I got this book for xmas and I'm just now getting around to reading it. I thought I understood E pretty well but this book is going to get me to another level. Electrons move through conductors with an average velocity of 0.001 in/s. It's the electric (E and D) and magnetic (H and B) fields that are actually transmitting all signals / information / power in circuits.

Yes, electrons are just pawns, which is why they are called "charge carriers", the electron itself is irrelevant its the charge that matters which produces the E field, in fact, ions also contribute to the movement of charge, for instance inside a battery. It is the charge inside a circuit that produces the E field and if charge starts moving through the cable, it produces the H field. The power transferred is the integral over time of the cross product of the E x H fields normal to a closed surface, the direction of travel of this power is defined by something called the Poynting vector, that is the real deal behind electricity, Ohm's and Kirchhoff's laws are just our lazy way to skip all over this stuff, that is, unless you reach certain frequencies at which Kirchhoff's laws cease to work as we know them and Maxwell takes the wheel.

The speed of the electrons that you mention is called "drift velocity"

To make things simpler, I am not going to explain the differences between E and D fields or B and H fields, for all practical purposes, it doesn't matter for the explanation I will give, E and D are related by a factor called 'permittivity' and B and H are related by a factor called 'permeability'. So when you see E or D think of Electric Field, and B or H Magnetic Field

The Ampere-Maxwell law teaches us that an H/B field can be produced either by conduction current (i.e. electrons moving in a cable) or by what its called 'displacement current', which happens when you have a D/E field varying with respect to time, and in this latter case, the electrons are not moving from one place to other. This displacement current happens, for instance, between the plates of a capacitor; if you ever wondered how can electricity travel from one plate of the capacitor to the other when there is a gap of insulating material between them, that is how: displacement current, that is also why capacitors block DC, since DC produces a steady D/E field, no displacement current occurs (the field has to be varying) and there is also no conduction current since there is a gap insulating both plates and electrons can't cross (assuming a perfect capacitor), but when you vary the D/E field with respect to time by applying AC instead of DC, you generate displacement current which also generates an H/B field, and that is why capacitors let AC through but not DC. The reverse is also possible, a D/E field can be caused either by an electric charge like an electron (Gauss' law for Electric Fields), but can also be produced by a changing B/H field (Faraday's induction law).

If you mess around with these equations, you end up with Electromagnetic waves which can travel through space, and in these, conduction currents and charges are not present (I am specifically talking about Radio waves travelling in the air or in space), its just a feedback of a changing magnetic field which in turn produces a changing electric field which in turn produces a changing magnetic field, which in turn... you get the idea. BTW, this is how light works as well, it has an electric and magnetic field, but frequency is much higher. That is why when we say that electricity travels at the speed of light, we are talking about the electromagnetic wave or the E and B fields, or the energy, not the electrons moving in the cable. There is a corollary here, electrons can move at the speed of light, but remember that electric current is not only one electron, but a group of electrons, and this group of electrons moves very slowly from place to place, even if them, individually, can move at the speed of light.

Then, one of the biggest realizations that you can make, is to become aware that Inductance is just a unit that relates current and magnetic flux, capacitance is a unit that relates electric charge and voltage, and resistance is a unit which serves to quantify the loss of electric energy into heat. It is then that you realize that inductance, capacitance and resistance, do not exist by themselves, but are fabrications for us to handle in terms of voltage and current a bigger reality which is comprised of Electric and Magnetic fields, in other words "there is no spoon".

Another interesting thing, we have always thought that voltage is voltage is voltage, and whilst the end result is probably the same, the source is not the same. Its not the same field which produces a voltage in a battery, or in an inductor. In a battery, the E field is the cause for the voltage produced in the battery, same thing with a capacitor, but in an inductor, it is the changing B field through the inductor which produces the voltage (Lenz Law), in a generator, again, its the changing magnetic field responsible of producing the voltage. And more over, the electric field produced by a charge is not the same as the one produced by a changing magnetic field! an E field produced by a charge produces an E field which points outwards from the charge or inside towards the charge, depending on whether the charge is positive or negative, but an electric field produced by a changing magnetic field, produces a whole different monster, an E field which 'revolves' in itself, with no beginning or end, very similar to a magnetic loop.

Here is a brief (simplified, since I wont use vector calculus) example to show you how everything comes from the electric and magnetic fields:

The relationship between the current in a cable (I) and the electric field (E) is:

I *rho/A= E (Current*resistivity of the conductor / cross-sectional Area of the conductor = Electric field)

if we multiple both sides by the length of the conductor (d)

I*rho*d/A = E*d

but what do you know, E*d is Voltage (V)

So we get

I*rho*d/A = V

lets group the terms rho*d/A into a single term called 'R' which shall be called resistance, so:

I*R = V , looks familiar?

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Another one for you, a bit harder:

Electric charge and the Electric Field are related by the following equation:

Q = ε*A*E (Charge = permittivity*Surface Area*Electric Field)

lets multiply both sides by the distance (d)

Q*d = ε*A*E*d

But we already know that E*d = Voltage, so:

Q*d = ε*A*V

lets divide both sides by 'd'

Q = ε*A*V/d

now, lets group the terms ε*A/d into a single term 'C' which shall be called capacitance.

Q = C*V

Differentiating the equation we get

dQ/dt = C*dV/dt

but Electric current (I) is defined as:

I = dQ/dt (Current = dQ/dt)

so

I = C*dV/dt

You can see, everything can be traced to the E field, but lets go further, applying a Fourier transform we get:

I = jω*C*V

Dividing both sides by I*jω*C:

V/I = 1/(jω*C)

But we know that Voltage over Current is Impedance, so

Z = 1/(jω*C)

Taking the magnitude or absolute value, and since ω = 2*pi*f, where 'f' is the frequency in Hertz

|Z| = X = 1/(2*pi*f*C) (looks familiar? its the reactance (X) of a capacitor)

With the inductor its a very similar procedure but starting from the B field rather than the E field.

The point I am trying to make, is that all the equations we use in circuits can be traced to the Electric and Magnetic fields. Impedance, Inductance, Resistance, Capacitance are all illusions, even Voltage and Current are not real entities, since they are derived units from the electric or magnetic fields, you could argue that what we call current is a real thing because electrons are moving, but what about displacement current in which no electrons are moving? in either case, the term 'current' describes something, like electrons moving, but it is not a thing or entity by itself, all that matters are the electric and magnetic fields, those two are the fundamental things in nature making all our gadgets work.

And if you want to go deeper into the rabbit hole, we can ask ourselves what is an electric field? its defined as force per unit charge, so in the end, we could say that it all boils down to forces of nature, but why does something like an electric charge produces forces? why does electric charge exists in nature? there is a Nobel Prize waiting for you if you answer that....

The truth is that even with all these fancy theories and math, our smartphones and TikTok, we are still as clueless as we were 10,000 years ago as to why things are the way they are....