On that class, the teacher was very adamant stating that the lump matter discipline can get you and you might find circuits that don't behave right if you don't follow those constrains.
I don't like this term "lump matter". I've never heard it before, and it sounds like something that could get one into a lot of trouble.
Traditionally (the way I learned it?), you learn lumped circuits in abstract -- a drawing on paper, nothing to do with reality. It is a schematic representation of, at the most basic, a matrix space. Each component has >= 2 pins, each of which connects to >= 1 other pins. The connections, bridging between >= 2 pins, are called nodes or nets, and closed paths around the graph are called loops. In the matrix (netlist) form, rows and columns represent nodes, and the entries along each row/column represent connections from one node to the other. (A linear, time-invariant matrix must be symmetric, because resistors for example can only deliver current to one node by subtracting it from another -- KCL.) Then, you learn E&M as fields in space, period -- how to set up the boundary conditions, how to evaluate the integral forms (loop and surface), and how to derive the Telegrapher's Equation for a given setup.
What I'm guessing from the picture is some weird hybrid of these approaches, perhaps attempting to introduce field theory from the comfort of the wire and node. This actually sounds practical in regards to E&M simulators -- generally, you are able to apply a nonphysical stimulus to a model, such as, well I want to apply exactly this voltage to these faces only, don't ask me how it's supposed to get there. Some of them, you can even hook up real SPICE to said nodes, and use the E&M model as an actual component. But that's a whole hell of a lot more advanced than introductory E&M, and I would be very weary of anyone who tries to teach it that way. It sounds like it could very easily confuse a student.
On the textbook they have a whole apendix A (11 pages) talking about Maxwell, lumped matter discipline and kirchoff, on top of what they mention in the actual book. So I did some research on the Maxwell equations in the book and they are Heaviside's equations and nothing to do with the actual Maxwell's equations (other than in spirit).
If Heaviside just pulled them out his ass, physics would be a clusterfuck. Fortunately, he didn't. He simplified them, from some 23 equations (I don't remember -- I haven't read Maxwell's original paper myself) to the somewhat more elegant four that are most commonly listed. To say that form has "nothing to do" with Maxwell is a great disservice not just to Maxwell, but to all those who worked so hard to develop this most marvelous and enduring of physical laws.
BTW, certain vector spaces admit an even simpler form. There's a combination scalar-vector space, from geometric algebra, which does this. Einstein expanded E&M, developing General Relativity, and expressed it with a single equation in R^4 (i.e., four dimensions, and using "three dimensional" matrices (i.e., rank 3 tensors) to express operations in that space). I'm sure I've misremembered the exact form of things, but that's the jist of it.
As for the slides of the course, note the last sentence of the 2nd slide. Maybe those online MIT courses are teaching crap
They may well be. So far, it sounds misleading at least.
It would be quite naive to think that MIT, or any other institution, should be an infallible paragon of their field. MIT itself is still well renowned, though I've heard suggestions of falling standards. It would be even more naive to think that online coursework would be exactly as reliable as in-person instruction. I haven't looked at MIT coursework myself, but given the...average level of quality offered by most online courses, they shouldn't need to be very good to still be better than everyone else, if that's one of their goals.
Anyway, what that last sentence in the slide is getting at is, conservation laws are true for infinitesimal elements; "use this for low frequencies" is the same as saying "don't use this for high frequencies" or "the speed of light is infinity".
When you do a static (or quasi-static) E or M problem, you only need to invoke one or two of the four equations, and as such, your equations have no concept of the speed of light, or the passage of time. When integrating all four equations, over a volume of space, the speed of light necessarily appears, and E and M are coupled as they should be.
But if they are not teaching nonsense then what happens when those three constraints are not met?
Enters Maxwell, but that is not really Maxwell, it's Heaviside.
So how many unknowns do we have and how many shortcuts did EE took just to get us to "close enough"?
So to me, revisiting a period where all research stopped because obviously we learned everything there is to learn and mastered electromagnetism. Of course, humanity can't be naive at those kinds of assumptions, saying there is nothing else to learn or be discovered on this field! that would never happen.
So my point is let them go back one hundred years and look into what Tesla was doing, maybe we do learn something new.
There's nothing new in E&M, it's quite remarkable really that it was perfect when discovered. It's so simple and proportional that, really, it shouldn't be seen as a physical law at all, but merely a normal attribute, a symmetry of the space we live in. This is, I think, what physicists are going on about when they talk about symmetry and gauge invariance in the higher levels of quantum mechanics, that this is just how space itself behaves, and when we talk about "particles", what we really mean is the algebra that describes how mass-energy manifests and interacts with itself in this space. And the simple difference between that and E&M being, we don't see almost any of that fancy behavior under normal conditions, because all that high-energy stuff can be approximated very well down at regular energy levels (i.e., anything less than high energy gamma rays).
What is new is the use of E&M. For a long time -- much of the 19th century -- only bits and pieces were known, published, discovered and rediscovered. But even after Maxwell's putting them all together, uptake was slow, especially in the lower level disciplines. By the turn of the century, EEs (such as the occupation was at the time) hardly knew anything about alternating current, radio waves, propagation, resonance and so on. Hertz' famous experiment was done in 1887, but it took decades before radio as we know it took off.
Even to this day, I suppose, few engineers know about this in much detail. And these days, hell, who needs E&M, just use an Arduino!
Tim
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