Math Tutorials and More
by George

Michael Faraday made many discoveries in chemistry and physics. In this section we describe some of his most notable contributions.

Chemistry

Miner Safety Lamp
One of Michael's first assignments as an assistant to Davy was to improve the safety of miners' lamps. Miners used candle lamps to see underground. Unfortunately, mines contained pockets of methane that was explosive when contacted by a flame. Michael and Davy found that wire gauze placed around the candle's flame allowed air to enter, but restricted the flame from spreading. This improvement probably saved many lives.

Bunsen Burner
An important piece of laboratory equipment is the Bunsen burner. Bunsen modified an original burner developed by Faraday.

Steel Alloys
Between 1818 and 1822 Michael worked with James Stodart, an institution member and cutlery manufacturer, to develop new steel alloys. After observing that copper manufacturers used noble metals such as gold, silver, and platinum to harden the copper, they developed steel alloys using noble metals. It turned out that these alloys were not practical due to the high cost of the noble metals.

Ether Anesthesia
In 1818 Faraday published a brief announcement that inhaling vapors of ether produces the same effects on consciousness as nitrous oxide. Since ether was much cheaper to apply, it eventually was adopted as a surgical anesthetic. The announcement was published anonymously, but it was later discovered from Michael's notes that he was the author.

Two New Carbon Chlorides
In 1821 – 1822 Michael produced two new carbon-chlorine compounds. He had been puzzled by the fact that chlorine didn't seem to readily combine with carbon as most non-metals did. Chemists in the Netherlands had successfully combined ethylene (C₂H₄) with chlorine (Cl₂) to obtain dichloroethane (C₂H₄Cl₂). Michael showed that exposure of dichloroethane to an excess of chlorine eliminated the hydrogen and produced a substance he called “perchloride of carbon” (C₂Cl₆). Passage of its vapor through a red-hot tube produced another chloride of carbon C₂H₄ that he called “protochloride.” Protochloride of carbon is now known as tetrachlorethene and is a solvent often used in dry-cleaning.

Liquefaction of Gases
Humphrey Davy was the first to recognize Chlorine as an element. He found it could be mixed with water to form a solid he called “hydrate.” One day in 1823 he asked Michael to heat this hydrate in a closed tube. Michael carried out this experiment and obtained an oil. Davy was puzzled by this result, but Michael finally determined that this was liquid chlorine. He realized that pressure had built up in the closed tube during heating. He was later able to liquefy a number of gases using pressure. His successful liquefaction of ammonia was of particular interest. When he let the ammonia evaporate again he noticed it caused cooling. The beauty of this discovery was that the gas could be pressured, liquefied, and left to evaporate and cool continuously in a closed system. This is the basic principle of modern refrigeration systems.

Rubber Balloon
In 1824 Michael and his lab assistant made rubber balloons in order to work efficiently with gases such as helium. Prior to this balloons were made of animal intestines.

Optical Glass
In 1827 – 1829 Michael did a series of experiments aimed at improving optical glass. After many trials he finally obtained a high quality optical glass with a very high refractive index that he later used in his experiments.

Benzene
In 1852 Michael was able isolate a component of illuminating gases in the form of crystals. These crystals were an important chemical known as benzene. Literally tens of thousands of useful chemicals have been derived from benzene. In particular, it is an important ingredient in the pharmaceutical industry.

Electricity and Magnetism

Electric Motor
In 1820 Christian Orsted placed a current carrying wire over a magnetic compass and noticed a slight movement of the compass needle. Not long after, André-Marie Ampèere showed that two parallel current carrying wires either attracted or repulsed each other depending on the whether the two currents were in the same direction or in opposite directions. A number of scientists were looking at ways to convert these electrical forces into motion. In 1824 Michael was the first to succeed. In effect, he created the first electric motor. Figure 8 is an illustration of his idea. A magnet is fixed in a container filled with mercury (a good conductor). One end of a wire that is free to move is placed in the mercury. A battery is connected to the wire and to the mercury. When current flows in the wire it moves in a circle around the magnet. Faraday then refined his device to show both a wire rotating around a fixed magnet and a magnet rotating around a fixed wire. Such a device is shown in Figure 9. Neither of these devices is a practical motor, but they do show that electric currents can be used to produce motion.

Electromagnetic Induction
Later in the 1820's William Sturgeon invented an electromagnet by wrapping copper wire around a horseshoe shaped iron core covered with an insulating varnish, When current was passes through the wire coil, the device acted like an ordinary magnet and could lift iron objects. When the current stopped, the magnetic effect also stopped. Michael became interested in the reverse effect. Could magnetism be used to produce an electric current? In 1831 Michael performed an experiment that would eventually lead to an electrical generator. He wrapped two wires around opposite sides of a doughnut shaped iron core as shown in Figure 10. A battery was attached to one coil and a galvanometer was attached to the other coil in order to measure any current produced. When the switch was closed, the galvanometer needle twitched and then settled back to its rest position. Michael realized that it wasn't the magnetic field that produced a current but a change in the field.

A few days later he set up a pair of hinged magnets with an iron core joining the north pole of one magnet to the south pole of the other (see Figure 11). A coil of wire was wrapped around the iron core and connected to a current measuring device. By moving either of the magnets, Michael produced a current in the coil. He had now produced an electric current using magnets alone.

He next looked at ways of producing a steady current. He accomplished this using a copper disk that rotated between the poles of a permanent magnet as shown in Figure 12. The center of the disk was connected by a wire to a brush contacting the outer edge of the disk. As the disk rotated, current flowed between the center and outer edge of the disk and through the connecting wire. Michael had built the first electrical generator. In addition, Faraday's original two coil experiment lead to the development of electrical transformers. Faraday's experimental observations were later put in the form of a mathematical equation by James Clerk Maxwell. Faraday's work on electromagnetic induction played a major role in the development of the electrical power industry, providing a basis for the efficient generation and transmission of electricity.

Laws of Electrolysis
In 1833 Michael performed electrolysis experiments using various electrolytes and came up with two laws governing electrolysis. His first law states that the mass of material deposited or released at an electrode in some time period is proportional to the total charge transferred through the electrolyte. His second law states that for a given charge transferred the mass of material deposited or released at an electrode is proportional to its atomic weight divided by its valence (the number of electrons given up or received by each ion). Electrolysis is an important chemical process. Some examples of its use are electroplating, purification of elements, extraction of metals from ores, manufacturing of certain chemicals, and electro-cleaning.

Capacitors and Faraday's Cage
In 1836 – 1837 Michael turned his attention to static electricity. Since Michael believed that electrical forces were not due to some action at a distance but involved the medium in between charges, he began to study the effects of placing insulating materials between charged surfaces. He performed several experiments on a pair of spherical capacitors, each consisting of two concentric spherical conductors separated by a small gap. The smaller inner sphere was supported inside the outer sphere by a glass tube. The electrical connection to the the inner sphere ran through the glass tube. Michael placed a charge on the smaller sphere of one of the capacitors and then made an electrical connection between this sphere and the small sphere of the second capacitor. He found that the charge was shared equally by the two spheres. He used a very sensitive Coulomb torsion balance to measure charges. He then placed an insulating material in the gap between the spheres in one of the capacitors and again connected the two capacitors. He found that the capacitor containing the insulating material always had a greater charge than the one that didn't. He was able to study the difference between various insulating materials using this method, and arrived at a material constant for each material (now called the dielectric constant) that was a measure of their ability to store charge. A picture of one of Faraday's spherical capacitors is shown in Figure 13.

Michael knew that the charge placed on a hollow conductor resided on the outer surface and there was no charge in the interior. He used this to construct a spectacular lecture demonstration. He built a wooden frame, 12 feet on each side. He covered the frame with wire gauze. He went inside and was unharmed even when huge amounts of static electricity was striking the outer surface. This structure has been called Faraday's cage and illustrates an important principle for electrical isolation.

Magnetism and Light
In 1845 Michael showed that magnetic fields can affect light. He took a piece of glass that he developed during his studies on optical glass and placed it across the poles of a powerful electromagnet (see Figure 14). He then passes polarized light through the glass. When the electromagnet was activated it was found that the plane of rotation of the polarized light was rotated. The observed effect is now called the Faraday effect. This was the first hint that magnetism and light were connected. James Clerk Maxwell later expanded on this connection.

Diamagnetism
In 1845 Michael suspended a bar of glass between the poles of a magnet. There was a slight but noticeable effect. He then repeated the experiment with a strong electromagnet. When sufficient current was applied to the magnet the bar rotated so that it was orthogonal to the magnetic field within the gap (east-west rather than north-south). This is quite different from ferrous materials that readily align in the direction of the magnetic field (north-south). Materials with this property Faraday called diamagnetic (dia means “across”). Those materials that aligned north-south were called paramagnetic. Of the materials he studied Bismuth was the most strongly diamagnetic. Faraday suspected that all materials were either diamagnetic or paramagnetic.

Other Contributions

As we have mentioned previously, Michael contributed greatly to science education through his Friday night lectures and his Christmas lectures for children. He also served as an advisor to a number of civic organizations. Although he had limited mathematical ability, a number of his intuitive insights, such as lines of force and fields, were picked up by others and were incorporated in mathematical theories. Science owes a great debt to Michael Faraday.

+++++