MAGNETISM

Early History of Magnetism. The history of magnetism is as old as the history of electrostatics. It begins with the observation at least 2500 years ago of the mineral magnetite, an iron oxide (Fe₃O₄) that was traditionally called lodestone, that it had the ability to pick up and hold pieces of iron. It was found in a region of Asia Minor near an ancient city of Magnesia (now called Manisa, in western Turkey). Unlike amber, which, when rubbed, attracted light objects of all kinds, the lodestone only attracted iron. A piece of iron that had recently been in contact with a lodestone acquired a slight ability to attract other pieces of iron; the magnetized piece of iron was called a magnet. The modern word "magnet" comes from the Greek name for lodestone, stones from Magnesia. This property to attract other pieces of iron, called magnetism, was not long lasting as the magnetic property of the lodestone. Later it was discovered that steel could be made to retain it magnetism, so that nearly permanent magnetic needles could be made. When an magnetized iron rod was suspended by a string at its center so that it could freely rotate, tended to turn itself into a north-south direction, like a compass needle. The early magnetic compass consisting of a magnetized iron needle supported on a cork floating in water came into nautical use about a thousand years ago. Later the needle was mounted to turn free on a pivot. The Chinese knew of the tendency of a magnet to orient itself north and south as early as the eleventh century. Magnetic compasses have been used for navigation by both Arabs and Christians sailors at least since the end of the thirteenth century.

Magnetism was one of the few sciences that made a progress during the Middle Ages. In the thirteenth century Pierre de Maricourt (also named Petrus Peregrinus of Maricourt), a native of Picardy, made a discovery of fundamental importance. He took a lodestone or natural magnet and rounded into a sphere, which he called magnes rotundus. Then he laid a needle on it and marked the line along the direction that the needle set itself. He laid the needle on other parts of the stone, and marked the lines that the needle took there. When the entire surface of the stone had been covered, the lines formed circles which girdle the stone in the same way that meridians of longitude girdle the earth. The circles converged on two points on opposite ends of the stone, just as all the meridians pass through the north and south poles of the earth. Being struck by the analogy, Peregrinus proposed that the two points on the lodestone be called the poles of the magnet. The end of the magnet that pointed toward the north, he called the north pole of the magnet and the other end pointing toward the south he called the south pole of the magnet. He published his discovery in a little book Epistola de Magnete in the form of a letter to a fellow countryman in Picardy dated 8th August, 1269, while Pergrinus waited in Charles of Anjon's besieging army outside the walls of the southern Italian town of Lucera. At the end of his treatise Petrus Peregrinus described improvements of both the floating needle and pivoting needle compasses. His floating needle compass was used with a reference scale divided into 360 degrees.

These observations of Peregrinus were greatly extended by William Gilberd or Gilbert (1540-1603). Gilbert was born at Colchester; after studying at Cambridge he took up medical practice in London, and later had the honor of being appointed personal physician to Queen Elizabeth I. In 1600 he published a work on magnetism and electricity, De Magnete, with which the modern history of both sciences begin. Gilbert acknowledged his debt to the little book of Peregrinus and he records his 18 years of researches in magnetism during which he made the discovery of the reason why compasses oriented themselves in a north-south direction with respect to the earth. He proposed the explanation that the earth itself is a great magnet, having one of its poles in the high northern and the other in high southern latitudes. Thus the property of the compass was explained by the general principle that the north-seeking pole of every magnet attracts the south-seeking pole of every other magnet, and repels their north-seeking pole. That is, unlike poles attract, and like poles repel. This is sometimes called the First Law of Magnetism. Thus the north seeking pole of the compass needle points to the north geographical pole because the north geographical pole is a south-seeking pole and attracts the north-seeking pole of the compass needle.

Gilbert went even further, and proposed that magnetic forces explains the earth's gravity and the motion of the planets. Gilbert suggested that magnetic forces were responsible for the daily spinning of the earth, replacing the explanation of Copernicus (1473-1543). Gilbert was an ardent Copernican, and one of the first, but he rejected Copernicus' explanation of the rotation of the earth that it was natural for spherical bodies to rotate on their axis of rotation. Gilbert also suggested that perhaps magnetism kept the earth from flying apart as it rotated. Kepler (1571-1630), a contemporary of Gilbert's, was deeply influenced by Gilbert's magnetic explanation. Gilbert's arguments led him to predict that the sun rotates on its axis, radiating a magnetic force that pushes the planets around their orbits. In fact, Kepler tried to show that magnetic forces would move the planets in elliptical orbits. Even though Newton (1642-1727) rejected Gilbert's explanation of the nature of gravity as magnetism, he saw in Gilbert's explanation that bodies attract each other when there is nothing between them, confirmation for his action-at-a-distance concept of gravity.

Sir William Gilbert was led to the conclusion that the earth was itself a magnet by the dip needle. During the 16th century it was discovered that if a magnetized needle is suspended so that it is free t turn in a vertical plane, the north end "dips" toward the earth (in the northern hemisphere). In 1576, Robert Norman, a retired sailor and London compass maker, designed a compass that rotate in a vertical plane. He found that his compass at London rotated until it made a "dip" angle of 71° 51' with respect to the horizontal. This phenomena and Gilbert's experiments with magnetic needles in the vicinity of a spherical lodestone that he called a terrella, a "little earth," led him to the conclusion that the earth itself is a magnet. This led him to the belief that gravity is a manifestation of magnetism.

One of the purposes of Gilbert's research was to make a clear distinction between magnetic forces and those manifested by amber and glass, that is, the electric forces. Gilbert found the following differences.

(1) The lodestone requires no stimulus of friction such as is needed to stimulate amber, glass and sulfur into activity.
(2) The lodestone attracts only magnetisable substance such as iron, whereas an electrified body attract almost everything.
(3) The magnetic attraction between two magnetic bodies is not affected by interposing a sheet of paper or a linen cloth, or by immersing the bodies in water; whereas the electric attraction is destroyed by these screens and by immersing in water.
(4) The magnetic force tends to arrange bodies in definite orientation; where the electric force merely tends to heap themselves together in a shapeless clusters. That is, when two magnets are brought near each other, the north pole are attracted to the others south pole, but their north poles repel each other as do their south poles. On the other hand, the electrics did not have any poles, when they were electrified. In his theory of electricity electrics always attract, never repel. In fact, Gilbert somehow never observed that electrified bodies sometimes repelled each other. He, no doubt, saw only what he believed.
(5) When a lodestone is broken into two pieces, it becomes two magnets. When an electrified body, like glass rod, is broken in two, there are two charged bodies. This aspect of magnetism, that "... the self-same part of [lodestone] may by division become either north or south," seemed astonishing to Gilbert. When the lodestone is divided, a north and south always appeared, so that each piece is a complete magnet with both kinds of poles. The magnetic poles are of two distinct kinds, north and south, but they can not be separated from each other. There appears to be no monopoles.

Coulomb's Law of Magnetism. An early suggestion that the law of forces between magnetic poles is an inverse-square law was made by the Cardinal Nicholas of Cusa (1401-1464) in 1450. Later in 1750, John Michell (1724-1793), who was at that time a young Fellow of Queens' College, Cambridge, published A Treatise of Artificial Magnets; in which is shown an easy and expeditious method of making them superior to the best natural ones. In this Michell states the following principles of magnetism.

(1) "Each Pole attracts or repels exactly equally, at equal distances, in every direction."
(2) "The Attraction and Repulsion of Magnets decreases, as the Squares of the distances from the respective poles increase."

After Michell, the inverse square law was maintained by Tobias Mayer (1723-1762) of Gottingen and by the celebrated mathematician Johann Heinrich Lambert (1728-1777).

The French engineer and physicist, Charles Augustin Coulomb (1736-1806), using the torsion balance, which was independently invented by Michell and himself, verified in 1785 the law of forces between electric charges. He verified that a similar law held for magnetic forces. This is called Coulomb's Law of Magnetism, and it may be stated in the following way. The magnitude of the force of attraction or repulsion between two point poles is directly proportional to the product of the strength of the two poles and inversely proportional to the square of the distance between them. This law has sometimes been called the second law of magnetism and, expressed as mathematical formula, is
F = k_m[(p₁p₂)/ r²], (1)
where p₁ and p₂ are the pole strengths of two magnetic pole, the "magnetic mass," r is the distance between the poles, and k_m is the constant of proportionality. In the rationalized MKS system of units, the pole strengths p₁ and p₂ are measured in webers, the distance r between them is measured in meters, the force between them in newtons, and k_m has a value of 6.3325 × 10⁴ newton-meter² per weber² in vacuum. This Coulomb's Law proportionality constant is equal to
k_m = 1/4πμ, (2)
where the Greek letter μ (mu) stands for absolute permeabilitiy and is by definition equal to the product of μ₀ and μ_r; that is,
μ = μ₀μ_r, (3)
where μ₀ is called the permeability of empty space or the permeability of a vacuum, and μ_r is called the relative permeability. The constant μ_r is a pure number (no units) and depends only for its value upon the intervening medium between the two poles; it is greater than unity for all materials and is equal to one for vacuum. The other constant 0 depends upon the system of units used in Coulomb's Law of Magnetism. In the rationalized MKS system of units μ₀ has a value of 4 × 10^-7 weber² per newton-meter².

Magnetic Fields of Force. Since other magnets and iron filings are affected at a distance from a magnetic pole, it is said that a magnetic field of force exists in the neighborhood of the magnet; so that any magnetic test pole pt placed in this region experiences a force F_t that is proportional to the magnetic field strength H. Hence the magnetic field intensity at a point in a magnetic field is defined as the ratio of the force exerted on a north test pole placed at that point to the strength of the test pole; that is,
H = F_t/p_t, (4)
where in the rationalized MKS system of units F_t is the force exerted on the north test pole at any point in the magnetic field, measured in newtons, p_t is the strength of the north test pole, measured in webers, and H is the magnetic field intensity at that point, measured in newtons per weber. The direction of the field at any point is the direction of the force on a north test pole at that point and the magnitude of field intensity is the ratio of the force exerted on a north test pole placed at that point to the strength of the test pole. The magnetic field intensity around a point pole can be found by using Coulomb's Law of Magnetism.
H = F_t/p_t = {k_m[(pp_t)/r²]} (1/p_t) = (1/4πμ)(p/r²) = (p/4πμr²), (5)
where p is the isolated point source of the magnetic field.

Magnetic Lines of Force. A magnetic field can be represented by magnetic lines of force. Magnetic lines of force are imaginary lines drawn in a certain way in a magnetic field in order to graphically represent it. The magnetic lines of force represent the direction and the magnitude of a magnetic field. The magnetic line of force represents the direction of a magnetic field at any point by being drawn in such a way that the direction of the line (the tangent) at that point is the same as the direction of field at that point. The magnetic lines of force represent the magnitude of a magnetic field by being spaced in such a way that the number of lines per unit area, φ/A, crossing a surface perpendicular on the direction of the field is equal to the product if the absolute permeability μ of the medium and the magnetic field intensity H of that area of the surface. That is,
φ/A = μH, (6)
where φ is the number of lines of magnetic lines of force radiating from or converging on an isolated point pole and A is the area of the surface perpendicular to the direction of the magnetic field at the surface. This means that in a region of the magnetic field where the magnetic field intensity is large, the magnetic lines of force will be closely spaced, and in those regions where the magnetic field intensity is small, the lines will be widely separated. Solving equation (6) for φ, we get
φ = μHA. (7)
Let φ equal the total number of lines radiating from or converging on a isolated point pole that is the source of the magnetic field and take A as the area of a surface completely enclosing that isolated point pole. Since the magnetic field intensity H is the same at a radial distance r from the point source pole and is on a spherical surface perpendicular to the direction of the field with a radius r and whose area is A = 4πr².
φ = μHA = μ(p/4πμr²)(4πr²) = p, (8)
using equation (5) to calculate the magnetic field intensity.

Thus the total number of lines of force φ radiating from or converging on a isolated point pole through a spherical surface enclosing the pole depends upon only upon and is equal to the strength of the pole p, φ = p. Thus since the pole strength p is measured in webers, then φ is also measured in webers.

Magnetic Flux Density. The magnetic lines of force are also called the magnetic lines of flux, simply magnetic flux, because it once was believed that magnetism flowed along the lines of force and caused the force exerted by the magnetic field. The density of this magnetic flux, called magnetic flux density, is defined as the ratio of the number of magnetic lines of force (magnetic flux) threading through a surface perpendicular to the direction of the field to the area of that surface, that is,
B = φ/A, (9)
where in rationalized MKS system of units, φ is the magnetic flux measured in webers, A is the area of the surface perpendicular to the direction of the field measure in square meters, and B is the magnetic flux density measured in webers per square meter.

Using formula (6) and the definition (9) of magnetic flux density, the relation between magnetic flux density and magnetic field intensity may be given by the following formula.
B = μH, (10)
where μ is called the absolute permeability and has value of 4 × 10^-7 weber² per newton-meter² in vacuum.

Magnetic Dipole. Since magnetic poles never exist alone, but always in pairs of a south pole with a north pole (never two north poles nor two south poles), they form what is called a magnetic dipole. Magnetic monopoles, that is, single magnetic poles, have never been detected. Each magnet is a magnetic dipole. When a magnetic dipole, like a small and thin bar magnet, is placed in an uniform magnetic field of magnetic intensity H, the field exerts a force on each end of the magnet. According to equation (4) the magnitude of the force on each end is F = pH, where p is the strength of the magnetic pole. The forces on the opposite ends of the magnet are in opposite direction, with the direction of the force on the north pole end in the direction of the magnetic field and the direction of the force on the south pole end opposite to the direction of the field. Each force produces torque on each end of the magnet. If the length of the magnet is d, the torque produced by the force F is
τ = F(d/2) sin α,
where α is the angle between the direction of the magnet and the direction of the field. The total torque acting on the magnet is the sum of the two torques produced by the two forces on the ends of the magnet.
τ = τ_N + τ_S = F(d/2) sin α + F(d/2) sin α = (pH)d sin α = (pd)H sin α.
The quantity pd in this equation is called magnetic moment of this dipole. The magnetic moment m_m of a dipole is defined as the product of the pole strength p and the interpole distance d. That is,
m_m = pd, and is measured in weber-meters.
Hence, the torque on the dipole is τ = m_mH sin α. This torque acts in such a way that it aligns the dipole parallel with the field where its torque is zero.