Back in 2011 when I was preparing for my JEE, I followed HCV for physics and tried to derive every equation myself by understanding the concept. My derivation did not give me a 2 in the denominator and I tried discussing it with my lecturer. Sadly, they were all focused only on formulae that mattered in exams and didn't want to discuss it. Now I feel relieved that I was thinking along proper lines and can mark the highlighted doubt as closed (if I ever open my HCV book again)! Thank you

I like how you force more on the intuition part rather than pen and paper proof , it at the end just starts to make sense.

Really got a deep understanding after seeing this, rather listening to this, the intuition. Had to repeat watching this 2-3 times to understand better. Thanks and please keep doing what you're doing 'cause many people aren't doing science the way it was and is meant to be.

Mahesh sir because of u i got 94 in physics in my board exam tq

Sir I have a doubt At 9:14 it's an avg time that mean most of electron collide exactly at 6 min not before it is'nt it. Therefore if we apply 2nd eq of motion for all electrons then it shouldn't be wrong, right?

I had the same issues with this derivation back in 2021. But yeah now I know. Thanks a lot.

The factor of 2 comes from rms time over mean time, as we know rms time is sqrt(2) times average time for sinsoidal curves hence the rms^2 is 2 times greater but for that we need to assume that distribution of the collision is a sinusoidal curve which might come from quantum wave function of electron in a substance, hence feynman probably got it right as he worked on field of quantum electrodynamics.

If u want to be so specific then u should also introduce some resistivity becoz different materials have different drift velocity due to different no. and type of collisions and the resistivity they offer.

Maybe there is a statistical solution to the problem which gets the numerator to be twice that of denominator, leading to the removal of 1/2.

Since collisions are random as they are taking place in uniform force field. One can assume that time interval between successive collision is same and it is considered to be the relaxation time.

I liked your videos on khan academy india but they haven't been arranged in a playlist so I don't know which one to watch after the first 4 videos of this topic(current electricity). Neither on the site nor in youtube playlists. Going back to HCV for now 😅

I was searching for a video on drift video derivation, I had a test next week and I suddenly remembered this video(I had seen this video for timepass and due to the thumbnail, I had not studied Electric current yet)

I too realized the discrepancy while I was preparing for JEE. I followed the physics book by DC Pandey where the correct derivation was there and also a comment on how some books derive the equation with a factor of half. Although theoretically not having the half made more sense to me, I believe there is no real way (not inferred from this formula*) to measure the relaxation time for electrons.

I think I am still confused about something, Comparing the derivations in both cases, The feynman lectures assumed the following - "It is just the acceleration F/m (where m is the mass of the S-molecule) times the average time since the last collision. Now the average time since the last collision must be the same as the average time until the next collision, which we have called τ" The fenman lectures said this before that line about τ - "If we start to observe an S-molecule at some instant we may expect that it is somewhere between two collisions. In addition to the velocity it was left with after its last collision it is picking up some velocity component due to the force F. In a short time (on the average, in a time τ) it will experience a collision and start out on a new piece of its trajectory. It will have a new starting velocity, but the same acceleration from F." Meanwhile for Hc verma the τ is defined as - " If τ be the averge time between successive collisions" I feel like in Feynman's definition the τ represents that if you are looking at a particle at a given instance, the avg time until the next collision and the time since the last collision is τ. The highest probility will be that you are looking at the particle when it right between the the past and the next collision. if you look at it like that, then the time between successive collisions will be 2τ, now if you take this value and plug it through hc verma's derivation(which assumed τ to be the time b/w successive collisions), you get L = (1/2)(F/m)(2τ)^2, for the drift velocity, you divide L by 2τ and you get v = (1/2)(F/m)(2τ) = Fτ/m. I think the problem lies in the assumtions sorrounding what τ represents, one assumes that it is the avg time until the next collision and time since the past collision, meanwhile the other assumes it as the time b/w 2 collisions, this why hc verma has a 1/2 in the value, hence his τ(time b/w succesive collisions) becomes τ/2 which then represents the time since the last collision and till the next collision.

can you link a proof for 18:20 ? I tried to find it online, didn't find it

i cannot speak to the physics, but i can confirm your statistics are perfect: the only way to make Σt²/Σt come out Verma's way is if the variance of t is 0. that's not just sufficient but also necessary

Such a coincidence, I was studying this an hour back!

I derived the equation in slightly different way and I got result without that 2 in the denominator.. That's what I have been teaching to my students.. If you provide your email so that I can send you the derivation to check by yourself, whether it is right or wrong? By the way it was nice explanatory video.

Sir there was a question of kinematics earlier of three particles on the corner of equilateral triangle. Sir you had done that question using relative motion but I want to know other ways to do that question too. Please If you can reupload and show us other ways to do that problem that would be very beneficial for me. Thankyou.

Can you solve it rigorously that how did you get that 2t term as in chat gpt i got the result that if t1 is not equals to t2 and so on then there's no direct proof

DC Pandey has also teased about this in his Understanding Physics series, just read it yesterday 😅

I'd be quite interested in knowing how the term you obtained (in place of tau) could be proven to be equal to twice the average time. Any hints, please?

Hi Mahesh. The part where you have made sigma( u t ) = 0 Can we also not say that each new ut also contains the memory of previous acceleration v = u + at Also the summation of t squares looks like can be done using rms value calculations

All of what you said makes complete sense mathematically. When we average some values, we think that 'this average would be the value if all quantities were to be equal'. So HC Verma has taken an average value to calculate the distance an electron would travel if collision times were equal. Is not what Feynman doing too in his book by saying V=a*𝜏 (where 𝜏 is the value of avg. time we'd get if all times were equal)? The logic is same and i thought about it the same way as both seemed equally correct. I thought maybe Newtonian mechanics break when dealing with electrons but no! because we assumed electron to be a particle. I also thought that both equations of motion connect then the derived formula for Vd must connect mathematically but they do not. { if d/t = (ut + 1/2 at^2)/t then how 1 result is half of the other- i wonder how a physicist did not think about this) Now that i think, it makes sense - how did he average out (ut) but not the square of t instead averaged out t first then squared it. According to my observation, all of the problem lies in not using the simplest forms for the physical quantities we are referring to (for example 𝜏) Is it because symbols are just used for short notations and while explaining mathematically we must refer to the simplest form and most original definition of formulas and physical quantities we are using? I am a newbie at Physics and go introduced to real Physics only by you Mahesh, so i am just thinking. I saw your comment in Verma's video and discovered that you have a channel too. Hope you read this.

Rajwant sir of pw also pointed out same think

Ok we need more of these for all concepts in HCV

I ask this dout when i m in current electricity but that time i did not get the satisfactory answer but now i am quite clear about it🙏

Can U please make a video Schrodinger wave eqn to explain it to 11th standard students...I mean it's there in the syllabus (Idk why they want to add as much syllabus as they can and don't give us time to allow to even think properly)...it's been many days I have been stucked in that topic..I don't understand what does this eqn tell us...does it tell probability?does it tell energy??does it tell momentum??does it tell the shape of orbital??does it tell the size of orbital?does it tell the orientation of orbital??.

Can u tell me the page number and volume of concept of physics HC Verma

I don't know much but the 1st problem you raised is insignificant as by taking the average time we are also considering the average distance. Therefore, the ratio ultimately remains almost the same with some negligible error (probably). I might be wrong. I am just in class 12. Sorry for the inconvenience caused.

But there is a mean free distance between collisions that depends on the density of the conductor.

Hi Mahesh! Wonderful video again. I think none of them are 'wrong' per se. Actually, the motion of electrons in a material is a very complex quantum mechanical problem. We have to come up with approximations in order to predict experimentally measurable quantities (like conductivity for example). H.C. Verma chooses a lesser sophisticated model for his calculation, and the one chosen by Feynman (Drude Model) is the just a more sophisticated model. But both of them are still models. They are simplications of the quantum mechanical problem using equations from classical physics. Now, the 'test' for a model is how well it can explain an experiment. As far as I know, people only roughly measure the order of magnitude in case of drift velocities, and for metals both the models work well. Both of them fail in case of other materials. Nevertheless, Feynman's model is indeed more sophisticated and has a subtle catch like you mentioned, which people usually miss. Thanks for making this video!

First time watching your video! Very intuitive! Thank you

Sir why are we applying the equations of motion here? I mean how are we sure of the fact that acceleration of particles is constant, like if we try to delve deeper into this problem can't we say that the electron, as it moves through the conductor would experience a number of different forces like repulsive force due to other electrons and attractive forces due to positive kernels and in the interval between the collision shouldn't these forces vary?

i would love to see the QM derivation of the Sommerfeld model. The problem is really that the classical physics is insufficient and the best we can do classically is to first establish the simple instantaneous velocity function as being qE/me times t . Now we can take the Expectation (averaging) but we have to then employ a "mean free path time". But this is problematic in QM and of course one needs to account for the fact that Expectations under any distribution obey: E[t^2]= E[t]^2 + var[t]. Getting the distribution right is where the real work s and this is why Sommerfeld makes the proper correction over the original Drude model.

Did Resnick Halliday made the same mistake? As Prof. Verma often mentions he referred Resnick Halliday before writing Concepts of Physics

well if you are dealing with this problem in this quantum state, then you can't take the acceleration due to electric field common for all the motions , you will have to take the components of acceleration along the direction of motion to use it in the newton's equation as you did at 11:22 ,so its better to solve it larger dimentions as in hcv

I asked this discrepancy between hcv and Resnick to my teacher. He told me that actually both of them are wrong and don't agree experimentally. But for jee domain we take the Resnick formula.

he has already made ideo on that actually what happens is that all these physicist try to model those quantum phenomens into very suffocative mathematics thats why these problems arises actually all these are just mere approximation of that quntum phenomenon.

a great teacher knows how to teach you well, but a legendary teacher knows where you can mistakes

just realized you're the voice behind Indian SyllabusKhan academy videos.

Hi makesh sir plz write physics textbook for class 11 and class 12 Surely ur book will be next halliday and Resnick book

15:18 the assumption "time gap between collision is equal" is mentioned in his book. And based on the the assumption he is quite correct, but yeah the assumption goes very far way from the actual values.

I think, he uses the equation of motion, s = ut + 1/2 at² Even if we assume that he's correct by saying that sum of all u will become 0, but in such case, we will find S rather V (v is drift velocity while S would be displacement) In order to find the correct formula using the formula HC verma derived, we just keed to differentiate both side with respect to time S = 1/2 a × t² dS/dt = 1/2 a × d(t²)/dt V = 1/2 a × 2t = a × t Then we can replace a by eE/m

yea thankfully our teacher explained this to us, and he told us that its not 1/2

I think in Richard feynman's book the velocity is of that instant when electron is just collidies with the next electron and in sir hc verma's book he has taken the avg velocity of the electron after colliding.( please correct me if i am wrong )❤

With arbitrary collision statistics, the general drift velocity is proportional to E(T^2)/E(T), where T is the random variable denoting the time between successive collisions. This follows from a simple application of the Strong Law of Large Numbers. This quantity is at least E(T) thanks to Jensen's inequality. Now, assuming T is exponentially distributed with mean t, this works out to be 2t.

What if we start with v=u+at and for each collision find out v and then average out v. then average v= [(u1+u2+.......) + a(t1+t2+......)]/N (Here, N represents the no of collisions considered) average v = 0 + a tau= a tau = ( e E / m) tau

No Mahesh your argument is totally fine. ProfHC Verma can also make mistakes he is a human I also found some errors in his book The problem is for over many years no one tried to correct it

I think there's a tiny mistake in your derivation ('mistake' might be a bit harsh tho). L₁, L₂ etc. are not the distance traveled in t₁, t₂ etc. Rather they are the displacements along the direction of electric field.

I studied the same topic 5 minutes ago and just opened KZfaq to see this recommended lol

Hi Mahesh, You are a talented teacher. But so is HC verma sir. He has brought a revolution in making physics accessible to school level children in an intuitive way. Seeing a big red cross sign on HC verma sir's photo in your video is little hurtful and disrespectful. You can make a point with words and content. Talented folks like yourself talk about ideas not people. Wishing you good luck!

isn't the path between successive collisions parabolic?

i think (v= u + at) is taken here finally after derivation (t= avg time for all collisions)

12:44 all the electrons can drift automatically . But what if half of them drift the other way ? Then the current would be zero right? 👀

I observed many did the average of final velocity before next collision to actually derive drift velocity . so how can we relate it llike I didnt get it

If we take infinite electrons at a single time and find drift velocity We get average final velocity of these infinite electrons as eEt/m but this average final velocity. Of we want to find out the drift velocity (which is the average velocity during the whole free path To find that we have to find average of inital average velocity and final average velocity. Means that drift velocity will be equal to (initial average velocity + final average velocity )/2 = (0 + eEt/m)/ 2 So the correct drift velocity will be eEt/2m

Super catch.Keep up the good work

u1t1 u2t2..might not add up to 0. Since the motion is not biased we cant have any biased initial velocity (from the point an elecyron strikes a lattice) so u1+u2+...un should be 0..not their sort of weighted timed mean.

Shouldn't quantum mechanics instead of newtonian mechanics be used? Moreover the length of path travelled by electron would be uncertain... due to hiesenbergs uncertainity , it would be impossible to accurately determine the position of the electron?

and just a suggestion you really should start teaching jee aspirants :)

I'm a year late to this video! Professor Walter Lewin in his 8.02x - Lect 9 video derives the drift velocity assuming a constant average time between collisions and arrives at (eE/m)t without the 1/2. It's the first few minutes of this video - kzfaq.info/get/bejne/hrChgsR5p83WY2Q.html

Excellent work and please keep up the good work. The problem is that a large cross-section of world population continues to live with tribal mindset and herds mentality even today. And we human beings are not to be blamed for this - indeed we lived the life of herdsmen and tribes million years back. This gives rise to cult following. Once somebody becomes a CULT - he becomes a GOD - other members of the tribe won't allow you to question that CULT - that's why you get to Jaggi Vasudev, Ramdev etc. Two years back I got into an argument with some kids over a KZfaq video by H.C. Verma - question was regarding the magnetic effect of a moving charge. I found H. C. Verma's explanation rather naive and incomplete and I have seen many such flaws (of Prof Verma) before. I commented that Prof Verma loves Physics and probably wants to learn Physics, but he is NOT an expert. This irked some kids - some of them appeared and probably about to appear at IIT JEE. They immediately started to throw their weight around by flaunting their IIT JEE ranks and all - which of course I won't cross-verify. I off course won't throw my weight around saying I completed my B.Tech in so and so year - did my Masters in so and so year - happened to work in so and so Semiconductor MNC Majors in so and so places and in so and so positions and took part in so and so R&D projects and that my son is a student at so and so IIT at that point in time. Honestly, when I wrote IIT in 1998 paper pattern was 40 X 2 + 15 X 8 in three hours - my son thinks it was tougher then paper-wise may not be competition wise. And anyway, an IIT rank itself isn't a testimony of one's understanding of Physics. I just tried to be humble. But finally I had to say that Prof Verma is more of a HYPE and a CULT. And it is extremely difficult to convince others that CULT-FOLLOWING isn't a good idea.

Drift veocity is average of drift velocity of large number of electrons and for each electron a is qE/m this can be checked in "drift velocity and collision time" by Donal M Title American General of physics. Lastly in my humble opinion in science we are all learning it is about betterment not about being right and wrong.

Because the drift velocity is considered not abs velocity instead

Yes u r absolutely right

In classical mechanics the half. Would occur but it doesn't. Occur in quantum mechanics

Can you please upload videos on electromagnetic waves topic? I have a exam next week. Please help me sir

Duh so... What should I do if a question comes from drift velocity in Jee Advanced.....

I have a doubt that In your solution as you have calculated the desplacement vectors separately And then added all up But wait!!! As the angel between all the vectors is not 180° You can not add the magnetudes to get the net despacement vector For doing your calculations we should also have the angle between tho disspacement vectors

Even walter lewin said about this, may be you should check his video

11:59 sir i see an issue here in my understanding would you please elaborate. Here you assume that a single electron has a zero net displacement without a potential difference introduced. First of all you say there are billions of electrons and they are identical spheres according to you then first of all how are you able to say that net displacement of one of that identical sphere in a long time t is zero ? Please elaborate sir how are you able to figure that out from that havoc of billions of identical charges

Here we are averaging distances but we are calling it a velocity... How its possible? Shouldn't we average displacement?

This page that you are showing doesn't exist in Feynman lectures series.

Instead of video u publish physics textbook sir.

I remember you commented on his video.

See prof. Verma has derieved ohm's law using his equation how do you justify that

so which formula do i use for jee

When we drop something from height h and we r asked about it's velocity *just before hitting the ground* we get it by eqn of motion....but in the eqn of motion we put distance as *h* and then we get the final velocity.... technically isn't the answer that we r getting telling us the final velocity after it has covered a distance *h*??But once it has covered h the velocity is 0?? But still the answer that we get is non zero..how??

Underated person HC verma got a good award not working for online videos spend time on solving problems with pen and paper. Your demise to do stupidity. Badma bhushan for Sir HC Verma.

I don't get it how (sig(tn^2)/sig(tn) = 2*tau) To simplify, let Tau = T If tn is the time taken at each instant n. If T is taken as time at each instant, "dtn" becomes the error tn = T + dtn => our expression becomes sig((T + dtn)^2)/sig(T + dtn) Simplifying a bit, sig(T^2 + dtn^2 + 2*T*dtn)/(nT + sig(dtn)) = (n*T^2 + sig(dtn^2) + 2*T*sig(dtn))/(nT + sig(dtn)) Evaluating at limit n -> infinity, = (n*(T^2 + sig(dtn^2)/n + 2*T*sig(dtn)/n))/(n*(T + sig(dtn)/n)) = (T^2 + sig(dtn^2)/n + 2*T*sig(dtn)/n)/(T + sig(dtn)/n) Finally since n->infinity, sig(dtn^2)/n = 0 2*T*sig(dtn)/n = 0 sig(dtn)/n = 0 => Expression becomes T^2/T = T Where does 2*T come from :P

Nice

umm.. can't it be done using the equation v = u + at... v being the average drift speed and u will result up to zero due to randomness... and then all those t1,t2,...tn divided by n will give tau? I was taught this while doing this chp...

He is not wrong even hcv made a video too you can check it out his channel

Sir khanacademy pr 11th class ki science ka content thoda zaldi daaliye

Average speed= (Average diatance / Average time ) is not the correct approach. Averge speed= ( Total distance/ Total time) is the correct approach.

This video gonna be viral

Dear Mahesh Shenoy, Beta Physics is all about concept. Beta you have to clear your concept first then dare to prove wrong someone like honourable prof. H C Verma ji.

My frnd just sent this to me :)

Good work 👍

what do you prove foriegner is right

This explanation is incomplete. You are right that due to the effect of variance, HC Verma's value is an underestimate. But there is no reason why the correction factor is multiplying by 2! The correction factor can be a any arbitrarily large positive number. Proof: Correction factor is [(t1^2 + t2^2 .... t^n))/n divided by [(t1 + t2 + .... tn)/n]^2 suppose t1 = t2 =t3... = tn = 1 (distribution with 0 variance); then correction factor is 1. But suppose t1 = 1 while t2 ... tn is 0. (distribution that maximizes variance). Then correction factor is (1/n) / (1/n^2) = n n can be made arbitrarily large is unbounded. All you've proved is that drift velocity lies somewhere between HC Verma's answer and Infinity. You've not proved that twice of HC Verma's answer is correct.

thanks

Yes sir you are right hcv sir has done wrong

is he a teacher in khan academy

My commerce brain is not gonna judge both.

Lol right now i was cramming this formula for my jee exam

Well done man i m agree with you 👍👍👍

i think its 1/2 at^2 cause s=ut+1/2at^2 s=l u is u t is tau a is a and u will be 0 as after the collision the electron starts afresh hence l=1/2at^2 (t is tau) does this justify it? i am not sure thats just what i think but thing where i also cant wrap my head around is why are we talking about such short distances when the book mentioned l is a distance in a long time

Hi FHP, Does electrons really push each other in a circuit Or is it really the field interaction? Can you make a video? I found the following discussion interesting: kzfaq.info/get/bejne/hZOHdr1ptdHWe2Q.htmlsi=Ggb4Y4Ud2VjThVFr If it doesn’t physically push does the equations apply?