Alright, sci, I've been studying physics throughout highschool and part of college. I'm in my second year as an undergrad and I'm having trouble understanding the teaching methods behind maxwells equations. Pretty much Ive only learned the integral form of his equations, my college was easy so it was just plug and chug. No real integration or though behind it. I
later I transferred into a STEM-based school and found their text book that approaches maxwells equations from the differential form (del operator), the textbook blew me away in terms of shit i didn't know and now I'm confused.
Textbook: Electricity and Magnetism - Edward Purcell
Why are we taught the integral form first? Whats the difference in thought behind them? And at what point in College should I be able to do del and curl stuff?
tl;dr Ive only learned integral form of maxwells eq, now ive seen the differential form. Why teach it like that and do i stick with one form or switch?
I don't know, I've been taught the differential form first.
Josiah Cooper
When you learned it, was it single variable or did you differentiate along x,y,z?
Chase Lopez
Our professor explained to us that Cartesians coordinates were not worth the hassle. We would always work in spherical coordinates, with symmetries and invariances so that only "r" would change.
So yes, it was single-variable in a way.
t. engineer
Evan Myers
Liberal arts college really screwed me over on this one....
Alright thats another thing I have yet to get into. Im taking calc 3 next semester, is that my missing piece?
Kayden Morris
i think the integral forms are easier to compute initially (dl, E, ds etc usually come out as constants) and they give more of an insight into what's actually happening in specific problems
the differential forms give you more of an insight into the general nature of EM and also require more vector calculus
Christopher Jones
I don't know what "calc 3" is, sorry. I'd say that it's vital to know how to switch from Cartesian to Spherical, it's vital to know how to derive the unitary vectors of Spherical coordinates. Having a good sense of geometry helps a lot, since there are symmetries everywhere.
As for calculus, you need to know how to do flux integrals and line integrals, plus a good deal of vector analysis, especially if you go into waves.
Adrian Barnes
makes sense, when did the transition happen from one to the other? freshman/sophomore year?
Brayden Myers
So then do you use spherical coordinates for each law? Or just Guass's laws for electricity and magnetism?
Colton Collins
Spherical coordinates for Electric field in electrostatic. Cylindrical coordinates for Magnetic field in magnetostatic.
I took the class quite a long time ago, so I don't really remember what happens when you combine the two, sorry.
Christopher Anderson
Ok gotcha, looks like I gotta study up before I get rekt. Thanks
Justin James
quaternion is the only way to understand Maxwell's equations. The inherent rotations and torques involved in magnetic field interactions require it
Benjamin Hernandez
Isnt this just unit vectors and cross products?
Jonathan Russell
Well, just look into the divergence theorem and stokes theorem and you'll see that the integral and differential form are the same. This is something you should be able to do in 2nd year of uni.
Start with some 2D vector calculus first, you'll need it to proof greens theorem, which you can use to proof stokes theorem. Some topics: - Vector fields, scalar fields - Nabla operator (gradient, curl, divergence, ...) - Vector identities and properties math.ubc.ca/~feldman/m317/vectorId.pdf - Helmholtz decomposition of a vector field - Line integrals - Surface integrals - Greens theorem - Stokes theorem - Volume integrals - Divergence theorem ...
Maxwell equations are really beautiful when you understand the math behind them.
Logan Reyes
Basically this. It's worth it to derive the differential form yourself from the integral form and it is pretty easy as well. I really like Griffith's book. He builds these things from the ground up using the most basic experimental results.
Hunter Reed
Integral and differential forms are completely interchangeable. Somewhere in that book it should tell you exactly how to do it. You may not understand it at first, due to inexperience with multivariable/vector calc and stokes/divergence theorems. Just pick up a multivariable/vector calc textbook from the library and look up del identities (there's two in particular you will need), and the aforementioned theorems. After a good while, if you're not mathematically retarded (I'm assuming you're not by this stage), you will be bale to understand and change between them like it's second nature. Understanding them conceptually may be more challenging though, and you will need to do physics problems in order to get a better grasp. Remember, understanding always takes time and persistence, but you know dat orgasm feel when you conquer something that previously perplexed you. Keep at it, user.
Nathaniel Baker
Combine the two and use rectilinear I think.
Aiden Foster
Griffiths also has a chapter devoted to multivariable calculus that might be helpful.
Nolan Price
That's because for time independent fields, electric fields are divergent (diverginging from a single point--spherical) and magnetic fields are divergenceless with curl (curling around a line makes a cylinder). Of course, there are plenty of charge and current distributions in which these won't be good choices.
We are able to see which coordinate system to use because we thought about the differential form.
Evan Martin
Yeah, that was one of the few things I memorised. The other is that electrical fields are "1/r^2" fields and magnetic fields are '"1/r".
Jaxon Butler
>Why are we taught the integral form first
Because charged point particles necessitates the use of delta functions / distributions to describe them.
Henry Campbell
>freshman, sophomore, etc you americants and your retard terms are so cute
Anthony Torres
It's the integral form that has physical meaning. The physical consept of a flux can be expressed mathematically using area integral.
Elijah Garcia
If you don't know multivariable, you won't know vector calculus well enough to understand the way of transforming the integral form into the differential form.
Joseph Hall
If you begin with Coloumb's law and the principal of superposition, the integral form is the intermediate step to deriving the differential form. There is probably some way around that to get the differential form first, but it would be much more difficult.
