Permanent Magnets

       Centuries ago, it was discovered that certain types of mineral rock possessed unusual properties of attraction to the metal iron. One particular mineral, called lodestone, or magnetite, is found mentioned in very old historical records (about 2500 years ago in Europe, and much earlier in the Far East) as a subject of curiosity. Later it was found that a piece of this unusual rock would tend to orient itself in a north-south direction if left free to rotate (suspended on a string or on a float in water), and it was employed in the aid of navigation. A scientific study undertaken by Peter Peregrinus in 1269 revealed that steel could be similarly "charged" with this unusual property after being rubbed against "poles" of a piece of lodestone.

       Unlike electric charges, magnetic objects possessed two poles of opposite effect, denoted "North" and "South" after their self-orientation to the Earth. As Peregrinus found, it was impossible to isolate one of these poles by itself by cutting a piece of lodestone in half: each resulting piece possessed its own pair of poles:

 

 

        Like electric charges, there were only two types of poles to be found: north and south (by analogy, positive and negative). Just as with electric charges, same poles repel one another, while opposite poles attract. This force extends itself invisibly over space, and could even pass through objects such as paper and wood with little effect upon strength.

       Rene Descartes, a philosopher-scientist, noted that this invisible "field" could be mapped by placing a magnet underneath a flat piece of cloth or wood and sprinkling iron filings on top. The filings will align themselves with the magnetic field, "mapping" its shape. The result shows how the field continues unbroken from one pole of a magnet to the other:

 

 

        As with any kind of field (electric, magnetic, gravitational), the total quantity, or effect, of the field is referred to as a flux, while the "push" causing the flux to form in space is called a force. Michael Faraday coined the term "tube" to refer to a string of magnetic flux in space (the term "line" is more commonly used). Indeed, the measurement of magnetic field flux is often defined in terms of the number of flux lines, although it is uncertain whether such fields exist in individual, discrete lines of constant value.

       Modern theories of magnetism maintain that a magnetic field is produced by an electric charge in motion, and thus it is theorized that the magnetic field of a so-called "permanent" magnets such as lodestone is the result of electrons within the atoms of iron spinning uniformly in the same direction. Whether or not the electrons in a material's atoms are subject to this kind of uniform spinning is dictated by the atomic structure of the material. Thus, only certain types of substances react with magnetic fields, and even fewer have the ability to permanently sustain a magnetic field.

       Iron is one of those types of substances that readily magnetizes. If a piece of Iron is brought near a permanent magnet, the electrons within the atoms in the iron orient their spins to match the magnetic field force produced by the permanent magnet, and the iron becomes "magnetized." The Iron will magnetize in such a way as to incorporate the magnetic flux lines into its shape, which attracts it toward the permanent magnet, no matter which pole of the permanent magnet is offered to the Iron:

 

 

       The previously un-magnetized Iron becomes magnetized as it is brought closer to the permanent magnet. No matter what pole of the permanent magnet is extended toward the iron, the Iron will magnetize in such a way as to be attracted toward the magnet:

 

 

       Referencing the natural magnetic properties of Iron (Latin = "ferrum"), a ferromagnetic material is one that readily magnetizes (its constituent atoms easily orient their electron spins to conform to an external magnetic field force). All materials are magnetic to some degree, and those that are not considered ferromagnetic (easily magnetized) are classified as either paramagnetic (slightly magnetic) or diamagnetic (tend to exclude magnetic fields). Of the two, diamagnetic materials are the strangest. In the presence of an external magnetic field, they actually become slightly magnetized in the opposite direction, so as to repel the external field!

 

 

       If a ferromagnetic material tends to retain its magnetization after an external field is removed, it is said to have good retentivity. This, of course, is a necessary quality for permanent magnets.

 

Permeability and Saturation

       It is easier to understand materials permeability on a graph, which will show it’s nonlinear. The field intensity (H) is the horizontal axis of the graph. Field intensity is equal to field force (mmf) divided by the length of the material. On the vertical axis is flux density (B), equal to total flux divided by the cross-sectional area of the material.

We use the quantities of field intensity (H) and flux density (B) so that the shape of our graph remains independent of the physical dimensions of our test material, unlike field force (mmf) and total flux (Φ). The purpose is show a mathematical relationship between field force and flux for any piece of a particular substance, in the same spirit as describing a material's specific resistance in ohm-cmil/ft instead of actual resistance in ohms.

 

 

       This is called the normal magnetization curve, or B-H curve, of any particular material. Notice how the flux density for the above materials (cast iron, cast steel, and sheet steel) levels off with increasing amounts of field intensity. This effect is known as saturation. When there is little applied magnetic force (low H), only a few atoms are in alignment, and the rest are easily aligned with additional force. However, as more flux gets crammed into the same cross-sectional area of a ferromagnetic material, fewer atoms are available within that material to align their electrons with additional force, and so it takes more and more force (H) to get less and less "help" from the material in creating more flux density (B). In economic terms, we're seeing a case of diminishing returns (B) on our investment (H). Saturation is a phenomenon limited to iron-core electromagnets. Air-core electromagnets don't saturate, but on the other hand they don't produce nearly as much magnetic flux as a ferromagnetic core for the same number of wire turns and current.

       Another peculiarity to confound our analysis of magnetic flux versus force is the phenomenon of magnetic hysteresis. In general, hysteresis is lagging of an effect behind its cause, as when the change in magnetism of a body lags behind changes in the magnetic field. For a better understanding, if you were to drive an old automobile with "loose" steering one would know that hysteresis is: to change from turning left to turning right (or visa-versa), you have to rotate the steering wheel an additional amount to overcome the built-in "lag" in the mechanical linkage system between the steering wheel and the front wheels of the car. In a magnetic system, hysteresis is seen in a ferromagnetic material that tends to stay magnetized after an applied field force has been removed (see "retentivity" in the first section of this chapter), if the force is reversed in polarity.

       Let's use the same graph again, only extending the axes to indicate both positive and negative quantities. First we'll apply an increasing field force (current through the coils of our electromagnet). We should see the flux density increase (go up and to the right) according to the normal magnetization curve:

 

 

       Next, we'll stop the current going through the coil of the electromagnet and see what happens to the flux, leaving the first curve still on the graph:

 

 

       Due to the retentivity of the material, we still have a magnetic flux with no applied force (no current through the coil). Our electromagnet core is acting as a permanent magnet at this point. Now we will slowly apply the same amount of magnetic field force in the opposite direction to our sample:

 

 

       The flux density has now reached a point equivalent to what it was with a full positive value of field intensity (H), except in the negative, or opposite, direction. Let's stop the current going through the coil again and see how much flux remains:

 

 

       Once again, due to the natural retentivity of the material, it will hold a magnetic flux with no power applied to the coil, except this time it's in a direction opposite to that of the last time we stopped current through the coil. If we re-apply power in a positive direction again, we should see the flux density reach its prior peak in the upper-right corner of the graph again:

 

 

       The "S"-shaped curve traced by these steps form what is called the hysteresis curve of a ferromagnetic material for a given set of field intensity extremes (-H and +H). If this doesn't quite make sense, consider a hysteresis graph for the automobile steering scenario described earlier, one graph depicting a "tight" steering system and one depicting a "loose" system:

 

 

 

 

 

       Just as in the case of automobile steering systems, hysteresis can be a problem. If you're designing a system to produce precise amounts of magnetic field flux for given amounts of current, hysteresis may hinder this design goal (due to the fact that the amount of flux density would depend on the current and how strongly it was magnetized before). Similarly, a loose steering system is unacceptable in a racecar, where precise, repeatable steering response is a necessity. Also, having to overcome prior magnetization in an electromagnet can be a waste of energy if the current used to energize the coil is alternating back and forth (AC). The area within the hysteresis curve gives a rough estimate of the amount of this wasted energy.

       Other times, magnetic hysteresis is a desirable thing. Such is the case when magnetic materials are used as a means of storing information (computer disks, audio and video tapes). In these applications, it is desirable to be able to magnetize a speck of iron oxide (ferrite) and rely on that material's retentivity to "remember" its last magnetized state. Another productive application for magnetic hysteresis is in filtering high-frequency electromagnetic "noise" (rapidly alternating surges of voltage) from signal wiring by running those wires through the middle of a ferrite ring. The energy consumed in overcoming the hysteresis of ferrite attenuates the strength of the "noise" signal. Interestingly enough, the hysteresis curve of ferrite is quite extreme:

 

Units of Measurement

       If you find converting between the English and Metric systems difficult, then you will be overwhelmed at the converting systems in the magnet field. Because of an early lack to standardize the science of magnetism, there are more than 3 different measurement systems for magnets.

       First, you must get acquainted with the various quantities associated with magnetism. There are quite a few quantities to be dealt with in magnetic systems so we will show the comparisons with Electricity to help give you an easier understanding.

       With electricity, the basic quantities are Voltage (E), Current (I), Resistance (R), and Power (P). The first three are related to one another by the first Ohm's Law equation (E=IR), while Power is voltage times current (P=IE OR P=I²R). All other Ohm's Law equations can be derived algebraically from these two.

        With magnetism, we have the following quantities to deal with:

• Magneto motive Force -- The quantity of magnetic field force, or "push." Analogous to electric voltage (electromotive force).
• Field Flux -- The quantity of total field effect, or "substance" of the field. Analogous to electric current.
• Field Intensity -- The amount of field force (mmf) distributed over the length of the electromagnet. Sometimes referred to as Magnetizing Force.
• Flux Density -- The amount of magnetic field flux concentrated in a given area.
• Reluctance -- The opposition to magnetic field flux through a given volume of space or material. Analogous to electrical resistance.
• Permeability -- The specific measure of a material's acceptance of magnetic flux, analogous to the specific resistance of a conductive material (ρ), except inverse (greater permeability means easier passage of magnetic flux, whereas greater specific resistance means more difficult passage of electric current).

       But it isn’t over. Now we have several different systems of measurement for each of these quantities. As with the common quantities: length, weight, volume, and temperature; we have the English and Metric system. However, in the magnet field, there are more than one metric system of units, and multiple metric systems. One is called the cgs, which stands for Centimeter-Gram-Second, denoting the root measures upon which the whole system is based. The other is originally known as the mks system, which is Meter-Kilogram-Second, which was then later revised into another unit called rmks, standing for Rationalized Meter-Kilogram-Second. This ended up being adopted as an international standard and renamed SI (Systeme International).

       The µ symbol is the same as the metric prefix "micro." This is especially confusing, because it uses an exact same character to symbolize a specific quantity and a general metric prefix!

As you might have guessed already, the relationship between field force, field flux, and reluctance is much the same as that between the electrical quantities of electromotive force (E), current (I), and resistance (R). This provides something similar to Ohm's Law for magnetic circuits:

 

 

        And, given that permeability is inversely analogous to specific resistance, the equation for finding the reluctance of a magnetic material is very similar to that for finding the resistance of a conductor:

 

 

       In either case, the longer the material the greater opposition, all other factors being equal. Also, a larger cross-sectional area makes for less opposition, all other factors being equal.

The major caution here is that the reluctance of a material to magnetic flux actually changes with the concentration of flux going through it. This makes the "Ohm's Law" for magnetic circuits nonlinear and far more difficult to work with than the electrical version of Ohm's Law. It would be related to having a resistor that changed resistance as the current that passed through it varied, like a circuit composed of varistors instead of resistors.