Electricity and Magnetism

By the first decades of the eighteenth century, mechanics alone of all the branches of physics had obtained a somewhat modern form. When Newton died in 1727, another major branch of physics, the study of electricity and magnetism, was still rather elementary. The most important discoveries in this area were made in the following hundred years, finally leading, unexpectedly as it often happens in science, to a new unified view of electromagnetism, light, and other kinds of radiation.

Naturally magnetized iron ore or magnetite was known in antiquity. Also the electrostatic attraction of amber was mentioned by Plato, among others. However, we may regard William Gilbert (1544-1603), the private doctor of Queen Elizabeth I, as a pioneer of the scientific study of electric and magnetic phenomena. Gilbert studied medicine and mathematics at Cambridge, and practiced medicine in London. He was also an early supporter of Copernicus and the moving Earth. His studies in physics (which were a hobby) appeared in the book De Magnete in 1600.

Nature of Electricity

Gilbert regarded electricity as a liquid which is created or transported by rubbing, for example, when amber is rubbed by fur. He called this liquid elektrica after the Greek word for amber (many related words derive from this term, for example electron). He also showed that the Earth is a huge magnet, and studied it by using a miniature model of magnetite (Fig. 13.1). This helped him to explain why the compass needle points roughly in north-south direction. The actual magnetic pole of the Earth is at a latitude of 83° in northern Canada and is slowly moving to the north, about 40 km per year. By definition, a magnet's north pole is the end that points roughly to north. As we mentioned, Kepler contemplated a role for magnetism in planetary motion which was, of course, on the wrong track.

Another Englishman, Stephen Gray (1666-1736) announced in 1729 that electricity from rubbing can be conducted from place to place. He divided materials into conductors (e.g., copper) and insulators (e.g., glass) on the basis of this

Fig. 13.1 An illustration from William Gilbert's book De Magnete (On Magnets). Gilbert knew that the compass needle was affected by Earth's magnetic field which he called Orbis virtutis. The compass had been in use in China since the early centuries AD, and it was known in Europe in the thirteenth century. The north and south magnetic poles are to the left and right

Fig. 13.1 An illustration from William Gilbert's book De Magnete (On Magnets). Gilbert knew that the compass needle was affected by Earth's magnetic field which he called Orbis virtutis. The compass had been in use in China since the early centuries AD, and it was known in Europe in the thirteenth century. The north and south magnetic poles are to the left and right property. Frenchman Charles Du Fay (1698-1739) heard about Gray's work and started his own research. He concluded that there are two kinds of electricity: glass electricity and amber electricity. The former is generated, for example, by rubbing glass by a silk cloth while the latter arises in amber when it is rubbed by a piece of fur. He made this distinction by noting that bodies charged with like electricity repel each other while bodies of opposite electricity attract one another.

Du Fay's discovery was interpreted in many ways: there could be truly two kinds of electric fluid, or the fluid is only of one kind, but there can be an excess or a deficit of it, as suggested by Benjamin Franklin, among others. He regarded glass electricity as real, positive electricity, while the amber electricity would imply a shortage, or negative electricity. In his view, rubbing or any other operation does not create or destroy electricity, but it only leads to a transfer of electricity from one body to another. Thus he anticipated the law of conservation of electric charge, one of the cornerstones of current physics. The same idea had been proposed earlier by William Watson (1715-1787).

Franklin not only was one of the "founding fathers" in the American Revolution but he also invented the efficient Franklin stove, bifocal glasses, and the lightning rod. Franklin started as an apprentice of a bookbinder, and later became a book seller and publisher. At the age of 40, Franklin was a well-to-do man who could do whatever he liked. By accident, he happened to see an exhibition of the miracles

Fig. 13.2 Benjamin Franklin (1706-1790) was a polymath whose versatile interests, in addition to diplomacy included electricity

of electricity in Boston, and was so captivated that he spent the following 10 years studying electricity. However, he had to share his time with diplomatic duties, like helping write the Declaration of Independence and the US Constitution, and serving as the American ambassador in Paris (Fig. 13.2).

It was natural to make a comparison with Newtonian gravity when analyzing the electric attraction or repulsion. In addition to the two kinds of charge, the electrical force is a stronger version of Newton's force law making studies easier. English theologian and physicist Joseph Priestley (1733-1804) was the first to demonstrate that the force law between charges was indeed an inverse square law like in Newton's law of gravity. The most thorough studies of the electric force law were carried out by Charles Augustin Coulomb (1736-1806) in France; the force law has been named after him as Coulomb's law.

The discovery of the electric battery by the Italian physicist Alessandro Volta (1745-1827) opened up the field for sweeping research which changed the picture completely. Earlier this strong electric currents were generated only temporarily during electric discharges. Now every laboratory could equip itself with a powerful battery (Fig. 13.3). The power of the electric current for research increased by 10 000 fold. New secrets of nature were thus revealed.

Fig. 13.3 The big battery in the vaults of the Royal Institution was used, e.g., by Humphrey Davy in his experiments

Electricity and Magnetism are Combined

The next big discovery happened almost by accident. Hans Christian 0rsted (1777— 1851), professor of physics at university of Copenhagen, was preparing a lecture on electricity and magnetism, and for that purpose he had brought a battery to the class to demonstrate the effects of an electric current. Next to it he had placed a compass needle for the demonstration of magnetic forces. He had noticed earlier that there may be some connection between electricity and magnetism, e.g., in the form of a compass needle flipping during a thunder storm. Since he had extra time, he decided to make a little experiment before the beginning of the lecture. 0rsted put an electric current close to the compass needle, and indeed his suspicions were confirmed: the compass needle moved at the introduction of the current. Thus the two separate phenomena, electricity and magnetism, which so far has been considered totally different, had after all some connection to each other. 0rsted continued his studies and published the results in 1820.

News about 0rsted's discovery spread fast. His article was read in the meeting of the French Academy of Sciences later in the same year. Among the members of the audience was Ampere who started immediately to work on explaining 0rsted's finding. The theory was ready in a week, and it provided the foundation for combining electricity and magnetism into the theory of electromagnetism.

Andre-Marie Ampere (1775-1836) was born near Lyon. His father was a well-to-do merchant who was executed during the French revolution when he held the position of Justice of the Peace in Lyon. One may still visit Ampere's home which is now a museum. Young Ampere did not go to school, but acquired knowledge by reading. He had a rare ability for memorizing and learning as described by the following incident. As a small boy he went to the library of Lyon and asked to read the works of the famous mathematicians Euler and Bernoulli. The librarian explained to the boy that they were difficult mathematical books which he could not possibly understand, and moreover they were written in Latin. The last part about Latin took Ampere by surprise, but he did not let his lack of Latin stop him. After a few weeks he came back to the library knowing Latin and started to read the books.

Ampere married when he was 24 and started to support his family as a school teacher. In 1808, he was appointed as inspector of schools, a position which he held for the rest of his life. In addition, he worked also as a professor in Paris. By 1820, when Ampere became interested in electromagnetism, he was already well known for his work in mathematics and chemistry. This versatile scholar started as professor of mathematics, then moved to the professorship of philosophy and later became professor of astronomy! Since 1824, Ampere was professor of physics at College de France.

Ampere was not satisfied to merely to explain 0rsted's results but started experiments of his own. For example, he demonstrated that by rolling up the electric wire into a coil it was possible to create an artificial magnet, an electromagnet, which corresponded fully to the natural magnets. Ampere concluded boldly, but quite correctly that natural magnets hold inside them small permanent current coils which act together to create natural magnetism.

Ampere realized right away the great significance of electromagnetic phenomena in information transfer. By turning current on and off one can make the compass needle move instantly in a far-away place. Messages can be sent as far as one can make the electric current flow. The development of telegraph machines working on this principle started soon. One of the first telegraph lines was established in Gottingen in 1834 between the physics laboratory of Wilhelm Weber and the astronomical observatory of Carl Friedrich Gauss. In the same year, the first commercial telegraph line between Washington and Baltimore in the USA was started by Samuel Morse (of Morse code fame).

Another scientist who immediately understood the great significance of 0rsted's discovery was the Englishman, Michael Faraday. Faraday was the son of a blacksmith and received only minimal formal education. At 13, he became an apprentice to a book binder. Besides binding books, he also read them. One of his customers gave him a free ticket to public lectures by Humphry Davy (1778-1829). Faraday made careful notes of the lectures, bound them nicely, and sent them to Davy with a note of enquiry whether Davy might have any job for him. Faraday was surprised when Davy invited him for a visit. The notes were neatly written and Davy got a good impression of the boy, so he decided to offer him a position as an assistant at the Royal Institution of London in 1820. Thus began one of the most remarkable

Fig. 13.4 Michael Faraday (1791-1867), in a painting by Thomas Phillips carriers in science. It was said that Davy's greatest scientific discovery was Faraday (Fig. 13.4).

Faraday learned his science directly from Davy. When Davy made a one-and-half year tour of the continent, he took Faraday along. Here he met, among others, Ampere and Volta. And while Davy worked with Louis Gay-Lussac studying the new element iodine in Paris, Faraday acted as an assistant. The practical chemistry experiments were part of his duties also at home.

With the exception of a short period of interest in electromagnetism inspired by 0rsted's discovery, Faraday was a professional chemist up to year 1830. In 1833, he became professor of chemistry in the Royal Institution. But by then his scientific interests had changed. Faraday was convinced that if an electric current can cause a magnetic force, then a magnet must be able to create electric current. Here he agreed with many others, among them Ampere who however was not able to confirm the intriguing idea.

Faraday carried out different experiments on electromagnetism over 10 years. In 1831, he put two coils together, one inside the other. When electric current was put through one of the coils, it became an electromagnet. Faraday studied whether the magnet would cause electric current in the other coil. A current was indeed generated, but only momentarily when the electromagnet was turned on or off. This led Faraday to an important discovery: a changing magnet, for example a magnet with changing power or a rotating magnet, generates electric current in the nearby coil. It was crucial that the magnet was changing.

This is how Faraday discovered the electric generator, a simple dynamo which formed the basis of the electric industry of the future. Once when he was explaining a discovery to William Gladstone who was Chancellor at the time he was asked, "But after all what use is it?" Faraday quickly responded, "Why sir, there is every probability you will be able to tax it."

Force Fields

One of Faraday's big achievements was his new interpretation of how a force is transmitted between bodies. He saw lines of force penetrating through space instead of the action at distance. Faraday continued to develop his concept of lines of magnetic or electric force through the 1830s and 1840s. Because this novel concept was not mathematical, however, it was rejected by most scientists. Two important exceptions were William Thomson and James Clerk Maxwell. Thomson demonstrated how lines of force could be interpreted mathematically, and he also showed how Faraday's concepts of magnetic and electric force could be treated analogously to theories of heat and mechanics, thus laying the mathematical foundations of field theory. Faraday recognized the support from these "two very able men and eminent mathematicians" and "it is to me a source of great gratification and much encouragement to find that they affirm the truthfulness and generality of the method of representation."

For Faraday the concept of lines of force came naturally from experiments with magnets. When he sprinkled needle-like iron filings on a piece of paper lying on a bar magnet, he found that the filings lined up in very definite directions, depending their position relative to the magnet (Fig. 13.5). He thought that poles of the magnet are connected by magnetic lines, and that these lines are visualized by the help of the iron needles which line up parallel to the lines. For Faraday these magnetic lines were real, even though invisible.

Faraday generalized the concept of lines of force also to electric forces, and he believed that gravity could be treated similarly. Rather than saying that a planet knows by some strange reason how it has to move around the Sun, Faraday introduced a gravitational field which guides the planet in its orbit. The Sun generates a field in its vicinity, and planets and other celestial bodies feel the field and behave accordingly. Similarly, a charged body generates an electric field in its surroundings. Another charged body recognizes the field and reacts to it. Also there is a magnetic field associated with magnets.

In Newton's view, the basic entities are particles bound together by forces; the space between is empty. Faraday visioned both particles and fields in interaction with each other, our current understanding. One cannot say that particles are more

real than fields. It is customary to represent fields by lines which point to the direction of the force at each point in space (Fig. 13.6). The more densely spaced are the lines, the stronger is the force. Let us take the gravity of the Sun as an example. One may say that a whole lot of lines of force end at the Sun, and that they come equally from all directions. We may draw spheres of different radii centered on the Sun, hence the same lines of force cross every sphere. The area of the spheres increases as the square of the radius; thus the density of the lines decreases as the inverse square of the distance. Thus the concept of field lines leads us directly to Newton's law of gravity (and to Coulomb's inverse square law for the electric field of a stationary charge; Fig. 13.7).

A few simple rules must be followed when using the concept of force field (for gravity, as an example):

negative charge

Fig. 13.7 Gravitational lines of force associated with a spherically symmetric distribution of mass. The number of lines of force crossing a similar area decreases inversely proportional to the square of the distance to the mass center

1. The acceleration of gravity takes place along the force field which passes through the body.

2. The magnitude of acceleration is proportional to the density of lines at the point in question.

3. The lines of force can terminate only where there is mass. The number of lines terminating at a given point is proportional to the mass contained at that point.

Now it is easy to prove a result which caused Newton a lot of trouble. While comparing the accelerations at the Earth's surface and at the orbit of the Moon, Newton assumed that the Earth attracts bodies as if all of its mass were concentrated at its center. Why is this so?

Assume for simplicity that the Earth is completely spherically symmetric. Thus, all parts of its surface are equally covered by incoming lines of force. The number of the lines is by the third rule only dependant on the mass of the Earth. If all the Earth's mass were at its center, all the same lines would continue to the center. Thus, the Earth's gravity field is quite independent of how the mass is distributed under its surface, as long as the spherical symmetry is valid. In particular, the Earth mass concentrated at the center causes exactly the same gravity as the real Earth.

Similar deductions apply to the electric field. Since there are two kinds of electric charges, positive and negative, the direction of the line of force changes to the opposite when the sign of the charge is switched. Lines of force start from a positive charge and end at a negative one as seen in Fig. 13.6.

Fig. 13.7 Gravitational lines of force associated with a spherically symmetric distribution of mass. The number of lines of force crossing a similar area decreases inversely proportional to the square of the distance to the mass center

Electromagnetic Waves

The lines of force were seen intuitively by Faraday, but he was not able to put the theory in mathematical form. This task was completed by James Clerk Maxwell, the greatest theoretical physicist of the nineteenth century. Maxwell had a strong educational background; he was enrolled at the University of Edinburgh only at the age of 15. Three years later he moved to the University of Cambridge graduating in 1854. Two years later he became professor of physics at University of Aberdeen in Scotland from whence he moved to London. In 1865, he moved to his country

Fig. 13.8 James Clerk Maxwell (1831-1879) predicted electromagnetic waves and Heinrich Hertz (1857-1894) demonstrated their existence

estate Glenlair, not far from Glasgow, where he wrote his famous work Treatise on Electricity and Magnetism, published in 1873 (Fig. 13.8).

In the meantime, the University of Cambridge received a large donation from the heirs of Henry Cavendish (1731-1810) who was renowned for his studies of electricity, for the purpose of setting up a laboratory of physics. Up to then the physicists in the university had carried out their experiments in their own college rooms. There was a new professorship associated with the donation; Maxwell was chosen to the job in 1871. He started the distinguished series of Cavendish professors whom we will discuss later: John Strutt, better known as Lord Rayleigh, Joseph Thomson, and Ernest Rutherford. Over the years about 30 Cavendish Laboratory scientists have been honored with the Nobel prize in the fields of physics, chemistry, and physiology.

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Building* Human* Pinhood PimtoSw» Mokxulci Atora Atomic Nuclei Fig. 13.9 Different kinds of electromagnetic waves and their wavelengths (credit: NASA)

Maxwell combined the separate laws of electromagnetism discovered by Coulomb, Ampere, and Faraday into what is known as Maxwell's equations, treating electricity and magnetism together as a single phenomenon, electromagnetism. From Maxwell's equations one could deduce that vibrating electric and magnetic fields can proceed through space with a high speed which Maxwell calculated. The value was so close to the measured velocity of light that Maxwell wrote in a long letter to Faraday (1861): "I think we now have strong reasons to believe, whether my theory is a fact or not, that the luminiferous and the electromagnetic medium are one____" And in a later paper he wrote: "The agreement of the results seems to show that light and magnetism are affections of the same substance, and that light is an electromagnetic disturbance propagated through the field according to electromagnetic laws."

Thus, light is made of electric and magnetic fields which oscillate perpendicular to the direction of propagation agreeing with the previous discovery of polarization. In a remarkable experiment in 1887, Heinrich Hertz tested Maxwell's hypothesis of electromagnetic waves. He was able to produce and detect another form of electromagnetic radiation, radio waves. The only difference between radio waves and light is that in the latter the oscillations of electric and magnetic fields have a much higher frequency than in radio waves. The consequence of rapid oscillations is a short wavelength; in typical light the wave crests are separated by half-a-micrometer (= 0.0005 mm). In radio waves the crest separation is from 1 mm upward, all the way to kilometer-long waves.

Between radio and light, infrared heat radiation has wavelengths between a micrometer and a millimeter. Waves too short to be detected by eye just beyond violet light are called ultraviolet radiation. In 1895, Wilhelm Conrad Rontgen (1845-1923) discovered x-rays by accident. They appered to go through matter like it was nothing. By placing his hand in front of the x-ray tube and a screen he was surprised to see the bones of his hand (the first x-ray examination). X-rays are electromagnetic radiation with wavelengths shorter than the ultraviolet. The very shortest wavelength radiation called gamma radiation was discovered a few years later during studies of radioactive elements (Fig. 13.9).

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