How Can I Best Prepare for My Second Semester in Electromagnetism?

[Nano-Passion]

I would like to prepare for my second semester of physics in electromagnetism. Its exciting because its my first taste of physics that isn't all about kinematics and dynamics.

What are good ways to prepare for electromagnetism? I don't want a rudimentary and superficial understandings. I went through my physics book and found the chapters periodic motion and mechanical waves to be very interesting. Would that be a good start?

Perhaps studying vector fields and vector spaces would help?

 

[SophusLies]

I would like to prepare for my second semester of physics in electromagnetism. Its exciting because its my first taste of physics that isn't all about kinematics and dynamics.

What are good ways to prepare for electromagnetism? I don't want a rudimentary and superficial understandings. I went through my physics book and found the chapters periodic motion and mechanical waves to be very interesting. Would that be a good start?

Perhaps studying vector fields and vector spaces would help?

Vector fields yes, but not vector spaces.. Where did you get that idea? What did your first semester of EM cover?

 

[niklaus]

Vector calculus sure would help too.

 

[jtbell]

In the USA, vector calculus is normally not a prerequisite for the second semester of freshman physics. The course introduces some concepts of vector calculus: surface and line integrals, and the gradient, but probably not the divergence and curl. Maxwell's Equations are presented in their integral forms, not the differentlal ones (with divergence and curl). The integrals use examples that usually (because of their symmetry) make the integrals themselves almost trivial. (I call them "Geico integrals": so easy a caveman can do them.)

I think the most important skill you can bring to this course is an ability to visualize in three dimensions what diagrams on paper have to present in two-dimensional form: patterns of electric and magnetic fields (vectors or field lines) around charges, conduductors, etc.

 

[dextercioby]

I would kindly recommend the Feynman lectures, because his pace is great and explanations clear.

 

[Nano-Passion]

Vector fields yes, but not vector spaces.. Where did you get that idea? What did your first semester of EM cover?

Actually this will be my first semester of electromagnetism. It's basically going to introduce Gauss' law, Maxwell's equations, electric and magnetic fields, etc.

Vector calculus sure would help too.

Hmm, any idea on what specifically?

In the USA, vector calculus is normally not a prerequisite for the second semester of freshman physics. The course introduces some concepts of vector calculus: surface and line integrals, and the gradient, but probably not the divergence and curl. Maxwell's Equations are presented in their integral forms, not the differentlal ones (with divergence and curl). The integrals use examples that usually (because of their symmetry) make the integrals themselves almost trivial. (I call them "Geico integrals": so easy a caveman can do them.)

I think the most important skill you can bring to this course is an ability to visualize in three dimensions what diagrams on paper have to present in two-dimensional form: patterns of electric and magnetic fields (vectors or field lines) around charges, conduductors, etc.

This should be fun, I'm a good visualizer. Now would it help if I studied periodic motions and mechanical waves? Electromagnetism does deal with a considerable amount of waves anyways?

I would kindly recommend the Feynman lectures, because his pace is great and explanations clear.

Okay, I will look into that.

 

[homeomorphic]

Vector fields yes, but not vector spaces.. Where did you get that idea? What did your first semester of EM cover?

Actually, I think vector spaces might help in the long run (so that you can bring differential forms into the picture, among other things), but probably not for a first course.

I don't want a rudimentary and superficial understandings.

That's a good attitude, but in a first course, particularly in this subject, it's not expected that you'll have the deepest level of understanding. I don't think I minded this when I took it for the first time, and I'm very fussy about this sort of thing. My memory of it is mostly overshadowed by the next electromagnetism class I took, so it could be that I didn't know what I was missing. Obviously, I understood it a lot better after the second class. As long as you learn it in the long run, it's okay if it takes two passes to do it. My third E and M class, with the EE dept. was a major factor in my decision to change majors to math because I couldn't stand the way it was taught. Very shallow, black-box type stuff. So, beware of electrodynamics. To this day, I still haven't completely come to terms with the subject, although I found that Feynman had some nice discussions of what makes those EM waves tick in his book (my favorite is the one with the sheet of moving charge producing a plane wave and the calculation of the speed of light going along with it).

 

[Nano-Passion]

Actually, I think vector spaces might help in the long run (so that you can bring differential forms into the picture, among other things), but probably not for a first course.



That's a good attitude, but in a first course, particularly in this subject, it's not expected that you'll have the deepest level of understanding. I don't think I minded this when I took it for the first time, and I'm very fussy about this sort of thing. My memory of it is mostly overshadowed by the next electromagnetism class I took, so it could be that I didn't know what I was missing. Obviously, I understood it a lot better after the second class. As long as you learn it in the long run, it's okay if it takes two passes to do it. My third E and M class, with the EE dept. was a major factor in my decision to change majors to math because I couldn't stand the way it was taught. Very shallow, black-box type stuff. So, beware of electrodynamics. To this day, I still haven't completely come to terms with the subject, although I found that Feynman had some nice discussions of what makes those EM waves tick in his book (my favorite is the one with the sheet of moving charge producing a plane wave and the calculation of the speed of light going along with it).

Yes, which is why I was hoping that if I study vector spaces/vector fields then it might help me grasp some of the concepts. It really bugs me if I don't know 'why'. I'll just focus on vector fields for now.

That is very unfortunate that they have a shallow introduction of the subject. I hope that changes in later physics classes?

 

[Lavabug]

Your single variable calculus should be solid and maybe some notion of multivariable and vector calculus (idea of a line, surface and volume integral, dot/cross products and their physical meaning(I assume everyone learns this in a general physics course?)).

It would probably be a good idea if you familiarized yourself with polar/cylindrical/spherical coordinates ahead of time.

 

[cmb]

What are good ways to prepare for electromagnetism?

I always recommend reading the history of the development/early work of a subject, and early texts.

In the history and original writings of a topic, you will, as it were, work with the people who struggled to comprehend the subject. Therefore, what you may read is to see which parts are the most difficult to comprehend and conceptualise - because if it were simple they'd have jumped to the right understanding straight away!

 

[theDRG5]

Learn PDE. Wasn't required at my school, but you sure use a garbageton of it. Other than that, I wouldn't worry about it.

 

[Nano-Passion]

Your single variable calculus should be solid and maybe some notion of multivariable and vector calculus (idea of a line, surface and volume integral, dot/cross products and their physical meaning(I assume everyone learns this in a general physics course?)).

It would probably be a good idea if you familiarized yourself with polar/cylindrical/spherical coordinates ahead of time.

Hey thanks for being a bit more detailed about what I should learn! And what physics will use polar, cylindrical, and spherical coordinates?

 

[Nano-Passion]

Learn PDE. Wasn't required at my school, but you sure use a garbageton of it. Other than that, I wouldn't worry about it.

PDE? I was referring to a first course of electromagnetism, as in "Physics II."

I always recommend reading the history of the development/early work of a subject, and early texts.

In the history and original writings of a topic, you will, as it were, work with the people who struggled to comprehend the subject. Therefore, what you may read is to see which parts are the most difficult to comprehend and conceptualise - because if it were simple they'd have jumped to the right understanding straight away!

Hmm, thanks. I've always loved history of physics and math so that would be interesting.

 

[Kevin_Axion]

PDE? I was referring to a first course of electromagnetism, as in "Physics II."



Hmm, thanks. I've always loved history of physics and math so that would be interesting.

Haha, don't learn PDEs right now. Be comfortable with single-variable calculus and multi-variate calculus and you should be well prepared.

 

[homeomorphic]

Yes, which is why I was hoping that if I study vector spaces/vector fields then it might help me grasp some of the concepts. It really bugs me if I don't know 'why'. I'll just focus on vector fields for now.

Well, differential forms are sort of a luxury, I think. Not really necessary to understand the basics--actually, that kind of "shallowness" is a good thing because you should really work up to that level, not just get there right away before you are ready. Once you know vector fields, then, you'll be ready for differential forms. I wouldn't recommend starting with differential forms. There are different kinds of "shallowness". Maybe some of it may be that they cut corners in understanding, and some of it is more of a question of coverage (as in, not getting to the more advanced topics), not using the most sophisticated tools, or just building up to things, rather than hitting you with the most sophisticated approach right off that bat.

That is very unfortunate that they have a shallow introduction of the subject. I hope that changes in later physics classes?

Depends on your luck, I think. Of course, it gets deeper in terms of the selection of topics, but whether it gets conceptually deeper--there you're at the mercy of the professors, unless you take matters into your hands. For me, I contemplated switching to physics, rather than math from EE, but promptly left physics after a terrible classical mechanics course. I just saw trouble ahead and steered clear of it, so I can't say much about it. I took a couple graduate level physics classes and they were better, though.

 

[sandy.bridge]

So this is calculus based, then? I'm unfamiliar with the US system, but here the first 2 physics are algebra based, and then you attack calculus based after completing Physics 1, and Physics 2.

 

[homeomorphic]

I should add that, ironically, the first semester of electromag with the EE dept (after taking physics II with E and M) was my very favorite electrical engineering class (mostly electrostatics), but the 2nd semester was my very least favorite EE class. Big change. But the physics version is a bit different than the engineering one (some physics people say it's totally different, but, browsing through a physics textbook like Griffiths, it looks pretty similar to what we did in EE). In EE, they focus more on antennas, and in physics, relativity replaces that.

 

[sandy.bridge]

Over here the physics version is more math intensive in comparison to the engineering version. Physics version requires a course in differential equations, while engineering does not.

 

[Nano-Passion]

Well, differential forms are sort of a luxury, I think. Not really necessary to understand the basics--actually, that kind of "shallowness" is a good thing because you should really work up to that level, not just get there right away before you are ready. Once you know vector fields, then, you'll be ready for differential forms. I wouldn't recommend starting with differential forms. There are different kinds of "shallowness". Maybe some of it may be that they cut corners in understanding, and some of it is more of a question of coverage (as in, not getting to the more advanced topics), not using the most sophisticated tools, or just building up to things, rather than hitting you with the most sophisticated approach right off that bat.

Hmm, first time I've heard of the term "differential forms." Alright, I'll look into that. ^.^

Depends on your luck, I think. Of course, it gets deeper in terms of the selection of topics, but whether it gets conceptually deeper--there you're at the mercy of the professors, unless you take matters into your hands. For me, I contemplated switching to physics, rather than math from EE, but promptly left physics after a terrible classical mechanics course. I just saw trouble ahead and steered clear of it, so I can't say much about it. I took a couple graduate level physics classes and they were better, though.

Haha, oh I know that.. lectures have always been rather shallow minded. I'm the type to rely on my own self so we will see how future classes will feel to me. You might have left physics a bit too early, for me most of the excitement comes from mathematically breaking down nature to its most fundamental level. I like to think about it as applied math. I haven't had a sufficient exposure to rigorous mathematics but I love the systematic breakdown of things and its ability to convey absolute truth! Though the think that makes me quirk is that it feels rather impersonal, while physics feels a bit more friendly to me.

 

[Nano-Passion]

I should add that, ironically, the first semester of electromag with the EE dept (after taking physics II with E and M) was my very favorite electrical engineering class (mostly electrostatics), but the 2nd semester was my very least favorite EE class. Big change. But the physics version is a bit different than the engineering one (some physics people say it's totally different, but, browsing through a physics textbook like Griffiths, it looks pretty similar to what we did in EE). In EE, they focus more on antennas, and in physics, relativity replaces that.

Hmm, this is how it goes in my school: Physics I, Physics II, & Physics II.

Physics one introduces basic kinematics and dynamics, physics two introduces electromagnetism, and physics three is an introduction to modern physics.

So this is calculus based, then? I'm unfamiliar with the US system, but here the first 2 physics are algebra based, and then you attack calculus based after completing Physics 1, and Physics 2.

Yes, I can't speak for all universities but most universities start off with calculus based physics. Some colleges allow you to take Calculus based Physics I as a co-requisite of Calculus I, while others require Calculus I as a pre-requisite.

 

[homeomorphic]

Haha, oh I know that.. lectures have always been rather shallow minded. I'm the type to rely on my own self so we will see how future classes will feel to me. You might have left physics a bit too early, for me most of the excitement comes from mathematically breaking down nature to its most fundamental level. I like to think about it as applied math. I haven't had a sufficient exposure to rigorous mathematics but I love the systematic breakdown of things and its ability to convey absolute truth! Though the think that makes me quirk is that it feels rather impersonal, while physics feels a bit more friendly to me.

Well, I like to think I never really left physics. I just freed myself of the obligation to be held accountable for it by other people's standards. Until I try to publish in physics journals, maybe with the help of some collaborators. By then, it will be too late for anyone to force me to learn things their way. Not that I consider myself a physicist. But I haven't altogether left it, either. My undergrad went so smoothly when it came to math that I thought I was completely safe from the mental rape that had been perpetrated on me in my classical mechanics class. But, as it happens, I was a mental rape victim two more times in math grad school (once in differential geometry, and then in PDE). And other classes, where I wouldn't go so far as to call it rape, it was less than ideal. So, math worked out for me, but not as well as I had thought. It doesn't matter that much. If I had gone for physics, I think I would have been a very mathematical physicist, and as it is, I'm a very physical mathematician.

 

[homeomorphic]

Hmm, this is how it goes in my school: Physics I, Physics II, & Physics II.

Physics one introduces basic kinematics and dynamics, physics two introduces electromagnetism, and physics three is an introduction to modern physics.

Was the same at my undergrad. I'm talking about the next classes. I didn't have to take physics III for my EE major, so I didn't take it.

After physics II or III, you would, at some point, take a year long course in electromagnetism for either a physics or electrical engineering degree. That's what I was talking about. Actually, I dropped the second semester of that, it was so painful. I have only dropped 3 classes in my life. All my EE classes that semester.

 

[Nano-Passion]

Well, I like to think I never really left physics. I just freed myself of the obligation to be held accountable for it by other people's standards. Until I try to publish in physics journals, maybe with the help of some collaborators. By then, it will be too late for anyone to force me to learn things their way. Not that I consider myself a physicist. But I haven't altogether left it, either. My undergrad went so smoothly when it came to math that I thought I was completely safe from the mental rape that had been perpetrated on me in my classical mechanics class. But, as it happens, I was a mental rape victim two more times in math grad school (once in differential geometry, and then in PDE). And other classes, where I wouldn't go so far as to call it rape, it was less than ideal. So, math worked out for me, but not as well as I had thought. It doesn't matter that much. If I had gone for physics, I think I would have been a very mathematical physicist, and as it is, I'm a very physical mathematician.

Ahahah.. its always good to avoid being mental raped. But a challenge is good every once in a while. To me Calculus based Physics I has been pretty easy, at first I was mental raped for some weird reason.. but then now I look back and ponder.. what was I thinking? I hope things will keep going on as smoothly as possible in subsequent courses because that is always a good feeling! I was also having a little trouble with Calculus in the beginning but then half way through the semester I looked back and wondered how I ever was challenged by it. It seems to me things should go smooth up to abstract algebra then we will see how things go. Anyways, I'm sure you would make a great theoretical/mathematical physicist. Physics welcomes you anytime. =D ahah. [I say this now assuming I won't switch to math.]

When did math start not working for you as you say? And what courses are you taking this semester?

 

[Nano-Passion]

Was the same at my undergrad. I'm talking about the next classes. I didn't have to take physics III for my EE major, so I didn't take it.

After physics II or III, you would, at some point, take a year long course in electromagnetism for either a physics or electrical engineering degree. That's what I was talking about. Actually, I dropped the second semester of that, it was so painful. I have only dropped 3 classes in my life. All my EE classes that semester.

Oh wow! I should have specified then to avoid confusion; for electromagnetism I meant Calc based Physics II.

I wasn't aware that physics major take a year long course in electromagnetism. I was under the impression that you take Physics I-III, then a year long course on classical mechanics, quantum mechanics, quantum field theory, etc..

 

[homeomorphic]

Ahahah.. its always good to avoid being mental raped. But a challenge is good every once in a while. To me Calculus based Physics I has been pretty easy, at first I was mental raped for some weird reason.. but then now I look back and ponder.. what was I thinking?

It can be like that in some ways, but in other ways, once you really understand it, you can see just how badly it was taught and how difficult they made it compared to how it ought to have been. Classical mechanics is great, now. I have a good intuitive understanding of it, and it just makes the class I took in undergrad just look like more and more of a joke. The more I understand classical mechanics, the funnier it gets. That's usually how it is. I always get the last laugh.

Of course, if it's taught well, you may never know how well it was taught if you never suffered through a bad version of it. It is mainly through bad teaching that you can appreciate that. So, I guess that's one advantage of bad teaching, if you can call it an advantage.

I hope things will keep going on as smoothly as possible in subsequent courses because that is always a good feeling! I was also having a little trouble with Calculus in the beginning but then half way through the semester I looked back and wondered how I ever was challenged by it. It seems to me things should go smooth up to abstract algebra then we will see how things go. Anyways, I'm sure you would make a great theoretical/mathematical physicist. Physics welcomes you anytime. =D ahah. [I say this now assuming I won't switch to math.]

Thanks.

When did math start not working for you as you say? And what courses are you taking this semester?

Grad school, pretty much. It's pretty tough. I don't mind it being hard, so much, except sometimes, I feel like the pace is too fast. But there have been times when the motivation was a little lacking. Some of this is probably due to some level of mathematical incompetence on the professor's part, but another factor is that sometimes the professor or textbook teaches as if they are teaching to people who already know the subject, negating the need for a lot of the motivation. When I started taking topics courses, though, everything went pretty well, again. Those have been great.

I'm taking ordinary differential equations this semester. It's been okay. Not perfect, but pretty decent, and much better than undergraduate differential equations. I'll be done with classes after that. I'm just finishing the take-home final, now. So, I'll be done with homework and being graded on stuff forever by next week. Pretty exciting prospect. Just thesis, and then I'm done with school, finally.

 

[homeomorphic]

Oh wow! I should have specified then to avoid confusion; for electromagnetism I meant Calc based Physics II.

I know. The year long E and M course usually covers the same stuff as physics II (and a lot more), but with a lot more depth.

 

[Nano-Passion]

It can be like that in some ways, but in other ways, once you really understand it, you can see just how badly it was taught and how difficult they made it compared to how it ought to have been. Classical mechanics is great, now. I have a good intuitive understanding of it, and it just makes the class I took in undergrad just look like more and more of a joke. The more I understand classical mechanics, the funnier it gets. That's usually how it is. I always get the last laugh.

Of course, if it's taught well, you may never know how well it was taught if you never suffered through a bad version of it. It is mainly through bad teaching that you can appreciate that. So, I guess that's one advantage of bad teaching, if you can call it an advantage.

Thanks.

Grad school, pretty much. It's pretty tough. I don't mind it being hard, so much, except sometimes, I feel like the pace is too fast. But there have been times when the motivation was a little lacking. Some of this is probably due to some level of mathematical incompetence on the professor's part, but another factor is that sometimes the professor or textbook teaches as if they are teaching to people who already know the subject, negating the need for a lot of the motivation. When I started taking topics courses, though, everything went pretty well, again. Those have been great.

I'm taking ordinary differential equations this semester. It's been okay. Not perfect, but pretty decent, and much better than undergraduate differential equations. I'll be done with classes after that. I'm just finishing the take-home final, now. So, I'll be done with homework and being graded on stuff forever by next week. Pretty exciting prospect. Just thesis, and then I'm done with school, finally.

Good luck! I agree to everything you've said, but I'll send you a visitor message because the topic is getting derailed [wouldn't like an infraction.] =D

 

[Mmm_Pasta]

I'd say a conceptual understanding of line and surface integrals is good. You'll only evaluate very basic line integrals (in my experience it actually helped to study this on my own). Know what a gradient is: the lecturer will teach you how to take partial derivatives and tell you what a gradient is. Make sure you are good with single variable calculus and know what a derivative and integral mean.

I would use Paul's Online Notes under the Calculus III section for references during the course:

3-Dimensional Space
~~3-D Coordinate System

Partial Derivatives
~~Partial Derivatives
~~Interpretations of Partial Derivatives

Applications of Partial Derivatives
~~Gradient Vector

Line Integrals
~~Vector Fields
~~Line Integrals Part I

Surface Integrals
~~Surface Integrals

It's not too important in your Physics II course to understand these topics completely, but the topics I listed should be useful as reference if something seems fuzzy to you.

 

[SophusLies]

Actually, I think vector spaces might help in the long run (so that you can bring differential forms into the picture, among other things), but probably not for a first course.

I agree. I was a bit thrown off because Nano-Passion said "my second semester of physics in electromagnetism." I didn't think it was his first class ever in EM.

I would say that the idea of a vector space could help but in physics we rarely ever construct those things. The same can be said for Hilbert spaces in QM.

Nano-Passion: I would focus on an intuitive concept of a vector field. Get a program like MATLAB (or Octave, it's free) then plot a bunch of vector fields and you can see how functions look in the field. Or use something like this:

http://web.mit.edu/jbelcher/www/java/vecnodyncirc/vecnodyncirc.html

and just play around with it. If you're goal is physics then the quicker you can get physical intuition the quicker you'll deeply understand the material. I take this approach in my learning even though I come from a physics and math background. I like to learn the intuitive physical picture then add more rigor to the math later on, which is why I chose physics over math in grad school.

Others take the opposite approach --> Math first then add physics later, if this approach works best for you then do that. Experiment with your learning style now because if you can figure it out this soon you'll be more prepared than most others in math and science.