Returning to Faraday’s experiment we concluded the current could be induced to flow in a coil surrounding a magnetic material where the magnetic field in that material was changing. More specifically, an electromotive force exists in the coil which causes current to flow. It turns out that we can generate the same electromotive force in the wire by keeping the magnetic filed constant and changing the position of the wire. For example, consider the diagram show here. We have a wire that is suspended in a magnetic field and we will now move the wire in a downward direction. This will result in voltage potential from one end of the wire to the other. But what is the polarity of this voltage? Well, to figure this out, we use something called the left hand rule. Simply stated if you line up the index finger of your left hand to point in the same direction as the magnetic field and your middle finger is pointing is the direction of motion then your thumb will point to the positive end of the wire. So try this for yourself and see what happens. Take your left hand and line up your index finger to point in the direction of the magnetic field. Okay now without changing the direction that your index finger is pointing make your finger point down which is the direction of motion. Which way is your thumb pointing? If you did everything correctly, it should be pointing at the back end of the wire. This will be the positive end of the wire. See how much fun this stuff is. However just be careful about doing these hand gestures in public because people might think you are a little strange.

Let’s do the same thing we did with the right hand rule and let’s see how we can apply what we have just learned to rotating system. In this case we can see the cross section of a cylinder which is once again rotating in a uniform magnetic field. Down the length of the cylinder on the left side, we have a wire segment labeled A and on the right side we have a another wire segment labeled B. also lets assume that these two sire segments are connected together behind the cylinder so as to form a loop of wire. We will define the flux which is threading through the center of this loop as Phi, the Greek letter Phi. From Faraday’s law, we see that the voltage which will be generated from this end of the wire A to this end of wire B, is equal to the change of the flux which is threading through the loop. But wait a minute, if the magnetic field is set to be uniform then how can the flux and the loop be changing. The answer is to change the cross sectional area of the loop with respect to the magnetic field by rotating the loop. Lets what happens as we spin this loop of wire in the counter clockwise direction. From this animation you can see that the flux in the loop changes most rapidly when the loop of wire is straight up and down which is right where the loop area collapses to zero. As predicted from Faraday’s law, this corresponds to the point where the voltage is also the highest. Conversely when the loop is horizontal, the flux in the loop is maximum but the change in flux in the loop is zero during this time. And this results in the voltage being zero when this occurs. Now what do you think would happen if instead go a single loop of wire, there were n loops of wire all connected together in series. The answer is that the voltages from each loop add together in series creating a much higher voltage. This has the same effect as multiplying the flux in the loop by a factor of n. In fact the flux in the loop when multiplied by n is referred to by another term called flux linkage and we typically represent that by this symbol, Lambda. So really, Faraday’s law can be rewritten in terms of the flux linkage as shown here. Before leaving this slide, I want to make one more observation about Faraday’s law as it applies to rotating machines. You see the change in flux linkage with respect to time can really be busted up into two separate terms. One term is how much the flux linkage changes as a function of the rotational angle which is related to the number of turns, the field strength and the geometry of the machine. This term also accounts of the ADC wave form as the machine rotates. But notice that all of the factors that go into this term are pretty much constant for a given machine. The second term however describes how much the rotational angle is changing as a function of time which is really the rotational velocity of the coil. So if we ignore the ADC component of the first term for a moment, we see that the voltage magnitude out of the coil is equal to the rotational velocity of the coil time the term which is pretty much fixed for a given machine. This term is often referred as the back DMF constant of the machine.

You may notice that the mechanical structure for the motor presented earlier in this tutorial and the mechanical structure of the generator which we just discussed are absolutely identical. So this raises the question is there really any difference between a motor and a generator? The answer is not really. It just depends on how you use them. For example, in some hydro electric applications, the water from a lake runs over a dam during the day, which turns dynamos acting as generators to generate electricity. But at night when the electricity rates are cheaper, those same dynamos are used a s motors to pump the water from the lower lake or river back up to the higher lake to be reused the following day. It’s pretty ingenuous. Anyway to illustrate my point about motors and generators, let’s take a look at the following demonstration.

Okay, let’s take a walk over to the lab bench here and see if we can demonstrate this principle. Now this is a contraption that I put together for this purpose. It actually consists of two brush DC motors which are connected together at right angles through this gear arrangement here and we also have for our load, we got these two 6 volt light bulbs that are actually wired together in series. So the question that we are trying to answer is which one is the motor and which one is the generator. So if you come on in into the lab bench here a little closer and we will hook this up. I will start by powering this motor right here with my power supply, and now let see if this motor can actually be made to work as a generator of this case. And as you can see this one is clearly acting as a motor but this one now is acting as a generator to power the load. We will also see that it really doesn’t matter because I can also power up this motor and hook my load in over here and it has exactly the same effect. So what we see here is that really every motor is a generator and every generator is a motor. It really doesn’t matter. It only depends on how you use them.

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See also:
Part 1/4: Magnetic Fields Introduction
Part 2/4: Freescale Magnetic Fields - Introduction