## Wednesday, April 17, 2013

### History of Science -- Part Six: Electromagnetic Force

A piece of silk rubbed on glass is attracted to the glass but repelled by another piece of silk also rubbed on glass. Walk across a rug dragging your feet and, when you touch a door knob, you’ll get a nice blue spark as electricity jumps to the door knob. Such “electric charge,” seen when different materials are rubbed together, was known in ancient times. The crucial step in understanding it was the bright idea of Benjamin Franklin. He noticed that when any two electrically charged attracting bodies came into contact, the attraction lessened. He realized that attracting charged bodies canceled each other’s charge.

Cancelation is a property of positive and negative numbers. Franklin therefore assigned algebraic signs, positive (+) and negative (-), to charged objects. Bodies with charges of opposite sign attract each other. Bodies with charges of the same sign repel each other.

Unfortunately, what Franklin didn’t realize was that the carrier of the charge was the electron. It flowed onto the objects that he called “negative” leaving a shortage of negative charge on the object providing the electrons making it “positive.” Later, when scientists figured out just what was “flowing,” it was the “negative electricity.” That makes some of the equations of electricity and especially circuit theory use negatives. It isn’t a big deal, but a lot of modern electronics engineering imagines a positive current flow in the opposite direction to the electron flow. This is called “conventional flow” and is positive. It just makes the mathematics a tiny bit easier.

We all wish Franklin had chosen the opposite bodies to be positive and negative, and then we wouldn’t need this fiction of “conventional current” to make the math a little bit easier. But, you can’t go back and change history. We’re just lucky that Franklin didn’t kill himself flying kites in thunderstorms.

Franklin’s work on electricity is in good part responsible for the existence of the United States. As ambassador to France, it was not just Franklin’s wit, charm, and political acumen, but his stature as a scientist that allowed him to recruit the French aid that was so crucial to the success of the American Revolution.

We now know that atoms have a positively charged nucleus made up of positively charged protons and uncharged neutrons. Electrons, each with a negative charge equal in magnitude to that of a proton, surround the nucleus. The number of electrons in an atom is equal to the number of protons, so the atom as a whole is uncharged. When two bodies are rubbed together, it is the electrons that move from one to the other.

A glass rod that is rubbed with a silk cloth, for example, becomes positively charged because electrons in the glass are less tightly bound than those in the silk. Therefore, some electrons move from the glass to the silk. The silk, now having more electrons than protons, is negatively charged and is attracted to the positively charged glass. Two negatively charged pieces of silk would repel each other.

An early scientific device for exploring these charge is called an electroscope. One such device, the gold foil electroscope, is made up of two thin leaves of gold suspended in a glass jar. The gold-leaf electroscope was developed in 1787 by British clergyman and physicist Abraham Bennet. It was a very sensitive device to detect charge. It consists of a vertical metal rod, usually brass, from the end of which hang two parallel strips of thin flexible gold leaf. A disk or ball terminal is attached to the top of the rod, where the charge to be tested is applied. To protect the gold leaves from drafts of air they are enclosed in a glass bottle, usually open at the bottom and mounted over a conductive base. When a charge is applied to the metal ball, it flows down to the gold leaves, causing them to spread apart. If the charge is negative, then the excess electrons on the two leaves repel since they are like charges. Same with a positive charge which is a shortage of electrons.

Coulomb's law describes the electrostatic interaction between electrically charged particles. It was first published in 1785 by French physicist Charles Augustin de Coulomb, and was essential to the development of the theory of electromagnetism. Like gravity, this force is an inverse square law. That is, the intensity of the attraction or repulsion is proportional to the inverse square of the distance between the two objects. Double the distance and you get one over two squared or one-fourth the attractive force. With this law you can calculate the forces in any arrangement of charges. That seemed to be the whole story of electric force — there was nothing more to say, or so thought most physicists in the early nineteenth century.

But Michael Faraday found the electric force puzzling. Let’s back up a bit. At the age of fourteen, Michael Faraday, the son of a blacksmith, was apprenticed to a bookbinder. Faraday, a curious fellow, was fascinated by some popular science lectures by Sir Humphrey Davy. He took careful notes, bound them into a book, presented them to Sir Humphrey, and asked for a job in his laboratory. (There is a lesson there for any young person wishing to break into a new field of endeavor.) Though hired as a menial assistant, Faraday was soon allowed to try some experiments of his own.

How, Faraday wondered, could one body cause a force on another through empty space? That the mathematics of Coulomb’s law correctly predicted what you would observe did not satisfy him. He therefore postulated that a charge creates an electric “field” in the space around itself, and it is this physical field that exerts forces on other charges. Faraday represented his field by lines emanation from a positive charge and going to a negative charge. Where the lines were most dense, the force of the field exerted would be greatest.

Most scientists, claiming that Coulomb’s law said it all, considered Faraday’s field concept to be superfluous. Faraday’s ignorance of mathematics, they noted, required him to think in pictures; abstract thinking was no doubt difficult for this young man from the “lower classes.” The field concept was ridiculed as “Faraday’s mental crutch.”

Actually, Faraday went further and assumed that the field due to a charge takes time to propagate. If, for example, a positive and a nearby negative charge of equal magnitude were brought together to cancel each other out, the filed would disappear in their immediate neighborhood. But it seemed unlikely to Faraday that the field would disappear everywhere immediately. (He as so, so right about that!)

The remote field would, he thought, exist for a while even when the charges that created it canceled each other and no longer existed. If true, the field would be a physically real thing in its own right, and not just a crutch.

Moreover, Faraday reasoned, if two equal and opposite charges were repeatedly brought together and separated, an alternating electric field would propagate from this oscillating pair. Even if they stopped oscillating and just canceled each other, the oscillating field would continue to propagate outward.

Faraday’s intuition was sound. A few years later James Clerk Maxwell, picking up Faraday’s field idea, devised a set of equations that encompassed all electric and magnetic phenomena. He combined Faraday’s law of moving charges with Ampère’s law that relates the magnetic field around a closed loop to the electric current passing through the loop and Gauss’s law which is the magnetic analog of Ampère’s. Finally, he added a term to Ampère’s law. Ampère’s law with Maxwell’s correction states that magnetic fields can be generated in two ways: by electrical current (this was the original "Ampère's law") and by changing electric fields (this was "Maxwell's correction"). Maxwell's correction to Ampère's law is particularly important: it shows that not only does a changing magnetic field induce an electric field, but also a changing electric field induces a magnetic field. I consider these four equations the pinnacle of Classical Physics. Like much of Classical Physics, they are just approximations and require some correction both to fit the requirements of Relativity and also Quantum Theory. In fact, in many ways, this set of equations open the door to these twin discoveries of the twentieth century that relegate all that came before as “Classical Physics” and just an approximation of Nature’s true methods.

James Clerk Maxwell was a Scottish physicist and mathematician and he published his results between 1861 and 62. His striking prediction was the existence of waves of electric field propagating along with waves of magnetic field — “electromagnetic waves.” Maxwell noticed that the speed of these waves was exactly what had been measured for light. He therefore proposed that light was an electromagnetic wave.

The four modern Maxwell's equations can be found individually throughout his 1861 paper, derived theoretically using a molecular vortex model of Michael Faraday's "lines of force" and in conjunction with the experimental result of Weber and Kohlrausch who had measured the speed of light. But it wasn't until 1884 that Oliver Heaviside, concurrently with similar work by Willard Gibbs and Heinrich Hertz, grouped the four together into a distinct set. This group of four equations was known variously as the Hertz–Heaviside equations and the Maxwell–Hertz equations, and are sometimes still known as the Maxwell–Heaviside equations. But, in most modern texts, all credit for the equations is given to Maxwell.

Maxwell's contribution to science in producing these equations lies in the correction he made to Ampère's circuital law in his 1861 paper On Physical Lines of Force. He added the displacement current term to Ampère's law and this enabled him to derive the electromagnetic wave equation in his later 1865 paper A Dynamical Theory of the Electromagnetic Field and demonstrate the fact that light is an electromagnetic wave. This fact was then later confirmed experimentally by Heinrich Hertz in 1887. The physicist Richard Feynman predicted that, "The American Civil War will pale into provincial insignificance in comparison with this important scientific event of the same decade."

The concept of fields was introduced by, among others, Faraday. Maxwell then combined all these ideas into this keystone of electro-magnetics. Albert Einstein wrote:

The precise formulation of the time-space laws was the work of Maxwell. Imagine his feelings when the differential equations he had formulated proved to him that electromagnetic fields spread in the form of polarised waves, and at the speed of light! To few men in the world has such an experience been vouchsafed … it took physicists some decades to grasp the full significance of Maxwell's discovery, so bold was the leap that his genius forced upon the conceptions of his fellow workers —(Science, May 24, 1940)

As Faraday had predicted, the jiggling of charges produces electromagnetic radiation. The frequency of the jiggling is the frequency of the wave produced. These are the waves we associate with radio and television broadcasts and, at higher frequencies, they are light. Infrared and red are lower frequency and violet and ultraviolet are higher. Even higher frequencies are X-Rays and Cosmic Rays.

Today the most fundamental theories in physics are formulated in terms of fields — Faraday’s “mental crutch” is a pillar upon which all of physics now rests.

The electromagnetic force in very important in many branches of science from electronics to chemistry. Along with gravity, it is the only force we normally experience.

When we touch someone, the pressure of our touch is an electric force. The electrons in the atoms of our hand repel the electrons in the atoms of the other person. Reach out and touch someone by telephone, and it is the electric force that carries the message over the wires and through space. The atoms making up solid matter are held together with electric forces. Electric forces are responsible for all of chemistry and therefore underlie all biology. We see, hear, smell, taste, and touch with electric forces. The processes in our brains are electrochemical, therefore ultimately electrical.

Is our thinking, our consciousness, ultimately to be explained wholly in terms of the electrochemistry taking place in our brains? Some believe so.

There are forces in nature besides gravity and the electromagnetic force. But, we only know of two others: the so-called “strong nuclear force” which binds the protons in the nucleus of an atom together and overcomes the repulsion of like charges, and the “weak force” which is involved in radioactive decay. Current theories combine the weak force and the electromagnetic force. Science is still looking for a combination of all four forces and it is possible there are additional forces we have not yet discovered. Since the strong and weak forces only operate over the very short distances found in the nucleus of atoms, gravity and electric force are what we encounter in our day-to-day lives.

The method used by Faraday is something that interests me personally. I know scientist that work entirely in the abstract realm of mathematics and don’t really worry much what it “looks like.” On the other hand, some of the greatest scientists of all time, including Einstein and Richard Feynman, seemed to use intuitive vision as much as mathematics to understand the physical world. I’m trying to decide which group I belong to. Sadly, in my day, there was a greater emphasis on geometry and especially solid geometry that ties together this visualization and mathematics. These topics are not as common in modern schools with the emphasis shifting to the pure math and away from vision. With computers taking over much of the calculation, I think the time is right to focus more on visualization and ask more "why" questions. That is one of many reasons I’ve added “Art” and “Design” to my “STEM” focus.

I’m as interested in the "why" and "how" as I am of the "what" and "where" and "when." Perhaps that is the source of my great interest in the history of ideas and science. Hopefully you share this interest with me and have found these discussions to your liking. There are other powerful ideas that have led to many scientific breakthroughs. One of those universal ideas is “conservation,” which turns out to be a function of “symmetry.” That is what I’ll explore next as I continue with the History of Science and look at “energy.”