# Tag Archives: magnetism

## Moving Charge, Magnetism, and Inductors

Last time I talked about how magnetization arises from the alignment of spins, which is favorable in some materials due to the quantum mechanical exchange interaction. But, there is another way to generate a magnetic field: it turns out that moving charges (i.e. an electric current) create a magnetic field as well! This was first observed experimentally by Ørsted, who noticed a compass needle moving in response to current running through a coiled wire. It was then incorporated into Maxwell’s Equations, which attempted to provide a unified framework for observed electric and magnetic phenomena.

But while the evidence that a moving charge generates a magnetic field was clear, explaining the mechanism by which this happens took some time. The key insight actually came from Einstein, who saw Maxwell’s Equations and had a question: why is the speed of light independent of the reference frame? That is to say, we know that if we are in a car that is passing another car, our car appears to be going only a bit faster than the other car, even though an observer standing on the sidewalk would say that both cars were moving fairly fast. The observed speed depends on the frame of reference of the observer! And so in classical mechanics, the speed of an object and the speed of its reference frame can be added together to give the total object speed. Why should it be any different for something moving at the speed of light? Well, the answer to that question gets into special relativity, but consider the same question with a moving charge from two frames of reference:

1. From the reference frame of the charge, an electrical field is induced by a static charge.
2. From the reference frame of a static observer, a magnetic field is induced by a moving charge.

The implication is that electric and magnetic fields, and forces, are simply two facets of the same phenomena, which is now called electromagnetism.

In fact, the magnetic field of the earth, shown above, is due to moving charge in the form of molten iron in the outer core of the planet. The charge flow is maintained because magnetics fields induce current flow, just as current flow induces magnetic fields, forming a feedback loop. The earth’s magnetic field is not very large, but it is enough to enable measurement devices such as compasses, which have long been used for navigation. Some animals are also able to sense the earth’s magnetic field to directly use for navigation, including homing pigeons, sharks, and even smaller organisms such as bacteria. Many different biological sensors for magnetic field seem to have evolved independently, likely due to the significant survival advantages associated with reliable navigation.

But another place where the magnetic field induced by a moving charge arises is in electronics. Any wire with a current running through it will generate a magnetic field proportional to the size of that current. That means that nearby objects that respond to magnetism may experience magnetic forces, or even have electric currents induced in them. Coaxial cable, which has an inner wire carrying current encased in an insulator and a cylindrical outer conductor, confines the magnetic field to the insulating region of the wire. It was developed specifically to shield the magnetic field of the current-carrying wire, and to shield the wire itself from stray external magnetic fields.

And there is a basic circuit component that makes use of this phenomenon as well, the inductor. An inductor, as you can see above, consists of wire coiled in a loop, possibly with many coils and possibly with a material lodged inside the coils of wire. The current on the wires induces a magnetic field in the center of the loop. The forces from this magnetic field act against any change in electric current, using the energy stored in the magnetic field. Because inductors are sensitive to changes in current over time, they are very useful in processing time-dependent electronic signals. The magnetic field of one inductor can also be coupled to the coils of a second inductor, inducing a second current which may be larger or smaller depending on the relative sizes of the coils of the two inductors. This is how a transformer is made, a device which inductively transfers electrical signals and is central to power transmission from the power grid to individual homes and businesses.

As you can see from all these examples, there are a lot of technologically useful things to do with the interplay between electricity and magnetism! And the realization that they were intertwined was a huge step forward for physics.

## Magnets, How Do They Work?

Most of us have had some experience with magnetism, whether it’s finding north with a compass, posting a grocery list with refrigerator magnets, or playing with magnetic toys that snap satisfyingly together. And from those interactions we can glean some basic information about magnetism:

1. Magnetic fields, even weak ones such as that of the earth, exert a magnetic force.
2. Magnetic forces are experienced by some objects but not others.
3. Magnets are cool.

But what causes magnetism in the first place? The answer is quantum mechanical in nature, and relates to an idea we discussed when we talked about the spin-statistics theorem. Recall that fundamental particles are indistinguishable, meaning that if we have two electrons and two available states, we cannot tell the difference between a system where electron 1 is in state 1 and electron 2 is in state 2, and a system where electron 1 is in state 2 and electron 2 is in state 1. In fact, we can’t even figure out which is electron 1 and which is electron 2; mathematically they are indistinguishable. This, of course, relies on the particles having identical physical properties such as charge and mass, but all electrons do. Another way of saying that particles are identical is to say that you can’t tell the difference if you swap two particles, which physicists call exchange symmetry. Mathematically, it becomes necessary to write equations for multiple particles so that the equation is not modified by exchanging the particles, and this adds a term due to the exchange interaction. We can think of the exchange interaction as another factor affecting the landscape of energy available to the physical system, much like gravity or electrical interactions are factors. Thus, how to minimize the energy of the system depends on the exchange interaction. And it turns out that for some materials, the exchange interaction term causes a system with aligned spins to be lower energy than a system where the spins are randomly oriented.

This is the origin of ferromagnetism, a property of objects that are permanently magnetized. Their spins align to minimize energy, creating a magnetic field that can interact with other magnetically sensitive objects. Some materials are susceptible to magnetism without being permanently magnetic, which usually occurs because small regions of the material magnetize but the regions never combine to create a material-wide magnetization. This is often the case with alloys that include iron or other magnetic materials, and the regions of magnetization are called domains. (Magnetic domains in a rare earth magnet are shown in a microscope image below.) So when you put a magnet on a refrigerator, you are placing a permanent ferromagnet on an alloy and aligning a small region of magnetic domains, creating a force that holds the two together. But the magnet can’t align the spins in a wooden cabinet door, because other terms besides the exchange interaction are more important in that material, so magnets won’t stick to wooden objects.

The polarity of magnets, which are usually described as having a north and a south pole, also stems from the aligned spins. Spins aligned in opposite directions, say one pointing north and one pointing south, are generating oppositely oriented magnetic fields. This is a very high energy configuration, as you know if you have ever tried to hold the south ends of two bar magnets together. But rather than one magnet reordering the other, the magnetic forces generated push the magnets apart.

You might be wondering, is there any way to change the magnetization of a ferromagnet? And actually, there is. While the exchange interaction is one factor controlling the configuration of many particles together, another factor is more mundane: temperature! At high temperatures, the high ordering of all the spins being aligned costs more and more energy to maintain, because there is plenty of thermal energy jostling the spins around. This is why sometimes people talk about ‘freezing in’ magnetism, because if you place some high-temperature materials with unaligned magnetic domains in a magnetic field and then let them cool, they will stay magnetized even after being removed from the magnetic field. And, conversely, if you melt a ferromagnet, it loses its magnetic alignment (but not its fundamental propensity to magnetize, which will return as soon as it cools back down!).

Compass needles are also ferromagnets, but the origin of the earth’s magnetic field is more complex, and ties into the use of magnetism in circuits. Next time!

## What is spin?

First the basics: spin is an intrinsic property of matter, like charge or mass. It is measurable in the real world by observing interactions with magnetism, and is the basis of technologies like MRI and hard disk drives!

We of course recognize the verb ‘to spin’, which means to rotate around a fixed axis the way that wheels, figure skaters, and the Earth do. But the word spin is also used to describe a fundamental property of particles. We have already talked a little about a fundamental property, charge, which was useful because a lot of the important forces at the atomic scale are electromagnetic and thus related to charge. And we remember that mass, another fundamental property, determines how matter interacts via the gravitational force. Spin is a bit different.

The idea of particles having an intrinsic spin first arose during the development of quantum mechanics, when Wolfgang Pauli and others noticed that part of the mathematical solution for particle states resembled angular motion, as if the particles were physically spinning around an axis. But unlike spinning at the macroscopic scale, quantum spin can only occur at a few discrete values: integer and half-integer multiples of ħ, the reduced Planck constant. The allowed values of spin are clustered around zero, and the ħ factor is dropped by convention because particle physicists like to make things look simple. So a photon, the quantum of light, has spin 0, whereas electrons and quarks, which make up protons and neutrons, have spin 1/2. There are also particles with spin 1, 3/2, and 2. As with charge, spin is reminiscent of a behavior we see in the macroscopic world, but its values are quantized into a few allowed values.

Spin can have one of two polarities, meaning we can have an electron with spin +1/2 and one with spin -1/2. And charged particles like the electron actually respond to magnetic fields differently if they have positive or negative spin! This is because the motion of a charged particle creates a small magnetic moment, which will be aligned in one direction for positive spin and the opposite direction for negative spin. This is the basis of the famous Stern-Gerlach experiment, in which atoms with one free electron are sorted by their spin under the influence of a magnetic field. But it’s also the basis of nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI), two related techniques for determining the composition and structure of either chemical substances or human patients! Strong magnetic fields can be used to align spins within any object, and how quickly the spins decay back to their original orientation gives information about what is inside the object. Currently, researchers are trying to build circuits that use spin instead of charge to carry information, which is called ‘spintronics’.

But at a more basic level, when we talked about chemical bonds we skipped over the importance of spin. The reason spin matters for bonding is due to the Pauli exclusion principle, the idea that no two electrons can share the same quantum state. In the development of quantum mechanics, it became clear from the data that even if all the available energy states were mathematically accounted for, there still seemed to be a degeneracy in which two electrons shared what was thought to be the same quantum state. This can be explained with a new quantum number, which we call spin. So spin is another factor of the electron cloud shape and is critical in the understanding of chemical bonding.

But there are actually even more strange things about spin than I can fit in this post, including the fact that the Pauli exclusion principle only applies to particles with half-integer spin! Half-integer and whole-integer spin particles are fundamentally different from each other, in some pretty interesting ways, but why is a story for another time!