How Can Electromagnetism Be Simplified for Effective Learning?

[Illuminerdi]

Does anyone know of any way to compartmentalize electromagnetism into much simpler material to work with? Let me clarify what I mean—Mechanics is very easy (at an undergraduate level) because knowing ∑F=ma and basic knowledge of Calculus and Differential Equations can lead to instantaneously deriving every formula.

Are there ways to better compartmentalize problem solving strategies with electromagnetism that anyone knows of? I operate best when I have the most robust methods.

 

[DragonPetter]

Does anyone know of any way to compartmentalize electromagnetism into much simpler material to work with? Let me clarify what I mean—Mechanics is very easy (at an undergraduate level) because knowing ∑F=ma and basic knowledge of Calculus and Differential Equations can lead to instantaneously deriving every formula.

Are there ways to better compartmentalize problem solving strategies with electromagnetism that anyone knows of? I operate best when I have the most robust methods.

I'm not sure exactly what you mean, but EM is compartmentalized in a number of ways.

One is that the problems can be classified as dynamic or static, where in static you can have just an electric or magnetic force field that does not vary with time, and in dynamic you have both varying with time and coupled to each other which can create radiation of the field as well.

EM is also compartmentalized into 4 laws, and each law has specific applications, simplifications, and forms. Most introductory physics books don't even organize these as Maxwell's equations, even though the laws are what his equations describe.

For example, you would use Gauss' law of electric fields to analyze problems involving capacitors or other static electric fields. When you first learned about capacitors, you were probably applying Gauss' law.

You would use Faraday's law of induction to analyze problems involving motors.

And many problems incorporate all of the laws.

 

[Illuminerdi]

I'm not sure exactly what you mean, but EM is compartmentalized in a number of ways.
Most introductory physics books don't even organize these as Maxwell's equations, even though the laws are what his equations describe.

For example, you would use Gauss' law of electric fields to analyze problems involving capacitors or other static electric fields. When you first learned about capacitors, you were probably applying Gauss' law.

You would use Faraday's law of induction to analyze problems involving motors.

And many problems incorporate all of the laws.

I know Maxwell's Equations are PDEs, which I don't really know how to work with. Is there a good resource for getting a working knowledge of PDEs enough to manipulate Maxwell's Equations to all forms necessary at an undergraduate EE level?

*I find that I understand something far more when I'm capable of deriving it on my own.

 

[DragonPetter]

Also, can you please tell us what way you have to compartmentalize EM problem strategies now? Asking for better ways to compartmentalize it without tellings us the current way you are doing it is impossible since we have nothing to compare.

 

[Illuminerdi]

Also, can you please tell us what way you have to compartmentalize EM problem strategies now? Asking for better ways to compartmentalize it without tellings us the current way you are doing it is impossible since we have nothing to compare.

I really don't have much of a strategy. I can reduce circuits easily, but that's simple. I know Gauss's Law, Ohm's Law, Kirchoff's Laws, the DifEQs for RLC circuits, Ampere's Law, Faraday's Law, Lenz's Law, Biot-Savart Law...it's a lot and it just seems like I need something far more general that gets me the information I need without hesitation and allows me to have a better understanding of what I'm doing. I can always do dimensional analysis if I'm stuck, but that's not as robust of method as knowing the most fundamental equations to work with.

 

[DragonPetter]

I really don't have much of a strategy. I can reduce circuits easily, but that's simple. I know Gauss's Law, Ohm's Law, Kirchoff's Laws, the DifEQs for RLC circuits, Ampere's Law, Faraday's Law, Lenz's Law, Biot-Savart Law...it's a lot and it just seems like I need something far more general that gets me the information I need without hesitation and allows me to have a better understanding of what I'm doing. I can always do dimensional analysis if I'm stuck, but that's not as robust of method as knowing the most fundamental equations to work with.

Well, I don't think you can get much more general than Maxwell's equations. Those reduce all of the things you listed into 4 equations. The problem with such a robust and powerful set of equations is knowing how to use them, which brings you back to expanding out to the special cases you described.

I guess learning how to use and apply those 4 laws in all cases is what you're looking for. I'd recommend Griffiths introductory to EM since it shows how to solve and apply the math.

The main difficulty is the application of those laws, and its often very complicated if not analytically impossible. That's why in the capacitor example, you assume very simple geometries.

 

[yungman]

I second Griffiths. I have many EM books, none of the engineering EM book have good explanation on the basic electromagnetics because a lot of the material thing is not exactly the most important for EE. EE electromagnetics books more emphasis on Transmission lines, EM wave, Smith Chart that is so so important for EE, but they all kind of lax on the physics side. You really need two books to understand EM...Griffiths "Introduction to Electrodynamics" and Chengs " Field and Wave Electromagnetics". Those are the best two I've seen.

Regarding to familiar and use the Maxwell's equation, the only way I found is to do the exercises on different books, study one book after another, each give you different insight. It takes a while to really get the feel of the subject.

As for PDE, I did stop and spent 10 months studying PDE. There is really no easy way, but for undergrad, I don't think you need too much other than in Chapter 4 or chapter 5 of either book where it deal with boundary wall. But to really understand and go beyond rectangular coordinates, you have to get into Bessel's Function for cylindrical coordinates and Lagendre Function for spherical coordinates. A lot of the numerical analysis type of math. I feel it really give me much more insight and appreciation of EM after studying PDE.

If you work through the exercise of Griffiths particular the chapter 10 onward, it is like an advanced course of vector calculus. You need to have good understanding on the meaning of divergence and curl...not the math part, but "see" the divergence and curl.

IT takes time, took me over two years ( over three years counting the 10 months I dropped everything and studying PDE in between) to actually feel comfortable in the two books mentioned. I don't even dare to say I understand as there are a lot more ahead of these...this is only undergrad. But for EE, I think that's enough unless you want to specialize in EM in grad school.

There are only 6 equations, 4 maxwell's and one continuity and one Lorentz force, but it is going to take a while to really "feel" it. Keep going over and over, one day you will feel like a light bulb turn on inside you.

 

[Illuminerdi]

I second Griffiths. I have many EM books, none of the engineering EM book have good explanation on the basic electromagnetics because a lot of the material thing is not exactly the most important for EE. EE electromagnetics books more emphasis on Transmission lines, EM wave, Smith Chart that is so so important for EE, but they all kind of lax on the physics side. You really need two books to understand EM...Griffiths "Introduction to Electrodynamics" and Chengs " Field and Wave Electromagnetics". Those are the best two I've seen.

Regarding to familiar and use the Maxwell's equation, the only way I found is to do the exercises on different books, study one book after another, each give you different insight. It takes a while to really get the feel of the subject.

As for PDE, I did stop and spent 10 months studying PDE. There is really no easy way, but for undergrad, I don't think you need too much other than in Chapter 4 or chapter 5 of either book where it deal with boundary wall. But to really understand and go beyond rectangular coordinates, you have to get into Bessel's Function for cylindrical coordinates and Lagendre Function for spherical coordinates. A lot of the numerical analysis type of math. I feel it really give me much more insight and appreciation of EM after studying PDE.

If you work through the exercise of Griffiths particular the chapter 10 onward, it is like an advanced course of vector calculus. You need to have good understanding on the meaning of divergence and curl...not the math part, but "see" the divergence and curl.

IT takes time, took me over two years ( over three years counting the 10 months I dropped everything and studying PDE in between) to actually feel comfortable in the two books mentioned. I don't even dare to say I understand as there are a lot more ahead of these...this is only undergrad. But for EE, I think that's enough unless you want to specialize in EM in grad school.

There are only 6 equations, 4 maxwell's and one continuity and one Lorentz force, but it is going to take a while to really "feel" it. Keep going over and over, one day you will feel like a light bulb turn on inside you.

Thank you.
What I'm studying is biosignal processing and bioimaging.

* P.S., Does anyone have links to PDF files of the aforementioned textbooks?

 

[yungman]

Thank you.
What I'm studying is biosignal processing and bioimaging.

* P.S., Does anyone have links to PDF files of the aforementioned textbooks?

Go on the web and look for free download. Not only you can get the PDF of both books, I got the solution manuals for both online! Shhhhhh, don't say it too loud!

You are not even in this field, why do you want to get so deep into this? You don't need any of these stuff. This is about the most difficult part of EE and I am sure it's no picnic for the physics people.

Sounds like you really need PDE for your major. there are a lot of Fourier Transform in Imaging and signal processing that you learn in PDE.

Two PDE books that I think is quite good. PDE by Asmar used by San Jose State is about the simplest book, it gives you a good start and is easy to understand. But it is too simple, there are a few section that is lousy to put it politely. The chapter on D'Alembert is bad, it is border line miss informing. The Green's function is not it's bright spot either. It only cover 2D Green's Function, not that bad but could be better. Asmar might not be deep enough, I supplement with Strauss which is very good book but kind of condense to use as a primary book.