 Imagine there are a lot of charged particles moving at different speeds. These could be electrons or protons or ions or any charged particle. And imagine if we want to select particles which have a very specific speed. Say for example, we want to select particles which only have a speed of, I don't know, maybe 3,000 meters per second, okay? How would we do that? From a bunch of these invisible particles which we can't see at all, how would we select few particles which have just the right speed? Well, that's what we're gonna explore in this video. The method is called velocity selector for obvious reasons because using this method we can select particles which have a very specific velocity. So how do you do that? Well, first let's look at just one particle moving with some velocity V. We're gonna put in a magnetic field. Let's say we put a magnetic field into the screen over here, here it is. You can do that by using, say a magnet. And before we move forward, you might already know what's gonna happen when charged particles are moving in a magnetic field. We've seen before that they experience a Lorentz force and the expression for the Lorentz force is given by this equation, q times V cross B. And so if I, using this equation, we can find the direction of the magnetic force. It's gonna be in the direction of V cross B. So can you quickly pause the video and think about what that direction is gonna be? You have to use your right hand rule. Use your right hand cross from V to B. Can you pause and do that before we go forward? Okay, here's how I do it. Let's do this quickly. So here is the velocity. Here is the magnetic field into the screen. I use my right hand. And when I cross from V to B, my thumb shows upwards and my thumb represents the direction of that force. So my charged particle is gonna experience a force upwards. F, B, let's call that. Now if this was the only field available, we can pretty much predict the path of the charged particle is gonna go up like this. But now, along with the magnetic field, let's say we also introduce an electric field. We will introduce an electric field to ensure that the force acting due to the electric field is in the opposite direction. So over here, since the magnetic force is upwards, we want the electric force to be downwards. And you'll see why in a second. It'll all make sense, okay? We want the electric force to be downwards. And so we'll put an electric field downwards. So let's do that. Here's our electric field. And you can imagine you're putting that by using large plates of charge. Now, if the electric field is downwards, it's gonna experience an electric force downwards. So let me write that. So here's going to be our electric force. And what will be the strength of that electric force? If the electric field is E and the charge is Q, I forgot to write the charge. Let's say the charge is Q. Then the strength of that electric field, F E, from the definition of electric fields, is just going to be Q E, Q times E, because E represents force per charge. And what will be the strength of the magnetic field? Well, if I just look at the strength of this, the magnitude of this, let me write that over here. The strength of the magnetic field is going to be Q V B sine theta. So let me write that Q V B sine theta. But since theta is 90 degrees, the angle between V and B is 90 degrees, sine 90 is just one. All right. So now my question is, what's going to happen to this particle? How will it move? Well, that completely depends upon which force dominates. Think about it. Now, let me bring all these charge particles, the charge particles, okay? Now, if the charge particles are moving with very high velocity, very high speed, then the magnetic force will dominate over electric force. It'll be larger. And as a result, what can happen for these particles is that they will end up moving upwards, somewhat like this. So this is where velocity is very high. But what will happen if the velocity of the charge particle is very low? Very, very low. Then there's a good chance that electric force can dominate for them. And if the electric force dominates, the downward force dominates, and so the net force will be downward. And as a result, these particles would go down like this. But there will be some particles whose velocity is just such that the electric force and the magnetic force are having exactly equal magnitude, okay? So if the two forces are exactly equal and opposite, their contributions cancel out, and therefore these particles are special particles with experience and no force. And so what would these particles do? They would just come straight as if without any deflection, as if there is no force acting on them because there is net force zero. And my question is, what will be the velocity of these particles? Let me call them special particles, V naught. What will their velocity be? Can you figure that out? We can because we know that for these folks, for these particles, we know that this is exactly equal to this. So I can equate them and I can figure out what V naught is going to be. So I want you to pause the video and think about, can you try doing that? You know what I think about it, but can you try doing that? All right, let's do this. So I know at that special speed, these two are exactly equal to each other. So I can write Q times, Q times V naught times B as that special speed, that should exactly equal, the magnetic force should exactly equal the electric force, electric force. And so the Q cancels out and therefore V naught, that special speed turns out to be E divided by B. And guess what? We now have a way to select a particular velocity. So imagine I wanted a velocity of exactly 3,000 meters per second. All I have to do is set my magnetic field and electric field values in such a way that their ratios would give me, if this number should be 3,000 meters per second, as an example. And now if I shoot a lot of charged particles, only those particles, which have 3,000 meters per second speed will come out of this particular arrangement. And we can make this arrangement very narrow. All the rest of them, if they have higher speeds, then magnetic force will dominate and they will just end up going upwards. They will not escape this. And if they have lower speeds, electric force will dominate, and they'll go downwards. Again, they will not escape this. So notice what we have found. We found a way to select charged particles that have a very specific velocity. Here's my question for you. What would have happened if instead of positive charges, these were electrons? Could I still use the same setup? Can you pause and think about that? All right, notice that charge does not come into the equation at all. So whether you use positive charge, negative charge, whether you use higher charge, lower charge, it doesn't affect our equation. So the velocity that you're selecting is completely independent of the charge that you're using because the charge cancels out. But it has to be a charged particle. If it's a neutral particle, then all particles would just come out, right? Because if it's a neutral particle, you will never have electric or magnetic forces. So the method only works for charged particles. It does not depend on the charge, but it has to be charged, it can't be neutral.