# How does a permanent magnet work

### General

For many people, magnets represent something mysterious. After all, humans can neither see, hear, smell, taste nor directly feel magnetism. In addition, magnets attract ferromagnetic objects or other magnets as if by magic. Do you think that it is an inexplicable phenomenon? This is by no means the case! Magnetism is something that science has known and understood for a very long time. Unfortunately, it is not very easy to impart knowledge about it to people who are not scientifically oriented, because you can neither grasp magnetism with your hands nor make yourself understandable by means of simple experimental set-ups at home. The following is an attempt to explain magnetism in a simple way using images rather than formulas.

I ask for your indulgence for the somewhat imprecise description in favor of simplicity. If you want to know more, you will usually find suitable literature in the physics books for high school or university. In my opinion, by the way, books intended for students are often better understood than school books, because they are often intended for self-study.

### Obvious effects of magnets

It should be known to everyone that a bar magnet has two ends, usually referred to as the south and north poles, based on the earth, also called poles. If you have two magnets, the north and south poles attract each other, while the same poles repel each other without having to supply energy. Compass needles also work on this basis: They are small, very light, movably mounted magnets that usually align themselves in the earth's magnetic field and, due to their alignment, provide information about the surrounding magnetic field.

Image 1: Effect of magnets on each other

By placing a bar magnet on a cardboard box with many compass needles, for example, you can study the effects of the strong magnetic field of a magnet on the environment, i.e. the weak magnetic fields of the compass needles. With a series of compass needles you can make magnetic fields "visible". This is illustrated in Figure 2 by means of a graphic.

Fig. 2: The magnetic field of a bar magnet

The compass needles are aligned with the magnetic field lines, four of which are shown as examples in red. These are only imaginary lines, because of course you cannot see them.

### Basics of magnetism '

As early as 1820, the physicist Oersted discovered that a compass needle is influenced by conductors through which current flows. Magnetism can therefore be generated by the flow of current. If you repeat the experiment described above with a current-carrying conductor, which is passed through the cardboard box provided with compass needles, you will notice that an annular magnetic field is generated around the conductor (Fig. 3, left side).

Fig. 3: The magnetic field around a current-carrying conductor

On the left-hand side of Figure 3, only those field lines are shown that are located in a plane at right angles to the conductor through which the current flows, since the compass needles are only arranged in one plane. But you can move the entire box with the compass needles back and forth on the ladder and always get the same picture. Thus, the situation shown applies to every point of the conductor, so that with a ring-shaped conductor the magnetic field shown on the right-hand side of Figure 3 results, whereby the field lines drawn in red on the left-hand picture correspond to those on the right-hand side. Of course, the field lines drawn are only exemplary, because there are an infinite number of them. All field lines together make up the magnetic field.

The important insight is: Magnetic fields are caused by electric current, i.e. moving electrons.

### Basics of permanent magnets / permanent magnets

Above it was shown how one can generate magnetic fields with electric current. But how do permanent magnets work? A permanent magnet, also known as a permanent magnet, generates magnetic fields without being able to detect a current flow. Nevertheless, a permanent magnet also works with electricity; however, this does not have to be supplied from the outside. A permanent magnet consists of many very small elementary magnets that are formed by a collection of atoms. In every atom at least one electron orbits the atomic nucleus. This is shown in Figure 4 using a hydrogen atom, which has only a single electron and is therefore the most simply constructed atom.

Fig. 4: The magnetic field of a hydrogen atom

This one electron acts in the same way as an electric current, e.g. through a copper wire, described above and generates a magnetic field through its movement. Because the electric current is nothing more than electrons moving in one direction. Are you surprised that hydrogen atoms are magnetic? Well, the gas hydrogen is completely non-magnetic, even if the individual atoms generate magnetic fields and thus the atoms can be aligned in an external magnetic field. The reason is that hydrogen atoms move in a completely disordered manner and therefore the sum of the magnetic fields of the individual atoms compensate each other. From a statistical point of view, just as many magnets are oriented in one direction as in the opposite. As experience has shown, hydrogen is therefore not a permanent magnet.

### Ferromagnetism

With certain materials (such as iron with low levels of impurities), however, small areas form in which the magnetic fields of the atoms are oriented in the same direction. They are called Weiss domains or elementary magnets. They can be imagined as tiny magnetic grains, which in practice are of course not as beautifully regular in shape as in Figure 5. Since these Weiss domains are initially completely randomly oriented after the melt has cooled down, they stand out as with the hydrogen atoms Magnetic fields of the individual elementary magnets to the outside completely. If, however, a sufficiently large magnetic field is applied from the outside, some elementary magnets align themselves accordingly and remain in this position even when the external field disappears. You can imagine that to align the elementary magnets a different force is required, which depends on how the elementary magnets are aligned in their virgin state and how they are "hooked" with the neighboring granules. The stronger the external field, the more Weiss' domains align themselves accordingly, until all elementary magnets are aligned at a certain field strength. If the Weißchen districts do not all turn back to their original position after the external magnetic field has been switched off (which depends on the material), a permanent magnet has been produced.

Figure 5: Weiss districts

### Materials permanent magnets / permanent magnets

Only a few substances are ferromagnetic, i.e. they have Weiss domains; it is a special material-specific property. The conditions that lead to the emergence of Weiss districts are too complex to be explained here. Many atoms of other substances can also be aligned in an external magnetic field (such as the above-mentioned hydrogen), but with them, for example, as a result of thermal effects after switching off the external magnetic field, the atoms very easily and very quickly get into disorder again.

The best known ferromagnetic material is iron. However, pure iron is very poorly suited as a permanent magnet material because the Weiss domains "turn back" very easily. Iron alloyed with carbon (i.e. steel) behaves better in this regard. But the so-called coercive field strength, which, to put it casually, indicates how strongly the magnet resists demagnetization by external magnetic fields, is relatively low. Other materials such as the well-known AlNiCo alloy consisting of aluminum, nickel and cobalt behave much better in this regard, but still have the disadvantage of being relatively easy to demagnetize. Ferrite magnets (i.e. a sintered and then magnetized mixture of barium or strontium oxide with iron oxide) are a good deal better in this respect and, compared to AlNiCo, have a coercive field strength that is approximately 3 to 5 times higher. They also have the advantage that they have a significantly lower electrical conductivity than AlNiCo magnets, which means that fewer undesirable eddy currents are induced in AC applications. This reduces the electrical losses (e.g. with motors) or increases the quality of a magnetic circuit (e.g. with guitar pickups).

In the search for materials for ever stronger permanent magnets, it turned out that some elements from the group of rare earths behave particularly favorably. Behind the rather unfortunate name "rare earths" hides a whole range of metals, so by no means around earth (who doesn't think of clay when you hear this word?). The best known are listed below with details of their common use:
• Scandium (additive for mercury vapor lamps)
• Yttrium (phosphors for fluorescent tubes and televisions / monitors, lambda probes and spark plugs in cars, LASER technology, permanent magnets)
• Lanthanum (flints for lighters, additive for high-quality optical glasses)
• Cerium (flints for lighters, glass dyes, polishing substances, catalysts, fire ointments)
• Neodymium (permanent magnets, glass dyes, LASER technology)
• Samarium (permanent magnets, LASER technology)
Incidentally, rare earth metals are not as rare in the earth's crust as their name suggests. Cerium is about as common as copper, the rarest of the rare earth metals (thulium) about as common as iodine. However, their extraction as pure metal is not that easy, which is why they are sometimes quite expensive.

The alloy SmCo, made from the rare earth metal samarium and cobalt, made permanent magnets possible in the 80s, of which one could only dream up until then. These samarium-cobalt magnets have a coercive field strength that is approx. 14 times higher than that of AlNiCo. Unfortunately, such magnets are quite expensive. Permanent magnets have been available since the 1990s that are manufactured using neodymium in the form of the alloy NdFeB (consisting of neodymium, iron and boron) and that are even stronger and at the same time a good deal cheaper than SmCo magnets. The coercive field strength of the magnets, which are often incorrectly referred to as neodymium magnets, is approx. 17 times as high as with AlNiCo. To improve the properties, the NdFeB alloy is ground to powder, pressed, sintered and given a surface coating. This surface treatment is necessary because the NdFeB alloy reacts easily chemically, i.e. it corrodes without protection. Compared to samarium-cobalt magnets, the maximum permissible operating temperature of NdFeB magnets is slightly lower, which is why they could not replace them in all applications. Rare earth magnets and especially "neodymium magnets" are still reasonably priced despite some price increases caused by Chinese export restrictions. At this point a safety note: If you handle larger NdFeB magnets or other high-coercivity magnets, please be very careful and wear protective gloves. The magnets attract each other so strongly at a small distance that they can be severely crushed if, for example, you get your finger between the poles of two magnets. Larger neodymium magnets are absolutely not children's toys!

### Electromagnets

As in Basics of Magnetism 'explained, every current flow creates a magnetic field. A simple conductor loop as shown in Figure 3 is already an electromagnet. However, extremely high currents must flow in order to generate a strong magnetic field. With a little trick, however, you can double the strength of the magnetic field: Instead of a single turn, you simply take two. The magnetic field lines are superimposed so that the strength of the electromagnet is doubled. What works with two turns also works with even more turns. Usually, the winding is designed as a cylinder coil as shown in Figure 6:

Fig. 6: Electromagnet with solenoid

Since the solenoid has a certain length due to the adjacent turns, the field lines do not completely overlap. As a result, the field strength is somewhat smaller than one would expect based on the number of turns. With a tight winding (i.e. without a gap between the turns) with a short coil length as a result, the field strength is greater than with a loose winding with a long coil length as a result. The greater the distance between the windings, the more field lines "shorten the path", as shown in Figure 6 using a single field line in blue as an example.

The strength of the electromagnet can be significantly increased by filling the inside of the winding of an electromagnet with ferromagnetic material. Ferromagnetic material is to magnetic field lines roughly what copper is to electric current. If they can, magnetic field lines therefore flow through ferromagnetic material instead of air, even if the path is longer. This collects the field lines along the winding, so to speak, i.e. there are significantly fewer field lines that "shorten the path". But this is only a small part of the effect. The significantly larger one results from the fact that the elementary magnets tilt due to the field generated by the winding and thereby drastically increase the strength of the magnet.

The advantage of electromagnets over permanent magnets is that they can be switched off, e.g. to let go of objects attracted by magnetic force. Of course, this only works if so-called soft magnetic material such as pure iron is used as a ferromagnetic material to strengthen the magnetic field. In this case, the Weiss domains return almost completely to their rest position after the external magnetic field has been switched off, in contrast to hard magnetic materials that are used to manufacture permanent magnets. However, a small amount of residual magnetism cannot be avoided.

### Generating electricity with magnets

As described above, magnetic fields are caused by moving electrons. Since most effects are reversible in physics, the interesting question arises whether this is also the case here. The answer is anticipated and is simply "yes". But you probably already suspected that, considering the existing power stations.

Fig. 7: Induction of a current

Two bar magnets are shown, between whose poles there is a magnetic field whose field lines run parallel to each other (shown in red). If the distance between the magnetic poles is very small, as in the example, all other field lines can be neglected as a first approximation because they are very weak in comparison and are therefore not shown for reasons of clarity. But of course they are there, and all field lines are always self-contained.

If you now move a conductor loop, i.e. a completely normal piece of wire to which a lamp is connected, from the outside into the gap between the magnets, the lamp lights up briefly. The faster you move the conductor loop into the magnetic field, the brighter the lamp shines. This is also the case when pulling out. With this very simple experimental setup it was shown that a current was induced by moving a conductor in the magnetic field. In this way, the dynamo of your bike works in the same way as the generators of the electricity company. By the way, a magnet cannot generate electricity out of nowhere, as the word electricity generation suggests. Rather, only electrons located in the copper wire are set in motion in a certain direction, which corresponds to a current flow. Electricity is by no means generated without an external energy supply, because the conductor loop is slowed down when it is immersed in a magnetic field. So you have to apply a force that sets the electrons in motion. With the help of a magnet one can only convert mechanical work into current flow, but no energy can be generated. You can easily check this in practice: If you drive the dynamo on your bike but pull the lamp off, you don't have to pedal hard on the flat to maintain a certain speed. When the connection is clamped, it is much more difficult, as part of your muscle strength is converted into current flow. For the few watts of electricity that you have to use for typical bicycle lights, you have to pedal hard. So electricity is by no means given to you. The fact that with a powered dynamo you have to pedal a little harder than without a current draw is due to the inevitable friction.

In summary, a change in the magnetic field induces a current in a conductor, i.e. the electrons present in the conductor are deflected in one direction.It does not matter whether the conductor moves into the stationary magnetic field or the magnetic field moves towards the stationary conductor. It only depends on the relative movement.

We "simulated" the changing magnetic field in the above experiment by moving a conductor into the magnetic field and pulling it out again. The last question is now: Does this also apply if nothing moves at all, but only changes the strength of the magnetic field? This answer is also "yes". With a permanent magnet, however, you cannot change the field strength without moving it away. For this reason you have to use an electromagnet, i.e. a current-carrying conductor loop. To prove this, you bring two conductor loops close together as shown in Figure 8 and change the current in one, e.g. by switching it on and off. But this time we use an ammeter instead of a lamp for closer observation.

Figure 8: Induction with two stationary conductor loops

The loop drawn in blue is called the primary side, the secondary side drawn in black. In the idle state, i.e. in the de-energized state, the pointer of the ammeter (on the right-hand side of the picture) is in the middle position, i.e. shows no current. If you now switch on the current with the switch on the primary side, you will see that the pointer of the ammeter on the secondary side jerks briefly in one direction and then returns to the middle position. This means that a current was briefly generated (it is said to be induced) on the secondary side. When switching off, the pointer jerks briefly in the other direction. A current is also induced at this moment, although it flows in the other direction. The current reversal is also given in the experiment above (moving the conductor loop out of the magnetic field), but you couldn't see it there because the lamp has no polarity and lights up regardless of the direction of the current.

Conclusion: When the magnetic field changes, a current is induced in a conductor loop. With a constant magnetic field, however, no current is induced.

Electric current can thus be obtained by periodically moving a conductor loop in and out of a magnetic field. This creates a current that is positive when you move in, zero when you stop and negative when you move out, i.e. the direction of the current changes continuously. This is called alternating current. In principle, a generator in the power station does nothing else.