Hey guys, in this video we're going to be discussing a concept called motional EMF, okay? Let's get to it. Remember guys, that a changing magnetic field, as we've seen multiple times before, can produce an EMF, okay? We'll cover this in Faraday's law, we covered this in Lenz's law. Something that we haven't covered up till now, is that motion can actually produce an EMF as well, okay? This type of EMF is referred to as a motional EMF, alright? Let's consider the case in the figure above me. We have a conductor moving through a magnetic field. Now, charges within that conductor feel a magnetic force, right? Any charge that is moving through a magnetic field will feel a magnetic force, alright? Positive charges feel this force upwards, you guys should confirm this using the right hand rule, and if I say that this is some positive charge, it's going to feel a force upwards. Now, what is going to lead to, is a whole bunch of positive charges accumulating at the top of the conductor and a bunch of negative charges accumulating at the bottom of the conductor, right? The fact that these charges feel a magnetic force, the positive charges upwards, the negative charges downwards, leads to a separation of charges, alright? Now, this separation of charges in itself leads to an electric field, just like in a capacitor, whenever you have a whole bunch of positive charges on one side and a whole bunch of negative charges on the other, you get an electric field between the two, okay? This electric field then puts a force on the charges that balances out the magnetic force. Eventually, when you get enough positive charges up here and enough negative charges up here, the electric field is going to be strong enough, but the electric force on any charge exactly balances magnetic force. In order for this to be true, the electric field strength has to equal the velocity that this conductor moves at times the strength of the magnetic field that it's in, alright? And how does the electric field get large enough? Well, as these charges separate, there is an induced EMF, equal to the electric field strength times the length of the conductor, which is going to eventually equal VBL. So, once the induced EMF or the voltage between the two ends of the conductor gets to a strength of VBL, then the charges will have a balanced electromagnetic force and they'll stop moving within the conductor, okay? Let's do a quick example. If the conductor of length 10 centimeters moves with a velocity of 20 meters per second in a magnetic field of 0.05 Tesla, what is the current through the conductor, if its resistance is 15 ohms. Now, the thing about this question is they give you enough information to solve for the induced EMF, which is VBL, the they give you enough information to find a current, which is the EMF over the resistance or VBL over R but this would be wrong, okay? You have an induced EMF, remember, on each, sorry, between the two ends of this conductor, right? You have a positive end, you have an negative end, this produces a voltage between the two points, but that voltage produces an electric field from the positive end to the negative end, that is strong enough, so that any charge place here q, will feel a balanced magnetic and electric field. So, charges are not going to move within this conductor, okay? So, this is kind of like a trick question, there isn't going to be a current, do not use this approach, alright? Now, there's a second way to get a motional EMF. If we have a conducting rod exactly like before on a u-shaped wire, right? Just like this, some sort of u-shaped wire, moving with the same velocity in the same magnetic field for instance. Because this conductor is moving, the magnetic flux through this loop is actually changing, why is the magnetic flux changing? Well, this length L, the height of this loop or the width, you could say, does not change, but the length of the loop X, we could call it, does change, as this conducting rod gets further, this thing gets wider, so it has more area, a change in the area of this loop leads to a change in the magnetic flux, which then produces an induced EMF. We know that from Faraday's law, anytime there's a change in magnetic flux, there's an induced EMF, okay? Now, what's the change in the area? Well, if this moves is small amount Delta X, then the change in the area is just A Delta, sorry, L Delta X, right? Length times width, okay? This leads to change the magnetic flux of what? B times Delta A, sorry, which is just going to be B L Delta X, and finally this leads to an induced EMF of what? B L Delta X over Delta T and Delta X over Delta T is just the velocity. This is the exact same equation that we got for a single conducting rod moving on its own through a magnetic field, okay? This is a motional EMF, both of these are examples of motional EMF and they're both the same, okay? The key difference is that this conducting rod is in a circuit, which means that this induced EMF can produce a current through the circuit, before whether it cannot be robbers on its own, there was no current, because a conductor odd was not part of a circuit, okay? So, let's do one last example. In the circuit below, if the wire has a resistance of 10 ohms, what is the current induced if the length of the bar is 10 centimeters, the speed of the bar is 25 centimeters per second and the magnetic field is 0.02 Tesla? What about the power generated in the circuit?
Practice: A thin rod moves in a perpendicular, unknown magnetic field. If the length of the rod is 10 cm and the induced EMF is 1 V when it moves at 5 m/s, what is the magnitude of the magnetic field?