Part 2/4: Freescale Magnetic Fields - Introduction

By samshekar May 7th, 2009

If you take a wire that is conducting current and you bend it into a loop as we have done in this example, we can see that the magnetic field generated by that wire will be concentrated in the centre of the loop as shown. We can use a variation of the right hand rule which we will call the right hand curl rule to find out what the polarity of the generated magnetic field will be. So, if you take your right hand and you curl your fingers so that they are pointing in the direction of the current flow, and then go ahead and extend your thumb like you are hitch hiking or something, your thumb will actually be pointing in the direction of the North Pole.

Next let’s increase the current by a factor of two and see what effect that has on the flux. What we notice is that the flux will also increase by a factor of two. So, the flux which is generated in free space recedes directly proportional to the current that’s flowing in the wire. But we can also get this same effect by using the same current by passing it through two loops of wire as shown in this example. So, we conclude that the amount of flux is also proportional to the number of turns in the loop of wire. From this we define a magnetic forcing function called Magnetomotive force or simply MMF which is the product of the number of turns in the wire and the current flowing through that wire. So, what kinds of things actually affect how much flux there is?

Well, we already know two of them. One of them being current and the other one being the number of turns of wire. But what else? It actually turns out that the length of the flux path itself also affects how much flux there is. The longer the path the fewer flux lines there will be. In fact you can think of flux as radiating out into space in all directions. The further you are away from the wire, the less flux there will be because the flux is inversely proportional to the length of the path it must take to get from the North Pole to the South Pole. What else? Well we see that the amount of flux generated is also proportional to the permeability of the material that its generated in. Permeability is nothing more than a measure of how dense the flux lines will be in a given material per unit of magnetomotive force. So, as you might expect different materials have different permeabilities. Air has a relatively low permeability compared to other materials like ferrous metals. We refer to the permeability of air or free space as mu of 0 as shown here. Finally the amount of flux cutting through a given area will obviously increase if we increase the area we are looking at. So, in a uniform magnetic field, the number of flux lines is directly proportional to the area we are considering as you might expect.

Let’s see if we can simplify this expression a little bit. The term n times i divided by l has a special meaning in magnetic applications. This is called the field intensity which is often denoted by the letter H. So, if we substitute this back into the original expression, we see that the amount of flux is equal to the field intensity times the permeability of the material times the area. But, we are not done yet. If we take the flux and divide it by area, we end up with flux density or DE as we have established earlier in this tutorial. So, the final expression states mathematically what we already know and that is the flux density is equal to the magnetic intensity times permeability of the material.

Let’s expand on what we have just discussed and see if we can establish a cause effect relationship in the equation. Let’s assume that the magnetic intensity is the cause and it’s plotted on the X-axis. The flux density will be the effect and we will plot that on the y- axis. As we crank up the magnetic intensity which by the way is often done by increasing the current, we see that the flux density goes up in linear proportion to the magnetic field intensity. But what happens if we put a magnetic material on the flux path and try again. We see that for the same magnetic field intensity, the flux density is now much higher. That’s because the permeability of magnetic material is much higher than that of free space and it amplifies the effect of the magnetic field intensity. But, the line shown in the graph is really a theoretical case and it doesn’t work like that in real life. In fact, the curve really looks something like this. It starts out pretty linear but as the magnetic intensity increases the material experiences a saturation effect in terms of the flux density.

Why is this? Well when there is no magnetic intensity all the tiny little magnetic domains inside the ferrous material are all oriented in random directions and the net magnetic polarization of the material is thus zero. But, as the magnetic intensity is increased more and more of these magnetic domains begin to align in the direction of the MMF and as a result a faint magnetic polarization can be detected. However, a point is eventually reached where all or nearly all of the magnetic domains are already aligned and cranking up the field intensity higher and higher cant make them align any better. As a result the material can no longer provide a magnetic advantage over that of free space. In fact, the permeability of the material in the case of high field intensities will asymptotically approach that of free space.

Now what do you think will happen when we decrease the magnetomotive force. Well, it turns out that instead of following the same path back down; it takes a totally different path as shown here. Notice that when the MMF reaches zero, some flux density is still retained in the material. In other words, the material has been permanently magnetized. This value of flux density is referred to as the Remanent magnetization of the material. We see that in order to coerce the flux density all the way back down to zero, a negative MMF has to be applied. The field intensity corresponding to this condition is referred to as the coercitivity of the material. If we continue to increase the field intensity in the negative direction, we see the same saturation effect that we observed for positive values of field intensity and also if we bring the magnetic intensity back to zero, it will take a totally different path once again just like we saw earlier. Since different paths are taken, depending on whether the field intensity is increasing or decreasing, the material is said to have magnetic historicis. The area bounded by these paths is proportional to the energy that will be lost in the material every time the field intensity completes one alternating cycle. This energy loss is usually in the form of heat. So, you can imagine that if an AC current wave form is applied to this magnetic material, the shaded area corresponds to the amount of core losses you will have for every cycle of the AC wave form. That’s why for certain applications, such as transformers or motor frames where AC wave forms commonly exist, you want to choose a material where the increasing and decreasing paths are as close together as possible thus minimizing the core losses. On the other hand if your desire is to create a permanent magnet, then a different material should be selected with different historisis properties namely one with higher coercivity.

This table shows the advanced magnetic materials since 1960. As you can see from this table, early ferrite materials were relatively weak and could easily be demagnetized in over current situations. But then, in the 1960s, a significant breakthrough was obtained as scientists found ways to make magnets out of rare earth materials. The latest and the most powerful of these rare earth magnets is a compound known as neodymium iron ore or simply neo for short. You really have to be careful when you are working with neo magnets. In fact, these magnets are so strong that something as simple as manually inserting a rotor with neo magnets on it inside of a motor frame can be very dangerous. It turns out that the attraction force increases dramatically as these two pieces come closer together. Some customers have even reported incidents of personal injury as the rotor gets sucked inside pesstator frame. Other customers have reported that dropping a neo magnet can be equally dangerous especially if the magnet shatters in the process. As the magnet is fractured, magnetic shards can become oriented in such a way that similar magnetic poles come into contact with each other. This causes them to fly apart with incredible speed just like shrapnel which can also result in personal injury. But on the positive side, neodymium magnets result in fantastic flux densities which result in higher horse power motors in much smaller frame sizes. In addition it has good mechanical properties which allow it to be economically manufactured into permanent magnet structures.

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