Hello, everybody. Welcome back to our lecture series Part three. So, this will be the last lecture of Part three, the Electrodynamics and Its Applications. My name is Professor Seungbum Hong, and to my right side, I have my teaching assistant, Melodie Glasser. So, let's think about motors and generators. Motors are devices transforming electrical energy into mechanical energy, and generators are devices transforming mechanical energy to electrical energy. However, you can see from the right side of this picture that you can realize both of them using the same structure. So, one of the excitements whenever there is a mechanical force, is the possibility of using it in engine to do work, instead of like horses in the old days, and immediately after the discovery, that there was a close connection between electricity and magnetism, people started to design electric motors using the forces on current-carrying wires. A permanent magnet, for example, soft iron, is used to produce a magnetic field in two slots. As you can see here, this is soft iron as a permanent magnet in the shape of horse shoe, and you can see there is a slit here where you apply magnetic field from north to south, so it's top-bottom direction. Across each slot, there is a north and south pole, as i just mentioned, and a rectangular coil of copper, which is shown here, is placed with one side in each slot. When a current passes through the coil, as you can imagine here. If I pass current through this way, so this will be a counterclockwise current flow. You see, it flows in opposite directions, so the forces are also opposite in this way, you see, and producing a torque on the coil about the axis. So, think about this. You have magnetic field down, you have electric current this way, so you will have a force in the perpendicular direction, and those two will be in opposite direction, creating a torque to make this rotate. So, this will be the basic principle of an electric motor. They used this principle for a lot of measurement equipment. For example, galvanometer, a sensitive instrument for electrical measurements, where an exceedingly small current will make the coil turn, and for small angles, the amount of rotation will be proportional to the current, and you have a restoring force by this coil mechanically, so we will have a balance. The needle going back and forth, which is proportional to the current through the other coil. So you can have a very sensitive measurement equipment. Voltmeters and ammeters work on the same principle as you can see here. Of course, these days we use digitized equipment, so these are no more in the market, but this is how you can apply electric or magnetic knowledge that you just acquired here. Also, if you look at the DC motors, right, also found in toys. This is an old one. This is a new one. In schematics, you can see you have a split in the electrodes to make sure that you change the polarity as soon as you rotate on half of your one part of the coil, so you make sure that you have the torque in the same direction all the time, okay? Michael Faraday in 1840 discovered the Induction Effect, so, electric effects exists only when there is something changing. In fact, he notified that, if i change the magnetic flux through a coil, you have induced current in the coil. So, that was a big, big discovery at that time. Gauss and Weber were first builders of a galvanometer, and if you recall in our first lecture, when Benjamin Franklin was playing with the electrical current-carrying wire to supply electricity to single homes with a magnet underneath. We already understood that if i move the wire left and right, then we have a current flow through the circuit. So, as you can see, because the electrons push the electrons farther down the wire for long distance, this was the beginning of a telegraph. So, the information that you record in one place can be retrieved in the other place, and that was used in World War II as well. Also, from the Relativity argument, we can also think about current induction. So, Melodie, from the picture in the previous slides, we are moving the wire back and forth. So, in that case, we could understand we have Lorentz force because the electron sitting on the wire has a velocity, and we have magnetic field coming from the magnet. Therefore, we will have Lorentz force by the equation of qvxB, this one, F=q(E+V*B), all right? So, because I have velocity, I have magnetic field. I can understand I have force acting on the electrons on the wire. However, in case I moved the magnetic magnets underneath, there is no velocity. So, how can we then understand we have a current through this circuit? I think it comes from the electric field in this case, and we learned about it in a past lecture, right? Exactly. We learned that in the past lecture. At the time Faraday was seeing this, he was understanding that magnetic flux change, which is also written in Maxwell's equation, the second equation, where if the magnetic flux changes as a function of time, you have circulation of electric field. So, that's the electrostatic motive force as well, and this is how people started to understand induction. Also, before even knowing that, they were able to do this kind of argument from the relativity standpoint. So, this is the new effect that Faraday found, namely the induction, current induction. So, let's take a look at the schematics before we move further and elaborate our induction effects. So, we know a permanent magnet with north and south poles can be described by a solenoid coil, where we flow current through the coils to make the same kind of magnetic field distribution and therefore if I move my magnet left and right, it is equivalent to moving my coils left and right. So that's one way to change magnetic flux. What would be the other way to change magnetic flux as described in this picture, Melodie? Well, one of the advantages of using this coil instead of using the magnet itself is we can change the current, so instead of replacing the small with a large magnet, we can actually change the current through this solenoid and then we'll get a similar effect. Excellent. As Melodie mentioned, we can change the current through the coil, so we can change the strengths of the magnetic field out of this coil, and in that way, we can change the magnetic flux, and we can also study the induction effect more efficiently. So, we will cover electromotive force as known as EMF, and as we mentioned before in electrostatics, if you have a closed loop of metal wires, we cannot induce a voltage because there will be no low point and high point. But in dynamic situation, by moving magnet up and down, you're changing magnetic flux and you can have setup of circulation of electric field meaning there is some kind of voltage setup, and we call it electromotive force. So, if we change the magnetic field of the coil not by moving it, but by changing its current, there is again an effect in galvanometer. In such a case, there is more push on the electrons in one direction than another and what counts is the push integrated around the complete circuit, so you will see by changing the strengths of the current, you will induce different types of current through the circuit and that will be recorded by galvanometer. So EMF again is the net integrated push on the electrons in the circuit and the tangential force per unit charge in the wire integrated over length, once around the complete circuit. So, in this slide, we're going to summarize Faraday's complete discovery. So EMFs can be generated in a wire in three different ways, EMF stands for electromotive force. Number one, by moving the wire. Number two, by moving a magnet near the wire. Number three, changing a current in a nearby wire. So, Faraday's magnetic flux rule can be applied to the generators, which has the same structures as motors. So, let's turn the loop by an external force by hand, so imagine you're turning this loop in let's say counterclockwise and when the coil rotates as wires are moving in the magnetic field as you can see, so it's cutting through the magnetic flux and we will find an EMF in the current circuit of the coil and the Faraday's flux rule states that the EMF is equal to the rate of change of the magnetic flux when the flux that passes through the loop is changing with time. So, magnetic flux is the normal component of B integrated over the area of the loop, but you can also imagine, if you have electron sitting on the wire and if you make them move, then you have Lorentz force, you have magnetic field top-down and because electrons on the top wire is moving to the left side, you have creating current to the right side so you have pushed normal to this display. So therefore, you will push electrons toward this direction, while for the bottom part, the opposite case is true. So you'll push the electrons toward us, so you will make a circulation of current, so that way, you are generating current out of your mechanical energy. So, equivalence of motor and generator, the reciprocity between motors and generators is nicely shown by using two identical DC motors of the permanent magnet kind with their coils connected with two copper wires and this is some of the toys my kids enjoy it and you can see you have motors in the cars and motors in this generators, so when the shaft of one is turned mechanically, it becomes a generator and drives the other as a motor, and the quantitative equivalence of motor and generator is related to the law of conservation of energy, and we're going to explain to you the phone transmitter or receiver in the old days. So, original telephone of Bell consisted of two earphones that can operate either to generate EMFs or to respond to EMF, and you can see the cross-section of the gadgets. So, you have a thin iron disk as a membrane, so it can vibrate and you have soft iron as a waveguide for magnetic flux and you have permanent magnets, so the magnetic field will circulate around this magnetic circuit and by changing the gap between the thin iron disk and this soft iron, you are changing the magnetic flux through the copper coil, which is being wound in one soft iron core. Okay, so a permanent magnet produces a magnetic field in two "yokes" of soft iron and in a thin diaphragm that is moved by sound pressure. When the diaphragm moves, it changed the amount of magnetic field in the yokes as I mentioned. Therefore, a coil of wire around one of the yokes will have the flux through it change when a sound wave hits the diaphragm. So, the vibration, which is transducing the voice or music into mechanical signal will be transduced into EMF in the coil, which means transforming it to electrical signal, so it's a way to have electrical representation of sound. Also if you look into the telephone designed by Alexander Graham Bell, you see have carbon-button microphone, it uses sound pressure to vary the electric current from a battery as you can see in this very old pattern.
