Lecture 3e -- Skin Depth & Power Flow

This lecture discusses skin depth and power flow for electromagnetic waves, including Poynting's theorem.

[@user-qd8li6zv7u]

You are just simply one of the best instructors the world has ever seen. Thank you so much!

[@empossible1577]

Thank you!!

[@pato42479]

Thanks a lot from the depths my heart

[@empossible1577]

You are welcome! I am very glad the material is helping you! Here is a link to the official course website where you can download the latest version of the notes, get links to the latest version of the lectures, and get other resources. empossible.net/academics/emp3302/

[@babotvoj]

Hello, I have problems in understanding of losses in conductive medium. I understand the mathematical part but I have problems to imagine it out of the Maxwell equations. So a magnetic field creates an electric field. And that field creates a magnetic field and a current? How does the field lose the energy to the material? Does the electric or magnetic field induce the current?

[@empossible1577]

Both magnetic and electric fields can push charges in addition to inducing other fields. Due to loss mechanisms at the atomic scale, some of that energy is not maintained in the wave and is converted into other forms. You can think of it as the charges crashing into other charges and thus causing vibrations in the atoms. It is these vibrations that we observe as heat.

[@babotvoj]

@@empossible1577 Thank you for your answer, it clarified it a little bit for me. But it opened up some new questions. Is there an electrodynamics explanation how the material interact with the wave or is the quantum mechanical the only one? And the loss term comes from the Ampere-Maxwell law. Is it possible that the E amplitude is split up into J and H?

[@empossible1577]

@@babotvoj The explanation that I think is most intuitive is the Lorentz oscillator model. This models bound charges as a mass on a spring. An equation of motion is written for the system and through a series of steps comes an equation for the permittivity due to an atomic scale resonance. The equation explains a lot of things like loss, dispersion, etc. Real materials have multiple resonances that overlap so the behavior can look a bit different that of a single resonance. Then in conductors, the charges are not bound and so the restoring force term disappears and the Lorentz model reduces to the Drude model. See Lecture 2 here: emlab.utep.edu/ee5390em21.htm

[@rahultheytv5347]

best explained sir

[@empossible1577]

Thank you!

[@meghjitmajumder3468]

Ok, so one silly question and one suggestion ahead.. Silly question: About the instantaneous power flow, how is the first term treated as constant when it decays? I mean how can we consider an exponential decaying term as constant? Suggestion: Sir please don't mind but for the first time, I'm little bit of disappointed with your animation (power flow). You can give it a thought.

[@empossible1577]

Happy to answer any question! 1. The first term does decay with distance due to loss. However, it is constant over time. There are no oscillations. The first term represents a steady (steady over time, not space) flow of power in the z direction. 2. What would you suggest to improve the power flow animation? Being new to the subject, I think you are actually in a better position than me to help with this. I am very open to suggestions! Thank you!

[@meghjitmajumder3468]

@@empossible1577 1. Thanks, sir for the explanation. 2. I don't know maybe if the power flow is shown separately or just with the E-field. Actually, the main subject of that animation which is "the power flow" and the changes in the flow along with the changes in the associated fields (i.e E & H-fields)isn't very clear. In this context, I'd like to say that, you can think of the style of "Physics videos by Eugene".

[@empossible1577]

@@meghjitmajumder3468 I will check it out