Drift velocity (concept & intuition)

you probably know who this guy is i'm pretty sure you can guess it by the equation his george ohm in around 1827 he established this famous ohm's law which said that current through a conductor equals the potential difference across it now back then we didn't know about electrons but soon we discovered it around 1900s and then people started asking the question can we derive ohm's law from the microscopic electrons point of view okay and that's what you and i will do together not in one video but over a set of three or four videos we will start from the microscopic version looking at electrons and we'll see how or why ohm's law is true what we'll do in this video is concentrate on the motion of the electrons inside a conductor and we'll introduce the concept of drift velocity so let's do that let me start by asking you a question consider a simple circuit with 5 amperes current through it you might know that this current is caused due to the flow of electrons and these electrons are flowing because they are being say attracted by the positive terminal of the battery now my question is this when something is being attracted they accelerate right just like when you drop a ball it accelerates down due to gravity it doesn't just flow down it accelerates down similarly these electrons these electrons must be accelerating towards the battery positive terminal of the battery right accelerating but if they are accelerating doesn't that mean that they should become faster and faster as they go closer and closer to this positive terminal and if that were to happen wouldn't the current increase because current is the amount of charges flowing per second if the electrons go faster over here there should be more current over it more charges flowing per second right but we know that the current must be same everywhere in the circuit hmm so what's going on what do you think is going on how do you answer this question pause for a while and just wonder about this question and see if you can come up with some answer all right if you're giving it a try here is the logic that i'm going with so my logic was without a battery i know there is no current so i'm assuming without a battery electrons are at rest and when i do put a battery electron start accelerating and that's where it's causing a problem so my assumption was without a battery electrons are at rest i think that assumption is not correct you see just like how air particles can keep moving randomly without any breeze these electrons are also moving randomly and with very high velocities without a battery they are moving in all directions so then why wouldn't we get a current without a battery well that's because they're moving in all sorts of directions and as a result they don't go anywhere let me tell you what i mean let me just elaborate a little bit imagine we could zoom into this conductor okay now here's an electron let's assume there is no battery right now this electron will be moving with extremely high speeds in random directions however because there are these positive metallic ions remember metals have these electrons and these metallic ions they will keep colliding with that metallic ions the electrons will keep colliding and as a result they'll keep on bouncing randomly and they don't get anywhere they don't go anywhere so for example let's say that this electron is moving this way randomly in this direction then it bounces off this particular metallic ion and then let's say it goes this way and then again it bounces from here and goes this way and again it bounces from here it goes this way and then it bounces from here and goes somewhere over here let's say and ends up like this and because of this zigzaggy motion because of this zigzag emotion the electron on a on a long time scale if you look over a large time the electron doesn't go anywhere it doesn't get anywhere so here's how i like to visualize it look the electron is moving randomly with very high speeds without a battery but notice it's pretty much in this part it's not moving anywhere and all your electrons are doing the same thing i'm just showing one of them and this is the reason why we don't get any current this random motion is extremely high speed and it's caused due to the temperature due to the heat energy and that's why this is called thermal motion so the thermal motion is very high speed but it's randomly bouncing off and on an average the velocity is zero and so it doesn't contribute to any current at all okay so now comes the question what happens when you do put a battery what happens then well now because of the battery the electrons will experience a force and they will accelerate so let's say the force would be in this direction over here because they're being attracted by the positive charge of the battery you can also think in terms of electric field but as of now it's not necessary so it'll experience a force in this way now as a result as a result the electron will now take a little different path so because it is being accelerated towards the right instead of bouncing from here instead of going here maybe it bounces off a little bit towards the right this is the new path okay and then from here it might instead of bouncing over here it'll bounce somewhere over here and then instead of bouncing from here it goes somewhere here and then it might go somewhere here and then it might end up somewhere over here and so what you now see is that in the presence of the electric field or in the battery instead of ending up over here the electron will end up a little bit to the right a little bit to the right and the same thing will keep happening and as a result now the electron will slowly and steadily start making its journey along the direction of that force so let's start moving in this direction again let me show you this just like before it's randomly moving but this time notice it's slowly and steadily making its way along the direction of the force along the conductor we like to say the electron is now drifting all the electrons will end up doing the same thing and it's this motion that contributes to the electric current this drift motion and what's important is that this drift velocity this average velocity that the electron has now acquired is a constant so let me write that down these electrons are accelerating yes but they drift they drift at constant velocity this is the most important part to take away over here so why are they on an average drifting at a constant velocity well because see the battery is accelerating them forward but the collisions are decelerating them and that balances out and as a result they end up moving with a constant velocity the drift velocity and of course you may ask how do we know that it's going to exactly balance out and remain a constant that's something that we will derive in another video with great detail we'll look at it mathematically i don't want to do it over here and rush things we'll do it slowly and we'll actually see that this drift velocity is indeed a constant and because it's a constant and that's the reason why we'll have the same current in the circuit and with this you can now also understand where the energy from the battery goes see when the battery is accelerating the electrons it gives the energy to the electrons but then every time the electron goes and collides with these atoms these ions the electron transfers its energy to the ions and the ions will now start vibrating and this is the reason as the ions are vibrating we macroscopically tend to experience this as heat and so we see the conductor heating up and that's what happens right when you pass current through something it heats up amazing isn't it so long story short electrons have a very high thermal velocity traveling at hundreds of kilometers per second but that doesn't get them anywhere and in the presence of a field or due to a battery they now start drifting with a constant velocity called drift velocity that constitutes the current and drift velocity is incredibly low it's in the order of millimeters per second all right now before we close the video to make sure that you really understood this i'm gonna ask you two questions and i want you to pause and see if you can answer this question okay under my first question is imagine i increase the strength of the field i maybe use a stronger battery and i increase the strength of the field i want you to think about under this condition what happens to the thermal velocity and what do you think will happen to the drift velocity what will happen to this will the increase decrease or remain the same similarly next i keep the field the same but i increase the temperature now what do you think will happen to the thermal velocity and also what you think will happen to the drift velocity can you pause for a while and think about this really think about this you no need to use any formula based on what we just learned all right if you give it a try let's see let's start with the thermal velocity the thermal velocity was due to temperature it's a random motion that is caused due to temperature not due to the field or due to this force and so in the first case if i'm not changing the temperature the thermal velocity will remain the same so let me just say vt thermal velocity remains the same okay what do you think happens to the drift velocity well notice because the field is stronger it'll get more acceleration the battery is pulling with more force so more acceleration so the accelerating force is more has increased what do you think will happen to the collisions well notice that the thermal velocity remains the same so the randomness remains the same so their collisions pretty much remain the same and therefore the net effect is that the accelerating force has now increased a little bit and as a result you can kind of sort of say see that now yes because the accelerating force has now increased they will end up having a higher average velocity and so the drift velocity would increase you'll expect the electrons to go faster and as a result you'll have more current which kind of makes sense you'd expect stronger battery to get more current again something that we will see in detail in another video where we'll derive an expression between the electric field and the drift current so you'd expect the drift current to increase over here all right let's take the second case in the second case the temperature is increasing so we would expect that the thermal velocity to also increase more temperature more heat energy and so it'll go faster and so thermal velocity will increase what do you think will happen to the drift velocity well let's see the accelerating force remains the same because i'm not changing the field now however because the thermal velocity has increased because the random motion has increased now there will be more collisions happening whoo because of more collisions i will have more retarding force more you know more opposing forces that's that's the word i wanted to use and as a result because there's a stronger opposition because of more collisions you can now kind of expect the drift velocity to become lower and of course you can stretch this and you can understand that that means that with an increase in temperature your electrons will drift slower and the current will decrease and that's indeed what we see again something we'll look at later on uh when we talk about the temp thermal effects of electricity that's pretty much it i want to close this by saying this model was first come up by a person named a german physicist named paul druda and so this is called the druda model and although the model is very primitive in the sense we are still using newtonian mechanics you might know by now that electrons are quantum particles i mean you'd use quantum mechanics but even with newtonian mechanics we're getting a pretty good insight as to what's happening and we will see even with just this neutron mechanics we will be able to derive ohm's law