 We know that an emf is induced in a moving conducting rod which is moving in a region of magnetic field and that emf is called motionally emf and the magnitude of that emf is given by BLV where B is B is the magnetic field strength, L over here is the length of the conducting rod and V is the velocity with which the rod is moving. Now the goal of this video is to derive the magnitude of motionally emf without using Faraday's law and also to understand why is there an emf induced in the first place. Alright so let's begin with the same setup. Now here we have the same rod which is moving to the right in a region of magnetic field and this conducting rod has all of these free electrons, all of these free electrons inside of it. So even these electrons are moving to the right in a region of magnetic field and when charges move in a magnetic field they experience a Lorentz force, they experience a magnetic force and that force is, the magnitude of that force is given by Q into V cross B. Now the direction of this Lorentz force is in the direction of V cross B. So in order to understand the direction let's try and look at this setup from a certain angle. So to do that let's have our axis and here is the rod. Now the rod is moving in this direction with a velocity of V and the magnetic field is vertically down. Now in order to figure out the direction of V cross B we need to take our right hand and curl our fingers in this direction and when we do that our hand should look somewhat like this. Now notice the direction of the thumb. The thumb's direction gives us the direction of the force. So that will be in this direction right here but this direction is for a positive charge and we are interested in the direction on electrons. So the direction of the force on the electrons is just opposite to this. So that will be in this direction and in the setup over here the direction of force will be vertically down like this. Now as a result of this all of these electrons they start moving towards the lower end of the rod and the lower end of the rod becomes negatively charged and that induces a positive charge at the top end of the rod. It is this charge separation that leads to an induced EMF and because this EMF is induced due to the motion of the rod we call it motionally. Now because there is a charge separation there will be an electric field which will be generated and the direction of this field will be from the positive to the negative. So apart from the Lorentz force that is acting on the electrons there will be one more force due to the electric field which will act on all of these electrons. So if we draw that if we draw one electron right here and represent all the forces acting on this electron there will be one Lorentz force that is acting down and then there will be one force due to the electric field which is which is acting on the top in this direction right here. Now it is acting vertically up because electrons would tend to move towards the positive charge. Now as more and more electrons move towards the lower end of the rod the negative charge at the lower end keeps on increasing and that keeps on growing the magnitude of this electric field. So the electric field looks looks like this it keeps on growing and as a result as a result the force on the electron due to the electric field keeps on growing. So it is very little to start with and then gradually it keeps on growing and it reaches a point at which it completely balances the Lorentz force and that is when the electrons stop moving that is when we have reached a maximum value of motionally MF that is when we have actually reached BVL. Now we can actually derive that magnitude of BVL so for that let us let us first balance these forces and figure out the magnitude of the electric field strength. So that would be the force on the electron due to the electric field that is charge on the electron multiplied by the electric field strength. This equals the Lorentz force and that is E into V into B and when you when you work this out you will get the magnitude of electric field strength as VB and now the potential difference across the ends of this conducting rod that would be delta V. Now this is equal to electric field strength multiplied by the length of this conducting rod EL. So this is right this is L right here and when we multiply this this would be VBL and that is the magnitude of the motionally MF. Now when we connect the two ends of the rod to a lamp using some wires what happens is these charges that are accumulated they start flowing so you have all of these electrons they start leaving the lower end of the rod and they flow through the wire pass a lamp and deliver some energy to the lamp and because of that the lamp starts glowing like this. Now when the electron leaves the lower end the magnitude of the force due to the electric field it weakens slightly and that is because the electric field strength E itself decreases slightly as some charge leaves the lower end of the rod. So the force on the electron is almost balanced it is not exactly balanced it is almost balanced and that lets the Lorentz force push more electrons down the lower end of this rod and then those electrons complete the entire journey through the circuit. Now the magnitude of the motionally MF can be also figured out using work turn per unit charge and that is something that NCIT does. NCIT calculates the work turn by the Lorentz force per unit charge but that can be slightly misleading because we know that Lorentz force or the magnetic force it doesn't do any work. For example if we have these field lines and we have this electron moving in this direction with a velocity V. Now using the right hand curl rule we can figure out the direction of the force on this electron and that would be in this direction right here. So as a result this electron traces a circular path just like this and when we try and think about the work turn by this force we can write that as work turn equals f dot ds a small displacement vector and ds is in the same direction as the velocity so it will be in this direction in this direction and now we can see we can see that the angle between the displacement vector and the force is 90 degrees. So if we expand this if we expand the dot product this will be f ds cos of 90 degrees and cos 90 is 0. So the work turn comes out to be as 0 but the NCIT says that there is some work turn by the Lorentz force and we can actually use that work turn to figure out the emotional EMF. Now it turns out that the electrons actually have two velocities they have a velocity in the horizontal direction which is V and they have a velocity due to the current that is generated in the circuit and they have some drift velocity in the downward direction and in the next part of this video we will see that there are actually two components of Lorentz force one component does a positive work and the other does a negative work so that the overall work done by the Lorentz force still comes out to be as 0.