The Special Theory of Relativity may be ultimately responsible for the magnetic field created by an electrical current that involves the motion of electrical charges, but what about magnets made of iron? The magnets we use to hold grocery lists to the front of our refrigerators don’t seem to have any moving parts, yet they still create magnetic fields. It turns out that relativity is ultimately responsible for the magnetism of a stationary hunk of iron, too.
Every proton, electron, and neutron in the universe has a tiny magnetic field associated with it. This field is barely noticeable compared with the Earth’s magnetic field, or fields created by an electrical current. The electrons orbiting the nucleus can be (very roughly) considered tiny current loops that generate magnetic fields. But even without this “orbital” effect, there is still an internal magnetic field within atoms. Where does this minuscule intrinsic magnetic field of subatomic particles come from? The answer involves quantum mechanics, which we will discuss in the next section. A principle of the Special Theory of Relativity is that space and time should properly be considered on an equal footing as a single entity, called space-time. When this relativistic adjustment is made to the basic equation of quantum physics, the theory predicts that electrons should have a very small internal magnetic field, the theoretically predicted magnitude of which agrees precisely with the measured value. The internal magnetic field of electrons, protons, and neutrons is understood mathematically only in the relativistic version of quantum mechanics. Even for stationary matter, relativity turns out to be crucial for understanding magnetism. So, no Einstein, no relativity, and, hence, no magnetism. No magnetism, no magnetic iron, and, most importantly, no refrigerator magnets! Therefore, without relativity there is no way to keep our shopping lists from falling to the floor and lying there, discarded and unread. Without Einstein’s towering achievement in theoretical physics, a slow and lingering death of starvation would await us all.
Normally, the small magnetic fields of electrons inside an atom like to pair up, just as when you bring two magnets together, they orient themselves to align at separate poles. When the magnetic fields inside an atom pair, there is no net magnetic field associated with the atom, just as an ordinary atom will have no net electric field, because the number of positive protons in the nucleus is balanced by an equal number of negatively charged electrons. Most materials, such as paper and plastic, are not magnetic, and even most metals, such as silver and gold, have all of their magnetic moments paired up.62
If most materials do not have net magnetic fields because their atomic magnetic moments are paired up, then how is Magneto able to levitate himself and other people, as shown in fig. 29? The physical basis behind this trick is that Magneto is able to generate such a large magnetic field that he essentially polarizes the internal magnetic fields of our atoms, turning us, or any other object, into a magnet.
Before we begin this discussion of magnetic levitation, I first must stress that Magneto does not lift people through his influence on the iron in their blood. Let’s leave aside the question of the effect of an inhomogeneous pressure on the veins and arteries in a person’s body (this would get messy), and focus instead on the blood’s magnetism. A few metals, such as iron and cobalt, have just the right configuration of non-paired electrons’ internal magnetic fields, so that the atom has a net magnetic field. However, the iron in your blood occurs primarily in the form of hemoglobin, a protein used to collect and transport oxygen and carbon dioxide as you breathe. Hemoglobin is a very large molecule that consists of four large proteins (called globins, which look like folded worms) bonded together. Each of these proteins contains a large molecule termed a “heme” group, composed of carbon, nitrogen, oxygen, hydrogen, and iron. The iron atoms in the center of each heme molecule are chemically bonded to their neighboring atoms. There’s another technical term for an iron atom chemically bonded to oxygen atoms: rust. As anyone who has dealt with scrap metal can confirm, rust makes for a very weak magnet. The common form of rust has three oxygen atoms bonded to two iron atoms (called “hematite”) and is nonmagnetic, though four oxygen atoms bonded to three iron atoms (termed “magnetite”) is magnetic. The magnetic field of the iron in hematite disappears when it combines with oxygen atoms, because the iron and oxygen chemically sharing their electrons pair up the remaining uncanceled electronic magnets in the iron. Depending on whether the hemoglobin has picked up an extra oxygen molecule to bring to the cells, or is carrying a carbon-dioxide molecule to be exhaled, the iron can either have an uncanceled magnetic field or not. But at any given moment only a fraction of your blood is even capable of being affected by an external magnetic field.63
Fig. 29. Scene from X-Men # 6 (above) and X-Men #1 (left), as Magneto attacks (above) or escapes (left) from the X-Man the Angel (the one with the wings), illustrating Magneto’s ability to levitate nonmagnetic objects, such as a boulder or himself, through the principle of diamagnetic levitation.
Even when iron is not chemically bonded to oxygen atoms, it is possible that it will be nonmagnetic, if all of the individual atoms are not properly aligned. Ordinarily the atoms inside a piece of iron or cobalt will line up, forming small regions termed “domains,” where all the iron atom’s magnetic fields point in the same direction. However, entropy considerations lead to the domains pointing in different directions, so their combined magnetic fields cancel out. Heat up a bar of iron so that the atoms have a lot of thermal energy and are free to rotate, and then place it in a strong external magnetic field. The external field induces the majority of the domains to all point in the same direction, so that the piece of iron, when cooled back to room temperature, has a large net magnetic field. If you hit the magnetized iron bar with a hammer or heat it in an oven, you will cause the magnetic domains to reorient themselves randomly, with the effect being that the magnet will lose nearly all of its field strength. Some flexible, credit card-size refrigerator magnets have their magnetic domains aligned in little strips along their length. Rather than have all of their domains point in the same direction, it is easier to line them up so that one strip has its north pole pointing toward the refrigerator, while the adjacent strip has its north pole heading away from the fridge, and so on.64
Materials that form magnetic domains with magnetic fields pointing in the same direction are called “ferromagnetic” (so named after iron, the most famous example). Many atoms in solids have a very weak magnetic interaction with their neighbors, so if placed in a strong external magnetic field, they will align in the direction of the field but will randomize again at room temperature once the field is removed. These materials (such as molecular oxygen, gaseous nitric oxide, and aluminum) are termed “paramagnetic.” And there is a third class of materials in which, due to the nature of the interactions between adjacent atoms and the chemical ordering of the atoms, their atomic magnets (generated by electron orbits within the atoms) line up opposite an external magnetic field. If an external magnetic field is applied to these materials and the field’s north pole points up, the atomic magnet’s north pole rotates to point down. These materials are called “diamagnetic,” and they try to cancel out any external magnetic field. Gold and silver are diamagnetic—if you are able to pick up your jewelry using a refrigerator magnet—someone has some explaining to do! Water molecules are also diamagnetic, and since we are primarily composed of water, so are we.
It is through our diamagnetism that Magneto is able to levitate himself and other people, as shown in fig. 29. In moderate-strength magnetic fields, the atoms in your body are not susceptible to being polarized. The diamagnetic interaction is weak, such that at room temperature, the normal vibrations of the atoms overwhelm the attempt to magnetically align them. In a very strong field, roughly two hundred thousand times greater than the Earth’s magnetic field (and more than one hundred times larger than the field of a refrigerator magnet), the diamagnetic atoms in your body can be induced to all point in the same direction—opposite to the direction of the applied field. Just
as two magnets repel if they are brought together so that their north poles are facing each other, the now magnetically polarized person will be repelled by the external magnetic field Magneto is creating—the very field that magnetically aligned the atoms in the first place. As Magneto increases the magnetic field he generates, the magnetic repulsion can become strong enough to counteract the downward pull of gravity. (That is, the upward force of the magnetic repulsion can be equal to or larger than the downward force of the person’s weight, and there is then a net upward force on the person, lifting him off the ground.) It takes a very big magnetic field requiring a great deal of power to accomplish this, and the heavier the person, the larger the effort. But it can be done, and the High Field Magnetic Laboratory at the University of Nijmegen in the Netherlands has amusing images and movies on their website of floating frogs, grasshoppers, tomatoes, and strawberries, demonstrating the reality of diamagnetic levitation.
If an electrical current generates a magnetic field, then could a moving magnetic field induce an electrical current in a nearby wire? The answer, as anyone who has read X-Men comics would know, is yes. In previous battles with the X-Men, and occasionally with puny humans, Magneto employed his mutant talent to transform any metal object into either an offensive weapon or a defensive shield. Magneto’s power is most effective on metals that are already magnetic. There are only three elements (iron, cobalt, and nickel) that are magnetic at room temperature. Magneto can manipulate a steel girder into any form he wishes through the iron it contains, but his power would be limited on a gold wedding band, unless he is willing to expend an extreme effort in polarizing the normally diamagnetic material. But Magneto’s real power lies not in his ability to exert forces on other magnetic materials, but in his control over electrical currents.
For example, the Mutant Master of Magnetism once constructed a computerized control panel that automated the power-dampening fields that neutralized the X-Men’s mutant abilities, keeping them from interfering with his plan of conquest. To prevent the X-Men from deactivating the device, Magneto configured it so that it has no buttons or knobs that can be reprogrammed. Magneto controlled the panel by altering the electrical currents that flowed through its circuits, affecting them through the magnetic fields that they create. Furthermore, by varying the magnetic field over the control panel, Magneto could cause these currents to flow.
How would a varying magnetic field create an electrical current? The answer brings us back to the point that started our discussion of electrical currents and magnetic fields: relative motion.
Just as a magnet can be pushed or pulled when a second magnet is brought near it, an external magnetic field can exert a force on an electrical current. As described in the previous chapter, moving electric charges generate a magnetic field that can attract or repel other magnetic fields, whether created by another electrical current or by a refrigerator magnet. When the charges are not moving, but are sitting in a wire placed in an external magnetic field, there will be no force exerted on them.65 What about if the external bar magnet is moved, while the charges remain sitting still in the wire? Assume that the magnet is moved toward the wire. From the magnet’s point of view, it is not moving at all, but it is the wire that is moving toward it.
Magnetism is, at its heart, all about relative motion. If you were a blindfolded passenger in a car moving at constant speed in a straight line, how could you prove that when you arrived at your destination, it was the car that moved, and not the scenery? If you change your speed or direction, then you will feel a force associated with the acceleration, and this will tip you off that it is you doing the moving. But for uniform motion, you cannot really prove whether you or everything else is moving. All you can say for sure is that you moved relative to your surroundings.
Similarly, when moving a magnet toward a wire, from the magnet’s point of view, it is stationary, and it’s the charges (both the mobile electrons and the fixed positively charged ions) in the wire that are moving toward it. But moving electrical charges create a magnetic field that will interact with the field of the magnet. So, by moving a magnet near a wire, the magnet sees two electrical currents from the positively charged ions and negatively charged electrons. A force is exerted on the charges in the wire and the electrons are free to move in response to this force. In this way, Magneto is able to affect the direction of electrical currents in any device at will, though the precision by which he can guide them depends on how sensitively he can manipulate these magnetic fields.
If relative motion is the only factor that matters when considering whether a magnetic field affects electrical charges, then how about a situation in which the magnet is stationary, but the wire is moved past the magnet? Would that generate a force on the charges? Sure!
If I pull a wire through space, the electrons in the wire are moving, just as surely as if I kept the wire still and applied a voltage across it. In either case, the electrons are moving past a fixed point at a certain speed. Relative to the magnet, it is as if there were an electrical current flowing by it, and we know that electrical currents and magnets interact. In this situation, the charges in the moving wire will feel a force that will induce them to flow. By dragging the wire through the external magnetic field, we convert the physical energy spent moving the wire into a form of electrical energy manifested by the electrical current. For a coil of wire, it does not matter whether the magnet is pulled through the loop or the loop is moved past the magnet. As long as there is a relative motion between the charges in the wire and the magnitude of the magnetic field threading the loop, then a current will be induced, even without an outside voltage. This mechanism may sound a bit far-fetched, but it is in fact how the electricity coming into your house is generated.
A power station, such as the one Electro employs to charge up for a night of crime, operates on the principle that when a magnetic field passing through the plane of a coil of wire is changed, a current is induced in the wire. This is called Faraday’s Law, after Michael Faraday, who was one of the first scientists to introduce the concept of electric and magnetic fields. The direction of this induced current is such that it creates a magnetic field that opposes the changing external magnetic field. This is a consequence of energy conservation, as we’ll explain in a moment. In certain circumstances, this current is termed an “eddy current,” but it occurs whenever the magnetic field passing through a coil is increased or decreased.
Imagine a large magnet bent in the form of a broken ring, so that the north pole faces the south pole, with a coil held in the open gap between its north and south poles. Initially the plane of the coil is at right angles to the magnet’s poles, so the magnetic field passes through the loop. If the coil is now rotated ninety degrees, the plane of the coil faces away from the poles, so the amount of magnetic field passing through the coil is very small. Another right angle turn, and now the coil again faces the poles, and the magnetic field passing through it is large again. A further quarter rotation, and the field through the coil is minimized again, and so on. For every change in the magnetic field passing through the coil, whether an increase or a decrease, a current is induced. The direction of the induced current flips back and forth as the coil rotates. What we have just described is an electric dynamo, and by continuously changing the magnetic field passing through the coil faces, an electric voltage will be generated in the rotating coils. There are tricks for converting an alternating current (referred to as AC) to a direct current (known as DC). There are many practical reasons that we won’t go into for using AC to supply our electrical needs. In the United States the coils are made to rotate sixty times in one second, which is why in the States the AC power has a frequency of 60 Hz (Hz is an abbreviation for the unit of frequency “Hertz” and measures the number of cycles or rotations per second), while in Europe the AC current’s frequency is 50 hz.
A current flows when the magnetic field passing through the rotating coil changes. From a conservation-of-energy standpoint, we
realize that it must take energy to rotate the coil, in order to create an electrical current that did not exist before. In The Dark Knight Strikes Again # 1—Frank Miller’s dystopian view of the future of the DC universe in which superheroes are forced into servitude and Lex Luthor runs the country—a third of America’s electrical power was supplied by coercing the Flash to continually run on a treadmill. Recall from Chapter 12 that the Flash has managed to find a loophole around the Principle of Conservation of Energy (presumably through his ability to tap into a “speed force”), so in Luthor’s view, one might as well get some economic benefit from this suspension of the rules of physics. In our world, where we have yet to find a single exception to the conservation of energy principle, the energy that turns turbines and generates electricity comes from the same mechanism employed for making tea.
Nearly all commercial power plants generate electricity by boiling water. The resulting steam turns a turbine (a fancy term for a pinwheel) to which the coils of wire in the powerful magnets are connected. As the turbines rotate, so do the coils, and electrical current is produced. To boil the water, one either burns coal, oil, natural gas, or bio-mass. Alternatively, the heat generated from a nuclear reaction can boil water and turn the turbine. But it all just goes toward creating steam in order to turn a pinwheel attached to a coil between the poles of a magnet. The stored chemical energy in the coal, oil, or garbage has the same source as the chemical energy in the food we eat—that is, from plant photosynthesis. The light from the sun is a by-product of the nuclear-fusion reaction running in the solar core. (So, all electrical power plants could be viewed as nuclear plants or solar plants, depending on your political bent.)
The rotation of the blades in wind-generated electrical power results from temperature differences in the atmosphere arising from spatial variations in the sunlight absorbed by the atmosphere or reflected by cloud cover. Obviously, solar cells (to be discussed in Section 3) require sunlight in order to function. Similarly, hydropower, in which the potential energy of water in a dam or waterfall is converted into kinetic energy to turn a turbine, requires solar-driven evaporation, followed by condensation, to replenish the high ground with water. Aside from harnessing the tides, and geothermal power, in which the internal heat of the Earth is used to boil water, all other mechanisms for generating electricity involve the conversion of energy from the sun in one form or another. Clearly, without sunlight, none of us would be here. Perhaps the writers of Superman were onto something when they changed the source of Kal-El’s powers from Krypton’s excessive gravity to the light from our sun.
The Physics of Superheroes: Spectacular Second Edition Page 25