,.....WOW. Thank you so much
amazing...love from heart
Love from Bangladesh
Make such videos on on other maxwell's equations also
very intuitive thankss
What is the book of Richard Feynman he is talking about?
Awesome 😎
This is so clear. Thank you!
maan this is really great. it kinda surprised me
great explanation!
Thank you a hundred times.
Beautiful and elegant proof!
Thank you very much!😊 I am so happy today. I was searching for it from so long time.
Beautiful trickery !
Great 👌👌👌
Great explanation ....👍👊
FloatHead Physics ? Mahesh is that your voice ?❤
thanks for this excellent video sir
make more videos i enjoyed it sir
Endlich eine zufriedenstellende Erklärung, wo die 1. Maxwell-Gleichung herkommt.
Thanks!
Very informative... appreciated
This is so cool!
Thank you sir
I LOVE THIS CHANNEL
beautiful!
beautiful
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?
2:30
9:50
Sir, please make awesome video more fastly
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?
thanks
amazing explanation. oof finally, my sch is nth compared to this...
It seemed cool bro
Fantastic
You always rock
Tku mesh keep on
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
i love you sir
💓
❤❤❤❤❤❤
Love from Pakistan
hell awsome
9:16 If diameter of smaller circle is rθ then shouldn't the diameter of bigger circle be nrθ?
yeah, So?
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 ?
SO fcking amazing explanation, I now love richard feyman.
Rivhard Feynman!!!
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
Is it true that the radius is nr, is it not n+r...
It kinda looks electric flux follows equation of continuity!
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 :)
God saved my life
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