Hey, guys. So for this video, we're gonna be taking a look at a special kind of EMF called motional EMF. Let's check it out. So remember the theme of these last couple videos has been about is that the changing magnetic flux through a loop or something like that produces an induced EMF. That's what Faraday's law tells us. Well, sometimes what happens is that this change in magnetic flux can happen through something moving. So it happens through motion. And when that happens, we call it motional EMF. So what I want you guys to take away from this video is that really motional EMF is just a special case of Faraday's law. Alright? So let's go ahead and check it out. So we have this bar or this conducting rod that is moving through a magnetic field. We have the velocity to the right, the magnetic field that points into the page, so away from you. And what happens is as this conducting rod moves through a magnetic field with some velocity, the charges on this magnetic rod So if I have a charge like this, they feel a magnetic force. Remember that charges inside of a moving inside of a magnetic field will produce will feel a magnetic force if they have some velocity. And to sort of figure out what the direction is, we have to fuse our right hand rule. So remember, what we're going to do is we're going to take our fingers and we're going to point our fingers in the direction of the magnetic field, which points into the page. And we also want our thumb to be pointing off towards the right, and then what happens is that the palm of your hand should face in the direction of the magnetic force. So what I've drawn here on the diagram above is that the magnetic force actually points upwards like this, and so what ends up happening is that positive charge will end up moving to the top of the rod like this. So positive charges will feel a force upwards, And what that means is that negative charges will feel a force in the opposite direction. So negative charges like this, so I have a negative charge over here, those will actually start moving in the opposite direction. So you'll start to get negative charges that build up on the bottom. Now, what happens here is we've actually separated these charges because we have a magnetic force, F B is equal to q v b sin of theta , and it depends on the q that's involved. So what ends up happening is these charges that have now separated to the ends of the rod have now actually produced an electric field. So we have an electric field that points sort of through this conductor like this, and what ends up happening is that these charges will eventually sort of work themselves out to balance the magnetic field. So what that means is that the force that is it that they experience due to this magnetic field is actually perfectly balanced with the magnetic force that's keeping them upwards. Now all that's really happening here is if we sort of write out some equations for this, remember that the electric force on a charge q is q times the electric field, and that's gonna be equal to q × v b . We can sort of drop this sin of theta term because we know theta is equal to 90 degrees for this particular example. The velocity goes to the right and the magnetic field points sort of straight out towards you or sorry, straight into the page. So that means that the angle is equal to 90 there. So what that means is that so we can cancel out the charges involved, and that means we have a relationship between the electric field e and the velocity with the magnetic field, so e = v b . Now what that's basically means is that we've now have an EMF that is induced on the charges or in this conducting rod. The EMF is just equal to Vb × l . So where do we actually come up with this equation? Well, remember, way back from a couple chapters ago, that the voltage, which is really just a, which is really what the EMF is, is equal to the electric field times a distance. This is an equation that we used a few chapters ago. Well, the electric field, which you have a relationship with the velocity and the magnetic field, that's just v b , and the distance is actually just equal to l , the length of the conducting rod . So really, this is the equation we're gonna have to use. It's like a special kind of EMF that's due to motion.
30. Induction and Inductance
Motional EMF
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