How is E&M done in the real world?

[DrummingAtom]

I'm currently taking the EE version of E&M 1 this semester and I'm fairly disappointed in how my professor is handling the material. Every problem is highly symmetric I honestly haven't actually evaluated an integral all semester. The integrals are just remembering the surface area or volume of a sphere. I have been trying to make sure I understand what a curl, divergence, etc. really are by evaluating them in a step by step process but it's never needed. I don't feel like I'm getting anything close to the tools needed to solve a non-symmetric E&M problem.

In my circuits classes, I figured out that node voltage is extremely powerful and I think I could actually come up with some ways to deal with more difficult circuits using MATLAB. Is Maxwell Equations similar? If I could find the proper conditions could I basically solve Maxwell's Equation to get the answer?

 

[ZapperZ]

Open Jackson's Electrodynamics text and solve problems from the first 3 chapters. You'll regret you asked for such things.

Zz.

 

[jasonRF]

It turns out that we can usually only find exact analytical solutions to problems that have relatively simple geometry - sometimes approximation techniques can be used to get useful approximate solutions to more difficult problems. So for designing real antennas, actual microstrip circuit board layouts, etc., computer simulation is necessary. However, often analytical solutions to similar simplified problems yields to much insight and can be essential in formulating the initial design that is then refined by simulations (the simulation does not produce a design from scratch, it just allows you to evaluate a given design).

Having said that, I am somewhat surprised that your EM course is "taking it so easy" on you. On the other hand, I have noticed that at the university I attended, the once year-long upper division EM sequence is now only a single semester and supposedly covers even more topics (and it is no longer required for EE majors!) - so mathematical details/techniques MUST be missing, and they are likely teaching it more like your course.

I'm guessing their goal is for you to understand the various phenomena, thinking that those of you that will need to know more details can teach yourselves the required math. In fact, the best way to think about your education is that it is supplying you with the tools you need in order to teach yourself the rest of what you actually need to learn in order to be a good engineer. So make sure you are at least learning the important concepts and how to apply them, and understanding how the professor/book derives the formulas that you are using. In fact, much of higher level electromagnetics (especially engineering electromagnetics) courses are not teaching you new physics, but teaching you more and more sophisticated mathematical techniques for finding exact and approximate solutions to Maxwell equations. Often times these more sophisticated techniques provide the foundations for the more successful numerical approaches as well.

jason

 

[ModusPwnd]

This is one of my complaints about E&M and physics classes in general. They appeal to special geometries/symmetries and special functions. This is a relic of the past when numerical methods were not as powerful. In the real word you don't reduce your problem to a nice symmetry so you can use some ad-hoc special function. You use a computer. The only reason to do that is to pretend you have a closed form solution and because you are teaching and following a tradition that is generations old.

 

[jtbell]

Every problem is highly symmetric I honestly haven't actually evaluated an integral all semester. The integrals are just remembering the surface area or volume of a sphere.

Is this the second semester of calculus-based intro physics, or an intermediate/upper level course that comes afterwards? What textbook are you using?

 

[DrummingAtom]

Is this the second semester of calculus-based intro physics, or an intermediate/upper level course that comes afterwards? What textbook are you using?

It's a junior level EE course. Text book is Introductory Electromagnetics by Popovic and Popovic.

 

[DrummingAtom]

In fact, much of higher level electromagnetics (especially engineering electromagnetics) courses are not teaching you new physics, but teaching you more and more sophisticated mathematical techniques for finding exact and approximate solutions to Maxwell equations. Often times these more sophisticated techniques provide the foundations for the more successful numerical approaches as well.

jason

Actually that is exactly what I was expecting from this course, more math. I actually checked out Cheng's EM book and I like it because the math is always there.The textbook I'm using jams all the vector calculus stuff into the appendix and we never once talked about it. I have a very good feeling that I won't be ready at all if I decide to venture into a more difficult EM course later on unless I backtrack and learn a bunch on my own. I've been trying to keep up my vector calculus skills during this course but there's just other stuff to do and since I'm not being tested on it I can't justify taking time to do it.

 

[jasonRF]

This is one of my complaints about E&M and physics classes in general. They appeal to special geometries/symmetries and special functions. This is a relic of the past when numerical methods were not as powerful. In the real word you don't reduce your problem to a nice symmetry so you can use some ad-hoc special function. You use a computer. The only reason to do that is to pretend you have a closed form solution and because you are teaching and following a tradition that is generations old.

Of course there is truth in your statement. My grad advisor was surprised that we were still deriving Green's functions in grad EM class, stating, "Why do they teach you that? Don't we just use numerical simulations do solve things these days?" But he was in the minority among the academics it seems.

The best counter argument I have, is that physical insight can often be found in solutions of "toy" problems. Simply deriving exact analytical solutions which are typically in forms of infinite series of yucky functions or integrals that no one can evaluate exactly doesn't help with understanding - it is an exercise in applied math. However, in my opinion insight can come from approximate solutions (asymptotic and small argument expansions, etc), or from actually plotting exact solutions (movies of exact solutions can be quite insightful!). Parametric investigations using numerical simulations can yield lots of insight as well, but sometimes CPU time can become an issue.

Ideally engineering students should learn both, but there is a limited amount of class time so something has got to give. I hope universities are experimenting with different approaches to determine what works best...

 

[DrummingAtom]

My grad advisor was surprised that we were still deriving Green's functions in grad EM class, stating, "Why do they teach you that? Don't we just use numerical simulations do solve things these days?" But he was in the minority among the academics it seems.

As much as I complained about my circuits classes they had a great blend of deriving results and using simulations with computers. MATLAB and Spice were constantly used in projects and homeworks. I felt that the mix of those two things gave me a nice idea of how a circuit works. By the end of the semester, I could almost feeling what a circuit was doing even if I never worked out a solution for it. Does anyone know of a book that maybe ties in MATLAB or some kind of programming with E&M? Maybe I'll try doing that over the summer to help my understanding.

 

[Lavabug]

Actually that is exactly what I was expecting from this course, more math. I actually checked out Cheng's EM book and I like it because the math is always there.The textbook I'm using jams all the vector calculus stuff into the appendix and we never once talked about it. I have a very good feeling that I won't be ready at all if I decide to venture into a more difficult EM course later on unless I backtrack and learn a bunch on my own. I've been trying to keep up my vector calculus skills during this course but there's just other stuff to do and since I'm not being tested on it I can't justify taking time to do it.

I used Cheng's book for my 2nd electromagnetism course, mainly for the bits on resonant cavities/waveguides and transmission line theory, it was pretty good.

Simple geometries are meant to illustrate concepts, "toy models" if you will, some of which are actually good enough for real life situations. A simple ferromagnetic circuit problem gives a fairly good estimate of how much a weight a C-shaped dumpster electromagnet can lift for a given current, for example. The experiment using a spinning copper wheel can give a good estimate of the Earth's magnetic field too, something that can be calculated analytically in 2 lines, no integrals required.

At the end of my first EM course we were proposed a few "challenges" in electro/magneto-statics which produced integrals that didn't have exact analytical solutions to drive home the point that there's much more to the subject than what can be covered in 2 or 3 semesters and that a "serious" problem is never as pretty as the carefully designed problems in textbooks. I envy the EE's/graduate EE's that get to take computational courses solving for fields in all kinds of geometries.

IMO I wish I had more EM as an undergrad (just had first year intro + 1 year at the sophomore level), but hopefully I'll get a chance to meet it again at the graduate level with Jackson's text, I actually WANT to.

 

[jasonRF]

Actually that is exactly what I was expecting from this course, more math. I actually checked out Cheng's EM book and I like it because the math is always there.The textbook I'm using jams all the vector calculus stuff into the appendix and we never once talked about it. I have a very good feeling that I won't be ready at all if I decide to venture into a more difficult EM course later on unless I backtrack and learn a bunch on my own. I've been trying to keep up my vector calculus skills during this course but there's just other stuff to do and since I'm not being tested on it I can't justify taking time to do it.

We used Cheng for the first semester junior level class - covering the first 8.5 chapters. I really like how clearly the analysis is presented, although sometimes Cheng doesn't give the most physical interpretation. It was taught by a theoretical plasma physicist, so it was more of a mathematical approach. For second semester junior year (an optional course that most students chose to not take) we used Ramo, Whinnery and Van Duzer. I still refer to both of those books often.

I would guess that the later EM courses at your university take into account the content of your current course (at least I would hope so!) so you are probably fine. If you switch schools, however, then you may be up for a little challenge! Don't worry about trying to supplement your course during the semester. You will likely not have time to do that, and it is important to do well in your current courses. If you are motivated and finding that you are bored during summer evenings you can always work through some more mathematical problems.

 

[jasonRF]

I used Cheng's book for my 2nd electromagnetism course, mainly for the bits on resonant cavities/waveguides and transmission line theory, it was pretty good.

IMO I wish I had more EM as an undergrad (just had first year intro + 1 year at the sophomore level), but hopefully I'll get a chance to meet it again at the graduate level with Jackson's text, I actually WANT to.

I understand - I now feel lucky that I was able to take a reasonable amount of EM undergrad (1 year at sophomore level from physics department, one year at junior level from EE, plus senior courses in microwave engineering and antennas/propagation). My grad department (actually stayed at same university) didn't have a lot of courses - one course that was (somewhat loosely) based on Jackson, and one that was (very loosely) based on "field theory of guided waves" by Collin. Today the department has dropped both grad classes and reduced the undergrad as well. Places like Ohio State are known to have TONS of EM classes.

The problems in Jackson's book are very hard, and involve lots of (at times tedious) calculations. The relativistic electrodynamics parts are rough for EEs - Jackson presumes you have already seen this out of Griffiths or Marion&Heald. My prof taught it easier (closer to Griffiths treatment), since he was assuming we had EE backgrounds, not physics. I don't think it is the best book for EEs, and very few EEs ever need relativistic electrodynamics! Our department did but we had essentially no traditional engineering electromagnetic research taking place - mostly plasma physics. For EE, Balanis (advanced engineering electromagnetics) is better, Harrington (time harmonic electromagnetic fields) is better, and Kong (electromagnetic wave theory) is better. I suspect the new and interesting looking book by Jin (theory and computation of electromagnetic fields) is good as it combines analytical and numerical analysis, but I have not had a chance to do more than flip through it. Jin is a prof. at Illinois which has an excellent electromagnetics group. It appears to be a slightly new breed of book, and probably takes the direction talked about in this thread.

jason

 

[ZombieFeynman]

If you want a more mathematical alternative, I must suggest Zangwill Modern Electrodynamics.

Although it is in its first printing, I would not be surprised if in a decade it sees more use than Jackson.