Velocity selector

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 you 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 3000 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 par you know particles which have just the right speed well that's what we're going to 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 going to 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 going to happen when charged particles are moving in a magnetic field we've seen before that they experience a lawrence force and the expression for the lorenz 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 going to be in the direction of v cross b so can you quickly pause the video and think about what that direction is going to 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 charge particle is going to 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 charge particle is going to 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 make it all make sense okay you 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 you know large plates of charge now if the electric field is downwards it's going to 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 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 would 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 qvb sine theta so let me write that q we be sine theta but since theta is 90 degrees the angle between v and b is 90 degrees psi 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 these are the charged 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 will 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 charged particle is very low very very low then there is 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 will experience 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 that 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 can you try doing that you don't have to 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 that's that special speed that should exactly equal the magnetic force would 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 [Music] and guess what we now have a way to select a particular velocity so imagine i wanted a velocity of exactly 3000 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 this number should be 3000 meters per second as an example okay and now if i shoot a lot of charged particles only those particles which have 3000 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 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