Intuition behind all the fields in Maxwell's Equations!

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Күн бұрын

Magnetic Vector Potential:
en.wikipedia.o...
Aharonov-Bohm effect:
en.wikipedia.o...

Пікірлер: 27

@yourfavouriteta 9 ай бұрын

Corrections: 1) At 0:34, the Divergence of E should be equal to ρ/ε0; not ρ_f/ε0, which is equal to the divergence of D. 2) At 3:57, I forgot a factor of μ0, which was supposed to be multiplied onto J. 3) At 7:26, the magnitude of P is actually the charge *density* (i.e. dq/dV) multiplied by separation distance; not simply charge multiplied by distance.

@thatoneguy7597 9 ай бұрын

Excellent video, thanks for making it! It's one of those topics that is almost taken for granted by professors who may assume it's quite obvious, but I'm glad you found it deserving to devote some time to explaining it more clearly!

@yourfavouriteta 9 ай бұрын

It is amusing to consider that a professor who is mid to late in their career is as close to a physics student in their early 20s learning about MWE for the first time as that student is to a todler who is just beginning to learn how to read. I suspect that just as an undergraduate student can barely remember what it is like to not be able to read letters, many profs struggle to recall a life before they knew MWE by heart and thus have a difficult time explaining their nuances to newcomers.

@AaB-wc8le 4 ай бұрын

Brilliant and concise but clear explanation of these fields. It helped me enormiously. Straight to the point with excellent images. Thanks for sharing man!! Hopefully you make more videos!! The abramahov effect looks really interesting! Is the B field outside 0 but A positive?

@yourfavouriteta 4 ай бұрын

I am happy that you found it useful! The interesting thing is that the B-field outside is 0 no matter the current in the solenoid, but nevertheless the interference pattern changes when the current is increased, which hints that A is the field affecting the particle! An "equivalent" experiment would be to send the particle through both one path with zero electric potential and one with a high electric potential (but somehow no E-field!) and let it interfere with itself. If Wikipedia is to be believed, this latter experiment has apparently not been performed yet!

@tuface262 8 ай бұрын

Thank you very much. I'm glad that such videos like this exist although they won't get as many clicks as it would deserve.

@yourfavouriteta 8 ай бұрын

Thank you very much! If you know someone who might be interested, feel free to share it :-)

@Arty_x_g 5 ай бұрын

tell me if i'm wrong, but i'm having a little trouble getting the hand of this things: i always interpreted the D and H fields in a "physical way" rather than a pure "helping tools" to study electromagnetism in a medium. I'll explain: for me it's easier to think that - the E vector is sort of an "INTENSITY electric field" that purely tells me how strong and in which way a point in space is affected by a charge distribution near them; - the D vector is, instead, the "INDUCTION field", which tells me how the electric field E is modified in a space occupied by a medium. This conclution sorted out in my mind by the relation between E and D: D = e0 * E + P, so "it's like D carries information (thanks to e0 and P) about E AND the medium"; - the H vector acts as similar as the E vector, i call it "INTENSITY magnetic field", and just like D, it got this meaning via his relation to B: H = u0^(-1) * B - M, that seams to tell me: "it's like B, but lacks information about the materials around him"; - last but not least, B is the "MAGNETIZATION field (maybe it's better calling it MAGNETIC INDUCTION)", that has a similar meaning as the D field, carrying information about how matters reacts to a magnetic field H. This seams to make much more sense to me, also reflecting the "symmetry" of electric and magnetic fields in the Maxwell's equations: usually when Maxwell's equation are written for EM-fields in a medium they they are written in terms of D and H (by my interpratation, induction and intensity field respectively), then, when they're written in the vacuum, they are stated in terms of E and B, so the other way around. Is this something i'm making up or has it some foundation? Also, sorry for my english, but it's not my main language.

@yourfavouriteta 5 ай бұрын

Hey, thanks for your comment! To clarify, when I describe E and B as "physical" I am referring to the fact that IF you know their magnitudes and orientations everywhere in space (and nothing else!!!), THEN you can always with 100% certainty predict how a moving charge will accelerate thanks to the Lorentz force law. Similarly, I consider φ and A to be "physical" because IF you know them, THEN you can predict the phase change of quantum mechanical particles, which can be measured using interference techniques. Conversely, IF someone tells you the magnitudes and directions of D and H everywhere in space (and nothing else!!!), THEN it only allows you to calculate the density of "free" charge and "free" current. However, individual electrons, protons etc. "don't know" if they are "free" or "bound"; that's a categorization that we have made for our convenience. For example, any "bound" charge can be made "free" if you apply a force that is stronger than the one binding it in place, so "bound"/"free" is not a fundamental distinction. To get full information about the acceleration of a test charge if you already know D and H, you also need to know ε and μ everywhere in space. These coefficients can be multiplied onto D and H to recover E and B. Instead of thinking about D=ε0 * E + P, as "The E-field minus the uniform contribution from bound changes" you can also think about the equivalent D=ε*E as saying "The true E-field gets reduced locally by the material, so let's scale it back up by a factor of ε to compensate". Cartoonishly, if your bank account balance "at the moment" (E) is $20 but it used to be (D) $100 "under normal circumstances", you can either say that (P) $80 has been "stamped out/removed" or that it has been reduced by a factor of (ε) 5. Same for the case of B, H and μ. Anyways, from what I can tell, D and H only have "nice symmetries" due to us artificially "throwing away" the field contributions set up by a particular subset of all charges/currents based on a categorization that is practically convenient for us; not due to any inherent properties of these particular charges/currents. This trick may be useful in certain situations, but for the sake of clarity, I would prefer if MWE were always stated using E and B first. Their roles in accelerating charges is very tangible and their magnitudes and directions are determined by all charges/current on an equal basis.

@Arty_x_g 5 ай бұрын

@@yourfavouriteta thanks for your reply. What i get is that i should think of D and H as a "correction" for what the "true" EM field should be. Considering the example of the D and E fields, when polarization charges form in a dielectric material and i consider the electric field E, it's not like the "real" free charges are not there anymore (observation i get by mesuring the electric field which is reduced in the medium), but more like that there are other charges, the polarization ones, that i counted but i "don't want". Same goes for B and H: there are surface currents that forms when an objects enters a magnetic field that i count but i don't want. Is that more like it?

@yourfavouriteta 5 ай бұрын

@@Arty_x_g My point is that since P is an "artificial" field that we define to point from negative to positive charges in dipoles, "D(x,y,z)=ε0 * E(x,y,z) + P(x,y,z)" simply takes the E-field and removes a specific contribution from it, which on one hand is very large, but which on the other hand is uniform and very predictable. The D-field is thus "constructed" from an "actual" field, E, and an artificial field, P. When we have done calculations on D, we can always recover E by using "D(x,y,z)=ε(x,y,z) * E(x,y,z)". To reiterate, D as a field does NOT completely ignore the entire effect of bound charges. Rather, it ignores the specific effect of bound charges that looks like a strong, uniform field. Same argument applies to B and H.

@Arty_x_g 5 ай бұрын

@@yourfavouriteta oooh, now i get it. Wow, this really helped. Thak you so much. Actually, i've watched some others of your videos and really liked them, you've got a new follower. Keep it up, your content is good.

@yourfavouriteta 5 ай бұрын

@@Arty_x_g You're welcome!

@PerJohannessen 8 ай бұрын

Tak for gode konceptuelle videoer, ærgerligt du går så hurtigt frem 🙂

@yourfavouriteta 8 ай бұрын

Mange tak. Har for vane at lade mig rive med, men gør mit bedste for at sænke farten. Du kan altid afspille dem på 0.5x hastighed, hvis det går for stærkt :-)

@alanx4121 4 ай бұрын

So,, q is both the source and the recipient of E,, and B is just a mathematical construct for the forces between moving and accelerating q's.

@JacobWatkiss1 3 ай бұрын

Now hopefully I won't fail my Electromagnetic Theory exam tomorrow!

@yourfavouriteta 3 ай бұрын

Good luck!

@kevconn441 6 ай бұрын

better at 0.75 speed.

@yourfavouriteta 6 ай бұрын

I have been trying my best to speak more slowly, but I am often carried away by the sheer excitement of talking about anything related to Maxwell's Equations :-)

@kevconn441 6 ай бұрын

@@yourfavouriteta I get that bro... some of us are just a bit slow on the uptake.