Expression for drift speed

There are many questions by students about the numerical factor of 1/2 in the expression of drift speed. A small note on this.

[Mahesh_Shenoy]

I think this is one of the rare occurrences, where one of my favorite professors, Mr. Verma, has made a mistake in his book. If you go to Feynman lectures - Chapter 43 -Diffusion -> Drift velocity, the last paragraph explains what's wrong with this logic.
Completely agree that we are dealing with classical assumptions here. But under these assumptions, the correct answer is -eEtau/m and not -0.5eEtau/m.

Details:
In the book, drift velocity is calculated as the 'average distance traveled between the collision'(L)/'average time taken between the collision'(tau)
and then L = 0.5 a(tau)^2. This is an error.
'L' should have been 0.5a[t1^2 +t2^2+t^3....]/N. notice, this is NOT equal to tau^2 [tau^2 would be (t1+t2+.../N)^2]. Here t1, t2, t3 represent the time between various successive collisions.

[shashanktripathi]

I always learn something new from you . ❤️👏🌠

[parthmittal]

Thanx a lot sir
I was totally confused after reading notes and from your book
Having same doubt but your lecture cleared it ❤️❤️❤️❤️

[EquilibriumClasses]

Finally I got this after many Gmail's and comments on fb thank you sir

[bababitchnoi]

Sir please make video lectures of your books hcv 1 &2☺️☺️☺️

[jeffkumar]

Wow Hc verma 😍 my doubt clear
You are LEGEND of physics ❤️❤️

[vibhorshukla]

Such Simplicity.... Sir I became ur fan... You have a truly beautiful mind and smile 😊

[PrinceKumar-hhyn]

Thanks to the one who asked the question.

Gratitude to sir🙏, He answered it.🙏🙏

[palkii]

Sir plz make a video series step by step on the entire syllabus of 11 and 12 plzz

[shreyasbhatt]

It depends on how the drift velocity is defined
in wiki and few texts it is defined as : drift velocity is the average velocity attained by charged particles, such as electrons, in a material due to an electric field.

under a force, the velocity attained is 'at' for the eqation 'v = u +at' with u as 0. in between every collition it is this velocity that is attained by the electron, many such collisions and many such in between period, the average of it is 'a*tou' where tou = average time between collitions.

so by definition Vd = a*tou

what it is not is the distance traveled by electron by time over long period. u can seperately define it that way but the two definations are different.

this second way of definition is used by H.C. Verma which makes sense, but as it is different from the first one, it will give different results. also it becomes a little bit complicated to get exact expression and needs bit more assumption

in the second way as the focus is on distance traveled, you use 's = ut + 1/2 a t^2' to calulate the distance traveled between each collitions. so 's1 = 1/2 a t1^2' now add all this s1 s2 upto sn to get '1/2 a * (t1^2 + t2^2 + ....)/(t1 + t2 + ....)'
and now to simplify it further u have to use more assumption like t1 = t2 = .... = tuo. this is again not necessary as it can also be assumed that t1, t2, so may be taken from some other destribution like normal destribution which may make better sense but will give different result(final expression).

the first feinition cuts out all this complications and straing way defines as the velocity attained making the expression easy to calculate, but we can not use it to calculate the distance covered by electron, the secaond way is focused to calculate the distance drifted by electron but is difficult to calculate and needs more assumptions like distribution of the time intervels.

but then again as H C Verma said if u want to calculate rigorously than we have to use quantum mechanics as electrons are not tiny balls and we can not apply kinematics in this simplified form.

[PhysicssimplifiedbySunilBalani]

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.

[Mrityunjayanandmaharaj]

I was also in doubt...

But now thanks a lot sir

[gulshansinghyadav]

Dhanyavad sir for this awesome explaination aap online physics Padahná shuru kar dijeya sir .

[ROHITMISHRA-jllw]

I am astonish to see the legends here who CLICK dislike button, no doubt they know more physics then "HC VERMA SIR".

[abhishekaabhi]

Yes sir it is absolutely right that someone take average velocity of whole element as same under someone take some different average velocity is like that this make changes for thanks for the clarity you have given to a sir thank you so much

[keshavcarpenter]

Sir if Kirchhoff's law in current electricity are only applicable for conservative fields then how do we apply it in case of inductor ? (As magnetic field of inductor is non conservative )
I am in doubt.
PS:- I was a Hindi Medium student and after heard that you have translated Concept of Physics in Hindi too then I was very happy. Thanks a lot Sir.

[ruksanashekhu]

I think what sir said is right.Because the part we are studying is based on assumptions and the answers vary as the assumtions vary.
Those who just want to cram the formula and are not interesting in gaining knowledge of the true origin of the formula will not believe in what sir said and would try to relate it with other books.

[SeemaSingh-xvbs]

Well I also had confusion in the expression for drift velocity in conept of physics . Thanks sir for addressing

[rajeshbhoir]

I don't know why but I feel motivated to study physics after watching hc verma sir lectures

[virenderbhardwaj]

But sir the problem still remains the same that why NCERT used v=u+at and you used s=ut+1/2at^2? I think the 2nd equation is more correct to calculate drift velocity because avg. Velocity is total displacement upon total time but if we go by ncert derivation we would find that the meaning of there drift velocity comes out to be the velocity at any instant but the avg. For all electrons in the wire, but by your derivation it comes out to be the average velocity for a single electron over a long Period of time so not just the expression the whole meaning of drift velocity is changed??it's so confusing