 In this lecture, we're going to discuss a concept known as emotional EMF. Now recall that electromagnetic conduction is the process by which a changing magnetic flux induces an EMF inside a closed loop of conducting wire. Now there are three ways by which a change in magnetic flux can take place. One of these ways is by increasing or decreasing by changing the area of the loop of conducting wire. So let's suppose we have the following U-shaped conducting wire as shown. And we take a metal rod and we place it on top of our U-shaped conducting wire so that we form the following closed conducting loop. Now this metal rod is allowed to move across our x-axis, so either to the left or to the right. Now this entire system is placed into an external magnetic field that is assumed to be uniform given by B, which points out of the board as shown by the following blue dots. Now we want to examine the following question. What happens if we move our rod to the right? So let's suppose our rod is allowed to move and we decided to move to the right. Now if the rod moves at a speed of V over an infinitely small time interval given by DT, then that implies by the distance equation the rod will move a total distance given by DT multiplied by V. Times the time gives us our length of distance that our object travels. Now since the length of the loop and the length of our movable metal rod is equal to L, so this distance is L and this distance is L that implies the change in our area of this initial loop of wire is given by the following orange region. So we take the height given by L multiplied by the width given by V times DT and that gives us our infinitely small change in area that takes place as a result of our moving conducting metal rod. So because this initial loop of conducting wire experiences a change in area as a result of our moving metal rod, that means there is a change in magnetic flux that is taking place and because we have a change in magnetic flux that implies by Faraday's law of induction there will be an induced EMF inside our conducting wire and an induced electric current will flow through this conducting wire, electrons will begin to move. Now recall by Faraday's law of electromagnetic induction this induced EMF given by this symbol is equal to the rate of change of our magnetic flux with respect to time. Now because magnetic flux is given by taking the dot product of our magnetic field B and our infinitely small change in area DA, we get the following result. Now because DA is equal to L times V times DT we replace DA with the following result and notice we have DT appears on the top and the bottom so we can cancel those out and we see that our induced EMF that is created inside our loop of conducting wire as a result of our moving conductor is equal to the product of the magnetic field B the length of our movable metal section given by L multiplied by V the speed of our movable conducting section. So this equation gives us the induced EMF on a moving conductor and it works as long as our B our V and L are mutually perpendicular with respect to one another. Now notice the B represents the external magnetic field in which our system our conductor is found in the L is the length of our conductor in this case it's this distance and the V represents the speed of our moving conductor. So we see that if a conductor is moving within a magnetic field there will be a change in flux and that will produce an EMF and this EMF is known as motional EMF.