Lecture 3a -- Electromagnetic Waves

[@mehdidjait608]

When studying Electromagnetics in the university one could be quick to conclude that these topics are hard and it is not the fault of the professors if the explanations are never easy to understand... and then you stumble upon these lectures! Just WOW! DR. Raymond C. Rumpf you are on a whole other level

[@empossible1577]

Thank you!! I work on these lectures almost every day to keep improving and adding more content. Have you been the course website? empossible.net/academics/emp3302/

[@veranimus4302]

These are very helpful for me. Thank you for including that last visualization. The animation also seems to show the wave fronts propagating so that you can also see why its referred to as a plane wave.

[@jeremylangford4767]

I can’t thank you enough for that last visualization 🎉

[@BrodyPianist]

I really like the visualization at 23:15, showing each individual dipole in space propagating the E-M wave. It makes it much more intuitive to think of placing a scattering object (e.g. a sphere) somewhere in this box, and how the induced dipole moments within the sphere would look. In terms of your comment on visualization, I don't think you can do much better than this discretized slab of dipoles (in reality I guess it is like this, but with these points being infinitely close together - similar to your 'cloud' or 'fog' idea). Quick question, when you say "imply things that aren't necessarily physically accurate" - what do you mean? Thanks a lot for the channel content, it is very well presented. (I have a PhD in Physics and am learning a lot!)

[@empossible1577]

Thank you! It is an interesting problem for us to visualize electromagnetic waves. We are even thinking about how to do this for virtual reality and augmented reality. There is just a bit more information to convey than our senses can take in all at once.

[@allanc3945]

@@empossible1577 I suppose all that difficult-to-visualize information must swirl together somehow to form the even less visualizable QM photon model. Thank you for all the amazing content!!!

[@empossible1577]

@@allanc3945 Thank you!

[@1729malli]

Thanks for the video, I am interested in electromagnetics , espicially to know how to handle EMI/EMC on PCB's.I have a question here. You said H is E/377, so H is 3 orders of magnitude less than E, Here it is shown like H ~ E/5. But you said, in reality H is not weak, it's only because of units B is E/377. I didn't get intuitive feeling of this. How do i know more information on this.

[@empossible1577]

This is confusing. One example is comparing one object that weighs 2.0 pounds to another object that weighs 1.0 kilograms. The object with units of pounds has a bigger number, but in fact the 1.0 kilogram object weighs more. That is simply because different units were used. In electromagnetics, E and H have different units so it is not completely fair to just look at numbers to determine which is “stronger.” To be more rigorous, think about the energy carried by the fields. In vacuum, the energy in the electric field is eps0*E^2. The free space permittivity eps0 = 8.854e-12 F/m. The energy in the magnetic field is mu0*H^2 and the free space permeability is mu0 = 1.257e-6 H/m. Let’s just track orders of magnitude. We know H is three orders of magnitude smaller than E, but the quantities are squared. So H^2 is six orders of magnitude smaller than E^2. The constant mu0 is six orders of magnitude bigger than eps0, so overall eps0*E^2 is the same order of magnitude as mu0*H^2. Thus, both fields carry the same amount of energy.

[@1729malli]

@@empossible1577 Thanks for the reply. I understood the reason and i am clear. I am thinking on the measurement perspective. If there is a way to measure D,B and E,H and see thier magnitudes difference.

[@empossible1577]

@@1729malli Measuring them separately...hmmmm....not sure....what frequency?

[@meghjitmajumder3468]

1. "Visualization of EM Field" part is fantastic!! 2. Suggestion: From 2:00 to 3:00, when you show that how oscillating E-field creates H-field which in turn...and so on. I am wondering that after showing the animation part by part if you'll show all that once again in a complete slide, that would be great!! 3.Question: Why positive exponent represents a backward wave while negative represents forward?

[@empossible1577]

1. Thank you!! 2. I like the idea! I made of note of it on my slides. 3. It is just a sign convention thing. A wave travelling in the +z direction is written in the positive sign convention as sin(kz-wt) and in the negative sign convention as sin(wt - kz). Both ways work. The physics/optics community tends to use the positive sign convention while engineers tend to use the negative sign convention. It can be very confusing! Here is a link to a summary sheet for sign conventions. empossible.net/wp-content/uploads/2018/03/Summary-of-EM-Sign-Conventions.pdf

[@한두혁]

Hello sir I have a question...When deriving wave eq from Maxwell's eq, most test book apply curl to both side of the curl eq. And then substitute the remaining curl eq.(Where your derivation makes more sense to me) But how do you expect the same solution from it? Does applying differential operator to both side of differential eq leave the form of solution unchanged? (Like adding/multiplying scalar to both side of an equation) Thank you!

[@empossible1577]

In essence, both approaches are substituting one curl equation into the other to derive a wave equation in terms of just a single field quantity. The problem with the approach of starting by calculating the curl of both sides is that this approach can only derive the wave equation in a homogeneous medium. That is because there is a permittivity or permeability left inside of the curl and you will not be able to use other other curl equation to eliminate it. The approach I take can still derive a wave equation valid for inhomogeneous media.

[@한두혁]

@@empossible1577 Thank you! But my question was..Does the solution of D.E(differential eq) remain unchanged after applying differential operators to both side of the D.E? I havent thought of it seriously before but I got curious..Thankyou.

[@empossible1577]

@@한두혁 Well, you have take the curl of both sides so that is different. I think otherwise, it is still a general equation. The problem is that you cannot take the permittivity or permeability outside of that curl option unless you assume the medium is homogeneous.

[@salmagamal5676]

Again, thank u sir.

[@khaledalhorani7965]

Thanks a million! Which textbook you recommend for the EM applications?

[@empossible1577]

There are many good choices. I teach using Sadiku's book. www.amazon.com/Elements-Electromagnetics-Electrical-Computer-Engineering/dp/0190698616/ref=sr_1_1?keywords=sadiku&qid=1572928748&s=books&sr=1-1

[@khaledalhorani7965]

@@empossible1577 Thanks! I'm so grateful :D

[@nasserhussain5698]

@@empossible1577 I'm using this book too in Iraq, teaching the introduction to electromagnetism.

[@empossible1577]

@@nasserhussain5698 Hello Iraq! Great to see you here!

[@nathanielkilmer5022]

Is it really fair to say that the magnetic field is 3 orders of magnitude "smaller" than the electric field? I would imagine the "size" of the field to be proportional to the force it exerts on charged particles, not the number assigned to it. Or are the force effects for those fields also 3 orders of magnitude apart?

[@empossible1577]

I am not referring to size or even to energy content. We have chosen units that make the magnetic field numerically around three orders of magnitude less than the electric field. It would not make sense to confuse amplitude of an electromagnetic wave with size or distance. Sorry for any confusion!

[@nathanielkilmer5022]

@@empossible1577 No worries! I just recall my physics professor warning us not to be deceived by the "small" number related to magnetic fields, because a small magnetic field could create a huge force. Thanks for the reply!

[@isaganicomia4958]

Thanks sir.

[@empossible1577]

Thank you! I am very glad the lectures are helping you!

[@carmelpule8493]

I propose that the best manner to show E/M waves is to be practical and less theoretical and in a plane wave it is all theoretical and it does not exist. All E and M field come in loops, loops and more interlaced or curled loops, I do not like the diagram shown at 21:46 as the Magnitude of the Fields need to coincide with the curl of the other or the maximum rate of change, That diagram would be fine if the sketch was rotating, as the rate of change of the Magnetic vector projected component will show the maximum curl coinciding with the maximum values of E and M components. The shown wave is polarised then there is no rotation and so the rate of change of the Magnetic field and the Electric field must emerge from the TRANSLATION along the radiated distance and so the diagram needs to be modified. As it is the diagram makes it difficult to see how the E and M fields loop or curls one another, A single vertical dipole would first create the Vertical E field and that will be followed later by the circulating M field. The whole pattern of loops will be like the anchor chain made up of quadrature loops being emitted in sequence along one axis. with their necessary phase changes in time and in space along the path of transmission, One can use these loops to describe a plane wave if one looks microscopically at a space close to the centre of the chain. Showing the E/M loops will facilitate the situation, and in my opinion it will even clear some of the misconceptions brought about by showing that diagram which appears in many books and which I am very hesitant to use, I find it very helpful to mix together the time angular component e^jwt , the space angular component e^-jkz and their rate of change jw e^jwt and --jk e^-jkz Using a graphical plot on a circle depicting B= e^jwt then dB/dt jw e^jwt at 90 degrees, then --dB/dt by a reversal, and these rotation will depict the Electric component E , then dE/dt will rotate to agree with B The same can be made with the space derivatives, say Bx and Ey where the curl of Bx= j dBx/dz and curl of Ey= -idEy/dz. and plotting curl of Bx and the curl of Ey using reverse rotation will give the full picture of Maxwell equation on a single circular diagram, Sounds complex, but it is not, and it will clear many issues about the representation of how EM field behave, including how circular polarised wave travels and translates, but does not rotate, Only the vectors sources at the transmitter rotate, but once vectors of the B and E are launched, they all keep their particular polarization all the way to the receiver, unless a purposeful rotating medium is introduced. .

[@empossible1577]

Have you created anything like this for us to see?

[@carmelpule8493]

@@empossible1577 Yes actually I made wooden models of all I said using kebab sticks as vectors. Unfortunately being an old man, I have not kept up to date with using modern equipment to send videos but I shall ask my daughter to do it for me. Here is what I made. I assumed that the By field is (1/c) Eo (e^jwt)(e^-jkz) e^jpi/2 Ex field is Eo (e^jwt)(e^-jkz) These were shown by inserting three sticks one representing the x axis the other the y axis and the third the z axis assumed to be the direction of propagation. This system ensured that the By is in space quadrature with Ex and both in space quadrature with the z direction. Then since the Time rate of change is due to e^jwt = jw e^jwt dB/dt and another stick in the xy plane was included at 90 degrees to represent the j due to the rate of change of time while with a rate of change of space -j was involved and so a --90 degree rotation was used. All other vectors in Maxwell's equations were added and the mathematical relations obtained from the geometry of the resulting model, It seems to work correctly.

[@empossible1577]

@@carmelpule8493 The problem with loops and plane waves is that plane waves are of infinite extent so there really is not a loop to draw. In this sense, plane waves are unrealistic.

[@carmelpule8493]

@@empossible1577 So true, thank you for replying. Still, E/M waves are fascinating.

[@nasserhussain5698]

Please Sir, I couldn't reach your lecture notes when I go through your university website emlab.utep.edu/academics.htm where the link is invalid or something wrong

[@angelacabyzhong8412]

Hi, sir ,what software do u use to do the visualization part?

[@empossible1577]

The animations in this video were created using MATLAB. I also use Blender, which is an open-source modeling and animation tool.

[@angelacabyzhong8412]

CEM Lectures Thank you sir!