2:05 maxwell's equations 5:30 review of vector calculus 12:20 solving Maxwell's equations in vacuum 17:20 solution - 3D wave equation 30:20 example solution: plane waves 56:17 plane wave interaction with a perfect conductor 1:11:39 Poynting vector of the standing wave
I’m still learning so I’m curious: if the fields do not cause each other then how would they propagate through a vacuum where there are no accelerating charges? Are you saying that accelerated charges will form the initial E and B fields, which then interact with each other to propagate through space to infinity?
@@dillonlabonte9685yes . Maxwells law proved that a changing electric field , by symmetry , is equal to the movement of an electron , meaning that the wave self propagates.
@@lil_ToT-XFZ1 even einstein in the end, in a letter to lorentz, concluded their has to be a medium. one null result does not disprove anything. further more i would like to add, these are not maxwell equations, they are heaviside equations. they are not the same. and to quote heaviside, " i took the baggage off of maxwell." this was in reference to the scalar component. i suggest everyone should read Elementary Lectures On Electric Discharges, Waves And Impulses, And Other Transients by charles protues steinmetz ( its free online)
I have been having this question in my head for quite some time, I hope somebody can help me wrap my head around the idea. Please feel free to comment and correct any mistake in my thought process as I am sure I am missing something. - So in this lecture it is shown how from Maxwell Equations, and under the assumption of vacuum (J equals to 0) we see that the EM wave equations are solutions of the Maxwell partial derivative equations (I assume there are other solutions as simply constant E and constant B, but I guess they are ommitted in the lecture as not interesting). - So back to the EM, these waves are described in the complete space and time domain (ok, let's say for all (x, y, z) and for all t > 0). Is that correct? - If this is true, at t = 0, there exists wave (maybe it is more accurate to say there exists E field and B field) in all the space, even beyond ct (even beyond the reach of the speed of light). - I know the wave travels at c speed (this means, a wave peak travels at c speed along the propagation direction) Knowing this, I am not sure what is understood by "Light taking X time to arrive to a place Y", if there is wave and field in all the space all the time. I guess what I am missing is that I may be confusing the presence of the field with the concept of a wave arriving at some place, maybe what needs to arrive is the perturbation (so the bending of the wave shape)? Thanks for the help in advance.
The key here is that where you say that the fields exist in all space, even beyond ct, is not true. The fields need time to propagate. And the speed by which they propagate is at the speed of light. In other areas of analysis, such as say electrostatics, we assume the electric field for an electron has already propagated outwards to simplify the analysis. The propagation of the electromagnetic field is itself the motion of light, so it moves at light speed. There is no field present before the field reaches it. The fact that light itself has a speed is evidence that the fields take time to propagate (and are not immediately present everywhere unto infinity). If not, for example, light from stars would reach us immediately.
Even WITH his accent, he explains it well. As someone who has the privilege of attending his lectures live, he is an incredible lecturer with passion and expertise for the subject and an amazing personality. Let's not caveat it with our prejudice against accents. The beauty of mathematics and physics is that it can transcend human language.
@@FX-hf6sk I mean, lets be honest here, I'm not trying to sound like an asshole, but trying to listen to this was rough I gave up like 10mins into the lecture, communication skills and how smooth it is, is very important when it comes to teaching.
Accents take time to get used to, so if you tried again you might get further. Professor Lee does an incredible job communicating scientific concepts and the beauty of physics, and it’s recognized as he’s celebrated among MIT undergrads as an amazing physics professor and has tenure in the department. :) For all those that make honest and humble efforts, his accent does not get in the way of his teaching or research; only prejudice does.
Electro-Magnetic Wave (EMW) actually is Magnetic Wave (MW) , enough.!! Electric implication is they need Conductor/Media such as Copper wire, Electrolyte Liquid or Humid Air (in case Lightning Bolt).. the Magnetic Wave only need Empty Space.!! when strikes into Antenna/Receptor, it's Converted into small Electric pulse that can be Amplified or processed. Electricity then, also NOT Magnetic Wave b'cuz it need Conductor/Media (copper wire) but Magnetic Wave is Pure pulse of Energy, travelling through empty Space-Time at the Speed of Light.(!?!).
One question. What happen when f(x) < 0, and what happen when f(x) >0, I know about gradient and divergent, but my teacher ask my to demonstrate this condition, please help. Also a situation ask us to evaluate the partial derivative at some point, the answer give a result of a negative number, but I don't know what it means.
If you put a charge at a point in the E field, the E field will make it move in the x direction. This x direction-pointing E field spreads in the z direction.
A case wherein the div and curl occurs one after another within a short time interval,thus how can we create or measure the deviation of energy if there and quantify this by Potential energy.
In the traveling wave graph when the magnetic field and eletric field are both zero at some point, what's the energy at those points if it not equal to zero ?
In a travelling wave, the energy is propagated along the direction of propagation (starting from the source of EM waves). Therefore, energy, at any given point, will fluctuate from zero to a maximum value.
With a mathematical approach, evaluating E=e^i(kr-wt), amplitude is imaginary if the phase of the wave function is pi/2. Implementing it on physical world, it means that real light is somehow converted into imaginary light.
What is the difference between pointing in x direction but propagating in positive z direction. If this is the case, then why the component of electric field is zero in z direction even when it is propagating in that direction? @34:20 minutes into video.
Well, imagine that a group of people is starts waving with arms from back to front, as it happens on stadiums. Although each individual rises his or her arm upwards and downwards, the wave itself propagates parallel to earth.
Try your personal equations in liquid solid or gas not in vacuum , there are liquids ,gases ,and solids , inside of us all , as well as inside and outside the earth , and being inside and outside the earth's atmosphere are similar in that regard the aether however is liquid I assure you . And the atmosphere's layer's can only be penetrated by discovering their design . EM waves it's in the game . Life.
The reason we use the complex exponential is because it's easier to work with than sines and cosines; the reason we use only one part is because the electric field is a real-valued vector quantity. As for choosing the real part over the imaginary, that choice is arbitrary-it's essentially whether you want to describe the wave with a cosine function vs a sine: no real difference aside from a phase of π/2.
It does seem interesting that the Universe would point us to use a mathematical construct that only has half of its interpretive value in reality, there could be hidden realities or Dimensions where the imaginary and real components have a dual realized aspect but we can't perceive it
electromagnetic waves require no medium of propagation. The wave equation for electromagnetic waves can be derived directly from Maxwell's equations under vacuum conditions
Two get the idea that arrive result of EM wave from Faraday's Law to we have two things . These are Law of Faraday equation and Maxwell's contribution for Ampere's formula. From these two physical reality How Maxwell get the result of wave equation ? When I listen the lecture First of all they introduce diverge , curl and Laplacian etc. Secondly take the Ampere Maxwell equation and Faraday Law into the Laplacian vector calculus formula. Thirdly Ahaaa get the wave equation form of EM !! This is not the intuation behind the discovery of EM wave radiation and Faraday's Law according to me. You show eggs you show chicken and say Ahaaaa... this where does the wave equation come from. Instead of this way of calculation. Lessons should be told How did Maxwell realize line integral of E is linked to partial derivate of x(space coordinate of x) ? Otherwise you only turn around the idea of which one come first chicken or egg ? (
@@arnabmondal5124 He called it partial operator. Sometimes partial vector. But I don't care what he called it. Del is the name of that operator. If you take 18.02, you'll know all about it. Btw, it's not a real vector. It just a vector operator mathematicians made up to make their lives easier.
@@arnabmondal5124 If you're talking about partial derivatives, and not the vector operator, yes it's called partial(just the curly d). E.g dx/dt is called partial x partial t
It's something you'll have to get used to in academia if you want to progress. Smart people come from all backgrounds and none of them are required to be able to speak english with native-level clarity. You can understand him, I'm sure of it.
@@tensorbundle tensorbundle I can understand everything he was saying and I'm not even a native english speaker. And do you think a room full of native speakers can't understand him? Also, not everyone can change their accent easily.
@@tensorbundle His accent is very different from my country's accent. Our accent is very similar to indian accent. And you know his is far from it. But I can't understand it not because I'm an asian but because I'm a good listener and a good listener should be able to analyze the pattern of every accent he/she listened. And I bet MIT students are very good listeners. Btw, in America, you can't even get a student visa, let alone teach to a bunch of college students, if your English is a disaster.
@@tensorbundle You just argued yourself. Previously, you said it's a mental torture for students to listen to what he says and now you're telling me he's understandable just after 5/10 minutes which would be no trouble at all for students who are spending entire semester with him and not mental torture at all at this state of the semester. Ergo, renders your first argument invalid. Make up your mind, man! And if you want to start limiting accents, you are limiting yourself from a wide range of good professors who aren't native speakers at all. So, you're also limiting your education. That's why most international schools have a wide range of professors with very different accents(and most of them might not have a very good accent for your taste).
his voice is an impediment to understanding. to learn one must understand what teacher is saying? question? all waves travel using a sinusoidal motion , magnet sin, electric cos, system, if you remove the magnetic sin fraction wave what does the cos electric part do? why does energy use this binary function instead of just a straight line? does the sinusoidal motion itself propel the wave? and if this is true? can i take a wave segment cut it into smaller sections are turn there headings? as long as i get a full wave and not a fraction of one?
By definition, if you have a cos(wt+kx) like dependence on the electric field, you cannot remove the magnetic field because it would violate amperes law.
@@partyxday my view is if you made a device that could separate the electric wave from the magnetic wave? how would this possible with advanced technology and advances in the function equation cos(wt+kx) pull a derivative ?
@@curlyhum1276 you can’t do that. A changing magnetic field generates an electric field. Read a textbook on E&M for more details. This is fundamental in maxwells ewuations
2:05 maxwell's equations
5:30 review of vector calculus
12:20 solving Maxwell's equations in vacuum
17:20 solution - 3D wave equation
30:20 example solution: plane waves
56:17 plane wave interaction with a perfect conductor
1:11:39 Poynting vector of the standing wave
الشكر الجزيل للبروفيسور على هذا الشرح الرائع
والشكر الجزيل ل الجامعة الكريمة على نشر العلم!
للجامعة تكتب هكذا.
The fields do not cause each other. The fields originate from accelerating charges. The equality in Maxwell’s equations is NOT causality.
I’m still learning so I’m curious: if the fields do not cause each other then how would they propagate through a vacuum where there are no accelerating charges? Are you saying that accelerated charges will form the initial E and B fields, which then interact with each other to propagate through space to infinity?
@@dillonlabonte9685yes . Maxwells law proved that a changing electric field , by symmetry , is equal to the movement of an electron , meaning that the wave self propagates.
The fields at a distance are just the time delayed result of the charge movement. There is a good video on this from atom and sporks.
"So one cannot be without the other, so they live together, forever" God, he's so cute hahahha
Lol nobody is ralking about how he just drew those mutually perpendicular field so flawlessly
a wave is not a thing. it is what something does. that something is the medium.
beautifully said, but i would call that something the spacetime curvature
@@lil_ToT-XFZ1 even einstein in the end, in a letter to lorentz, concluded their has to be a medium. one null result does not disprove anything. further more i would like to add, these are not maxwell equations, they are heaviside equations. they are not the same. and to quote heaviside, " i took the baggage off of maxwell." this was in reference to the scalar component. i suggest everyone should read Elementary Lectures On Electric Discharges, Waves And Impulses, And Other Transients by charles protues steinmetz ( its free online)
Thank you, Professor! It was helpful.
UR WELCUM MY DELICIOUS FRIEND
Crazy he didn’t write a single number the entire lecture
Sir how you decide the reflected EM wave equation from perfect conductor.
I have been having this question in my head for quite some time, I hope somebody can help me wrap my head around the idea.
Please feel free to comment and correct any mistake in my thought process as I am sure I am missing something.
- So in this lecture it is shown how from Maxwell Equations, and under the assumption of vacuum (J equals to 0) we see that the EM wave equations are solutions of the Maxwell partial derivative equations (I assume there are other solutions as simply constant E and constant B, but I guess they are ommitted in the lecture as not interesting).
- So back to the EM, these waves are described in the complete space and time domain (ok, let's say for all (x, y, z) and for all t > 0). Is that correct?
- If this is true, at t = 0, there exists wave (maybe it is more accurate to say there exists E field and B field) in all the space, even beyond ct (even beyond the reach of the speed of light).
- I know the wave travels at c speed (this means, a wave peak travels at c speed along the propagation direction)
Knowing this, I am not sure what is understood by "Light taking X time to arrive to a place Y", if there is wave and field in all the space all the time. I guess what I am missing is that I may be confusing the presence of the field with the concept of a wave arriving at some place, maybe what needs to arrive is the perturbation (so the bending of the wave shape)?
Thanks for the help in advance.
The key here is that where you say that the fields exist in all space, even beyond ct, is not true. The fields need time to propagate. And the speed by which they propagate is at the speed of light. In other areas of analysis, such as say electrostatics, we assume the electric field for an electron has already propagated outwards to simplify the analysis. The propagation of the electromagnetic field is itself the motion of light, so it moves at light speed. There is no field present before the field reaches it.
The fact that light itself has a speed is evidence that the fields take time to propagate (and are not immediately present everywhere unto infinity). If not, for example, light from stars would reach us immediately.
Wish if Professor Yen-Jie Lee shows why the EM waves are transverses using Maxwell's eqs.
He really explains it well apart from his accent.
i have learned a lot .. thank you professor
Even WITH his accent, he explains it well. As someone who has the privilege of attending his lectures live, he is an incredible lecturer with passion and expertise for the subject and an amazing personality. Let's not caveat it with our prejudice against accents. The beauty of mathematics and physics is that it can transcend human language.
can u and ur room temperature iq shut up
@@FX-hf6sk Hs accent is better than my accent :)
@@FX-hf6sk I mean, lets be honest here, I'm not trying to sound like an asshole, but trying to listen to this was rough I gave up like 10mins into the lecture, communication skills and how smooth it is, is very important when it comes to teaching.
Accents take time to get used to, so if you tried again you might get further. Professor Lee does an incredible job communicating scientific concepts and the beauty of physics, and it’s recognized as he’s celebrated among MIT undergrads as an amazing physics professor and has tenure in the department. :) For all those that make honest and humble efforts, his accent does not get in the way of his teaching or research; only prejudice does.
Electro-Magnetic Wave (EMW) actually is Magnetic Wave (MW) , enough.!! Electric implication is they need Conductor/Media such as Copper wire, Electrolyte Liquid or Humid Air (in case Lightning Bolt).. the Magnetic Wave only need Empty Space.!! when strikes into Antenna/Receptor, it's Converted into small Electric pulse that can be Amplified or processed. Electricity then, also NOT Magnetic Wave b'cuz it need Conductor/Media (copper wire) but Magnetic Wave is Pure pulse of Energy, travelling through empty Space-Time at the Speed of Light.(!?!).
excelent this lecture. Thank you !!!!!!
Please upload the video of superconductivity
It's really helpful for me. Thank you
The poynting vector is energy per area per time
he' s just amazing
Why did he say without electromagnetic field you cannot see him?
Light is an electromagnetic wave. Light is responsible for vision. I guess.
One question.
What happen when f(x) < 0, and what happen when f(x) >0, I know about gradient and divergent, but my teacher ask my to demonstrate this condition, please help.
Also a situation ask us to evaluate the partial derivative at some point, the answer give a result of a negative number, but I don't know what it means.
Please what did he mean when he said the field is pointed to x but the direction is actually z ?
If you put a charge at a point in the E field, the E field will make it move in the x direction. This x direction-pointing E field spreads in the z direction.
@@hershyfishman2929thanks
A case wherein the div and curl occurs one after another within a short time interval,thus how can we create or measure the deviation of energy if there and quantify this by Potential energy.
Yen dropped a negative sign in the integration at ~43:30 or so.
Is canceled
In the traveling wave graph when the magnetic field and eletric field are both zero at some point, what's the energy at those points if it not equal to zero
?
In a travelling wave, the energy is propagated along the direction of propagation (starting from the source of EM waves). Therefore, energy, at any given point, will fluctuate from zero to a maximum value.
With a mathematical approach, evaluating E=e^i(kr-wt), amplitude is imaginary if the phase of the wave function is pi/2. Implementing it on physical world, it means that real light is somehow converted into imaginary light.
Por que nadie desarrolla las ecuaciones de Maxwell junto a las del material cuando rho y j valen cero
thank Prof.
What is the difference between pointing in x direction but propagating in positive z direction. If this is the case, then why the component of electric field is zero in z direction even when it is propagating in that direction? @34:20 minutes into video.
Well, imagine that a group of people is starts waving with arms from back to front, as it happens on stadiums. Although each individual rises his or her arm upwards and downwards, the wave itself propagates parallel to earth.
@@timurpryadilin8830 electric field will be always perpendicular to the direction of propagation of wave.
at 8 minutes when computing del cross A shouldn't the determinant be x^ - y^ + z^?
inside the bracket the terms are changed: - (A - B) = (B - A)
Try your personal equations in liquid solid or gas not in vacuum , there are liquids ,gases ,and solids , inside of us all , as well as inside and outside the earth , and being inside and outside the earth's atmosphere are similar in that regard the aether however is liquid I assure you . And the atmosphere's layer's can only be penetrated by discovering their design . EM waves it's in the game . Life.
why do we only consider the real part of the plane wave equation? why not the imaginary or entire complex value? for visualization purposes?
The reason we use the complex exponential is because it's easier to work with than sines and cosines; the reason we use only one part is because the electric field is a real-valued vector quantity. As for choosing the real part over the imaginary, that choice is arbitrary-it's essentially whether you want to describe the wave with a cosine function vs a sine: no real difference aside from a phase of π/2.
It does seem interesting that the Universe would point us to use a mathematical construct that only has half of its interpretive value in reality, there could be hidden realities or Dimensions where the imaginary and real components have a dual realized aspect but we can't perceive it
good
Thanks for helping. God bless u.
استخدام المعادلة الاتية يمكن المادة المضادة والتوالد والتكاثر في المادة وكذلك الاتصال بين العامة والكم F=E^2/hc=c^4/G مشكور
Sir which book you have preferred for this
Try Electrodynamics by David Griffiths.
Ap French
@@Upgradezz lol
Nice sir
Professor I have 1 question :
What is the medium of propagation for electromagnetic waves? on what ocean do they run?
electromagnetic waves require no medium of propagation. The wave equation for electromagnetic waves can be derived directly from Maxwell's equations under vacuum conditions
Mechanical waves require medium, electromagnetic waves don't
this is the prove of your failing country education.
aether
@@frankguo1363 aether doesnt exist
There's a small typo in the title. It's "Maxwell's Equations" - there's four of them (2 scalar + 2 vector, so arguably 8 in fact).
MIT expensive. understanding the lecturer?
Cosmoluzetion old
Two get the idea that arrive result of EM wave from Faraday's Law to we have two things .
These are Law of Faraday equation and Maxwell's contribution for Ampere's formula.
From these two physical reality How Maxwell get the result of wave equation ?
When I listen the lecture
First of all they introduce diverge , curl and Laplacian etc.
Secondly take the Ampere Maxwell equation and Faraday Law into the Laplacian vector calculus formula.
Thirdly Ahaaa get the wave equation form of EM !!
This is not the intuation behind the discovery of EM wave radiation and Faraday's Law according to me.
You show eggs you show chicken and say Ahaaaa... this where does the wave equation come from.
Instead of this way of calculation.
Lessons should be told
How did Maxwell realize line integral of E is linked to partial derivate of x(space coordinate of x) ?
Otherwise you only turn around the idea of which one come first chicken or egg ? (
12.16 yo, get a room
z piccolo quando è onda cambia Z grande quando è particella è come "e" forza motrice del buco nero
Time stamps would have been much better!!!
what does he call a partial derivative operator? is it partial?
Has no name, it is just call operator of partial derivative
It's called 'del'. You can google it.
@@thetaung3034 I think he's calling it partial.
@@arnabmondal5124
He called it partial operator. Sometimes partial vector.
But I don't care what he called it. Del is the name of that operator. If you take 18.02, you'll know all about it.
Btw, it's not a real vector. It just a vector operator mathematicians made up to make their lives easier.
@@arnabmondal5124
If you're talking about partial derivatives, and not the vector operator, yes it's called partial(just the curly d).
E.g dx/dt is called partial x partial t
I don't know but this teacher.... don't explain really good....
nice
👍
That accent tho'! I mean i am okay with different accents, but that one where he chews letters and words, bit difficult 😞! Thanks for the content tho!
U can turn on the captions CC
i thought this was in china, hmmm i thought that US hate china
(just a joke) thank you for the lectures
Almost impossible to follow the lecture. I am sure he is very smart guy and all that, but his English is barely understandable.
there is subs tho
It's something you'll have to get used to in academia if you want to progress. Smart people come from all backgrounds and none of them are required to be able to speak english with native-level clarity. You can understand him, I'm sure of it.
@@tensorbundle
tensorbundle
I can understand everything he was saying and I'm not even a native english speaker. And do you think a room full of native speakers can't understand him?
Also, not everyone can change their accent easily.
@@tensorbundle
His accent is very different from my country's accent. Our accent is very similar to indian accent. And you know his is far from it. But I can't understand it not because I'm an asian but because I'm a good listener and a good listener should be able to analyze the pattern of every accent he/she listened. And I bet MIT students are very good listeners.
Btw, in America, you can't even get a student visa, let alone teach to a bunch of college students, if your English is a disaster.
@@tensorbundle
You just argued yourself.
Previously, you said it's a mental torture for students to listen to what he says and now you're telling me he's understandable just after 5/10 minutes which would be no trouble at all for students who are spending entire semester with him and not mental torture at all at this state of the semester. Ergo, renders your first argument invalid.
Make up your mind, man!
And if you want to start limiting accents, you are limiting yourself from a wide range of good professors who aren't native speakers at all. So, you're also limiting your education. That's why most international schools have a wide range of professors with very different accents(and most of them might not have a very good accent for your taste).
😕😴😴😴😴 really is this MIT course :-(
What do you mean by this?
Welcome to China
his voice is an impediment to understanding. to learn one must understand what teacher is saying? question? all waves travel using a sinusoidal motion , magnet sin, electric cos, system, if you remove the magnetic sin fraction wave what does the cos electric part do? why does energy use this binary function instead of just a straight line? does the sinusoidal motion itself propel the wave? and if this is true? can i take a wave segment cut it into smaller sections are turn there headings? as long as i get a full wave and not a fraction of one?
By definition, if you have a cos(wt+kx) like dependence on the electric field, you cannot remove the magnetic field because it would violate amperes law.
@@partyxday my view is if you made a device that could separate the electric wave from the magnetic wave? how would this possible with advanced technology and advances in the function equation cos(wt+kx) pull a derivative ?
@@curlyhum1276 you can’t do that. A changing magnetic field generates an electric field. Read a textbook on E&M for more details. This is fundamental in maxwells ewuations