I think "result 1" 0:41 is not yet proven here, because (m/n = j/k) → m=j, n=k assumes a bunch of reduced form/relatively prime relationships that you haven't really asserted or proven. If you don't assert those requirements without loss of generality, you would need to show why a 2 and 1 are the only unique integers that solve (a/b)², and I think that might end up being a circular argument. Basically, show why you're not using a² = 4, b² = 2 instead (for example).

In eq 31, for example, is there a good estimate of er (not infinity) that we can use for a good conductor?

thanks

5:17 What do you want to tell when making the quadratic characteric polynomial to an artificial cubic polynomial with a coefficient of zero in the cubic term? This step is superflous.

The derivation process is not the best, there's a mistake the expression of apha, it end with -1 and beta with +1 at 9:12

@7:41 Eqn 19 and 20 are not correct. The boundary condition, Etan=0, requires Ex ~ sin(pi m y / b) and Ey ~ sin (pi n x /a). Otherwise, nice video!

Take a drink whenever he said "Jordan canonical fooorm"

Very cool

💎 Honeywell International 🌎 Corporation (HON) 💎

quantamagazine has interesting article "New Breakthrough Brings Matrix Multiplication Closer to Ideal"on an improvement in matrix multiplication.

Thanks for this! Needed it for school

Interesting

Nice to see actual code in a youtube

Excellent :)

These sorts of equations are found in the Harmonic Balance method

Would as small signal work with this method. I would think so, since only the distance between each half wave would be further apart.

Perfect. No video has derived skin depth more cleanly than this video. thank you. -from South Korea.

Great video, but missing the formulas for Ey

Thank you very much sir

this was crazy interesting. please make more

Thanks a lot, you answered a question of mine I have had for several years...Could you please tell me why does some people refers to complexe numbers when represented on the complexe plane as vectors ? In my point of view it is a mistake because we can multiply complexe numbers (because they form a field as you proved) but we can't multiply vectors. Perhaps we can establish a homomorphism from the field of complexe number to the R-vector space of dimension 2 but in this case the homomorphism doesn't apply to the multiplication of complex numbers, it applies only for the addition...which is not really formal... If you have a hint I will be happy to hear it, thanks again

This is crazy, dunno why I watched it but I loved it-

great

shouldn't there be an infront the kx aswell? (in the equation for E)

I believe that there is a mistake at 9:37 . I think the w should be sqrt(w) on the third equation from the top. Please correct me if I am wrong. Still trying to wrap my head around the whole thing.

Perfect explanation bro

𝙥𝙧𝙤𝙢𝙤𝙨𝙢

Can they use the quaternions for this analysis?

I gave this video its first 'like'. 🙂 I really like the way you broke down the proof to very simple axiomatic steps, and even went so far as to explain that you're using the axioms in forwards and reverse directions to expand first and contract later. I prefer this kind of proof, especially when learning or teaching what proofs are and how to do them in the first place. There's an interesting project you may be interested in, called Metamath, in which they've attempted to break down most of mathematics and logic into proofs like this, where you can even drill all the way down to the level of axioms. I don't think they've really made the proofs easier to understand, though, so it's not quite the same as something like this video. But the principle that we should have access to the *entire* proof, all the way down to the axioms, is IMHO an admirable one.

double notation is wacky

I calculated the skin depth for a problem I am working on ~11,000 m but need to see how much the magnetic field would be reduced at 250 m. Conditions: sigma - 5 f - 4.166666666666667e-04 m - 1.256627e-6 Could you help point me in the correct direction? My initial thought is that 250<<<<<110000, so the amount the magnetic field would be reduced is close to 0 but I am supposed to give specifics.

At 10:13 the element in the 5th row and 5th column of the right lower matrix should be f(beta).

1:45 you used property that you are supposed to proof... how dumb is that??

In minute 8:33 you write the third term of the left hand equality as a_1, I think it should be a_2

Really good video, I'd love to see more like this

Hi sir

I have one doubt: electric field cannot reside into the conductor,right? That means, em waves cannot pass through conductors (because em wave has electric field components). Then how does radio signals/gamma rays pass through metals?

Excellent derivation explanations! Thanks for sharing. If a DC current pulse (passing through a good conductor) with a climbing-up time of 500ns rising from 0 to 10000A and immediately followed by another 500ns but with constant 10000A, then dropped from 10000A to 0A within 500ns. Will the skin effect the same all this time?

thanks....great work

Great video, if u r still doing videos then plz make one how to convert log(x) into continued fraction.

0:40 Franz Ernst Neumann was the first to write down the magnetic vector potential in his 1845 paper "General laws of induced electrical currents." He used it to write the equation summarizing Faraday's induction experiment (Faraday's law). I just looked at it, he did NOT use the letter "A." According to the book "History of Wireless" by T. K. Sarkar, Robert Mailloux, Arthur A. Oliner, Maxwell used the letters "F,G,H" for what we now know as "A." Per Wikipedia: Historically, Lord Kelvin first introduced vector potential in 1851, along with the formula relating it to the magnetic field. The easiest guess is that you start with the magnetic vector potential, A, then take the curl of it to get the magnetic induction field, B. "A" comes before "B."

When you calculate the skin depth of an EM wave of 3 MHz in Iron, why do you use the permeability of free space instead of the permeability of iron?

Awesome. Maybe you can recommend any literature on Solid State Physics? Would love to hear your recomendations.

Wrong

Well explained, after wasting so many time in searching, finally found u

Which country you belong sir

Only one word: excellent... Thanks very much. 3AM and I am very glad so watch your video. From which book did you take all your explanation?

Great video! 😀 In the very last example, there appears to be a misprint on the diagram showing "B" circling the wire in the wrong direction since "I" is blue meaning electron current. At any rate, the "A" vector being negative in the answer and in the diagram implies that it is the "B" field that is wrong. Please verify. Thnx 😀

I or A🥴

Good explanation,,Thanks ☺️