A Newtonian description of nature requires an understanding of the basic forces that operate between the various constituents of the universe. So far, the only force we have discussed in any detail is the gravitational force. We shall now turn our attention to the electric and magnetic forces, which, we will soon discover, are intimately connected to each other and are referred to collectively as the electromagnetic interaction. The electromagnetic interaction plays a major role in determining both the structure of matter and the general interactions of matter. The reason for this is, that of the three major constituents of matter, the proton, the neutron and the electron, two of them, the electron and proton, are charged and hence, exert an electric force whereas all three possess magnetic moments and hence, exert magnetic forces. As a result of this the structure of atoms and molecules, as our future studies will reveal, are governed by the electromagnetic interaction. For example, the electrons of an atom are held in their orbits about the nucleus by the electric force. Not only are the forces inside the atom and molecule electromagnetic, but also the forces between atoms and molecules are electromagnetic. Molecular bonds are responsible for the structure of gross matter. Hence, the resistance one feels when one tries to penetrate solid matter is electromagnetic as is the force exerted by a coiled spring. The forces produced by chemical action are also electromagnetic since all chemical reactions are governed by the electric properties of an atom's outer electrons. The production of light, as we will soon see, is also a result of the electromagnetic interaction.
In addition to the natural phenomenon referred to, we encounter the effects of the electromagnetic interaction in a steadily increasing number of devices and machines invented by man for his pleasure such as the light bulb, the neon sign, the radio, the television, the computer and the laser, not to mention the electric streetcar, the electric stove, the electric dishwasher, the electric iron, the electric broom, the electric can opener, etc. etc. etc.
Let us begin our study of the electromagnetic interaction by turning our attention to the electric force which, in some ways, is like the gravitational force. The strength of the electric force, like the gravitational force, is inversely proportional to the square of the distance between the two interacting bodies. In addition to the inverse square law the force in both cases acts along the line joining the two bodies and is equal and opposite for the two bodies as is illustrated in the accompanying diagram.
The electric force differs from the gravitational force, however, in two vital ways. First of all, the gravitational force is only attractive whereas the electric force can be both attractive and repulsive depending on the signs of the charges involved. A charged particle is either positive like a proton or negative like an electron. Charges of the same sign repulse each other whereas charges with opposite signs attract each other. The other difference in the two forces is the fact that the strength of the electric force is considerably greater than that of the gravitatinal force. In fact, the electric attraction of a proton and an electron is 1040 times stronger than their gravitational attraction. This accounts for the very stron forces which hold the atom together, create the chemical bonds in molecules and produces the molecular bonds in solids and liquids.
Because of the fact that the electron and proton are exactly equal and opposite in charge, gross matter is electrically neutral. In fact, if there was a slight difference in the magnitudes of the electron's and proton's charge of only one part in 1020 macroscopic matter would be completely unstable for the repulsive forces generated by such a minute difference in charge would be enough to completely destroy all the molecular bonds which hold matter together and scatter it to the four corners of the universe.
Fortunately for our existence the equality of charge for the proton and electron, two particles which differ in so many ways, is apparently identical. Macroscopic matter becomes electrically charged, however, whenever there is a slight excess or shortage of electrons. This occurs, for example, when a rubber rod is stroked by a piece of cat fur in which case electrons are transferred by friction from the fur to the rubber rod. The rubber rod has an excess of electrons and hence, has a net negative charge whereas the fur contains more protons than electrons and hence, has a net positive charge. If, after rubbing the rod with the fur, one were to put these two objects in contact, electrons attracted by the positive charge of the fur would flow from the rod to the fur until electric neutrality was once again established. Electric neutrality can also be established by placing a copper wire between the rod and the fur which would permit the passage of an electric current of flow of electrons.
Not all materials, however, permit the passage of an electric current. Some materials such as wood, asbestos and rubber, referred to as insulators, do not permit the flow of an electric current because all of their electrons are tightly bound by the chemical bonds holding the material together. In certain materials, however, such as metals, not all of the electrons are so tightly bound. These materials, referrred to as conductors, permit the flow of an electric current. When an electric current flows, electrons do not flow from one end of the wire to the other, The electrons in a conductor behave more or less like the molecules in a gas. When there is no current flowing in the conductor, the free electrons move back and forth within the wire in a random fashion colliding with each other. When a current is flowing there is a general drift of the electron in a particular direction. The net effect is that a current flows from one end of the wire to the other although no actual electron makes this trip. The wire is acutally electrically neutral with as many electrons flowing into any one segment as flow out of that segment. (See the above figure). The heat generated by an electric current is due to the collisions of the electrons in the conductor. These collisions are also responsible for the resistance of the conductor. This explains why, for a given current, the amount of heat generated in a conductor is proportional to its resistance.
Rubbing a rubber rod with a piece of cat's fur and placing a wire between them is not the most efficient way of creating an electric current. However, the more efficient methods of producing an electric current are based on the same idea of creating two polarities of charge which a flow of current will neutralize. This is the principle of a battery with the difference that the separation of the positive and negative charge is a perpetual process brought about by a chemical reaction. A battery is simply two different metal bars placed in an acid solution. When the acid acts upon the metal, it combines chemically with the metal depositing an excess of eoectrons on the rod. Since the acid works on one of the metal rods of the battery faster than the other, more electrons build on one of the metal rods than the other. If a wire is placed between the two metal rods of the battery an electric current will flow in order to neutralize the excess of electrons. However, this flow of electrons activates the battery to continue acting chemically on the metal rods to produce an excess of charge which causes a current flow and so on until the acid finally eats away one of the rods and then the battery can no longer generate an electric current.
From the study of electric currents generated by devices like the battery, it was discovered that electric currents exert a force on each other. This force can not be attributed to the electric force. Although an electric current involves the flow of electrons, the current in a wire is neutral. As stated earlier, the current is due to the drift of the free electron in the copper wire in one particular direction. This direction is actually opposite to the flow of the current. This apparent backward way of defining the current is due to the historical accident that Benjamin Franklin defined a current as a flow of positive charge at least one hundred years before the electron was actually discovered. Although there is a current due to the drift of the electrons, the wire itself is electrically neutral. If one examines a given section of a wire, as much charge flows out of it as in it. The force observed between wires carrying currents is therefore not due to the electric force but some other force.
It was also discovered that an electric current exerts a force on a magnetic compass. In fact, one can make an artificial magnet by wrapping copper wire around an iron bar and passing a current through the wire. It is clear from these two experiments that an electric current behaves like a magnet and that the force between two currents is magnetic. Further study showed that the magnetic force, like the electric force, is also inversely proportional to the square of the distance between the two currents. Since the current in a wire has a net charge of zero, one can not ascribe the magnetic force solely to the charge of the particles within. It is clear that it is the motion of the charge particles that produces this new force which differes from the electric force in a number of ways.
Perhaps the best way of comparing the two forces is to consider the interaction of two positively charged particles moving parallel to each other. There is a repulsive electric force between these two charges whose strength is proportional to the product of their charges divided by the square of the distance between. In addition to this electric force there is also an attractive magnetic force whose strength is also proportional to the product of the charges divided by the square of the distance between them. The magnetic force is also proportional, however, to the product of their velocities divided by the velocity of light squared. Since the velocity of a particle cn never be greater than the velocity of the light, the magnetic force is always less than the electric force.
The force depends on the relative direction of the two currents in a complicated fashion. When the two currents are parallel (anti-parallel) the force is attractive (repulsive). The force acts along the line connecting the two currents and is equal and opposite. For other configurations, the force is not always directed along the line connecting the two currents and it is not always equal and opposite.
Consider the two positively charged particles moving perpendicular to each other as indicated by the arows in the above diagram. Particle B exerts a magnetic force on particle A acting in the same direction that B is moving whereas A exerts no force on B at all. It is clear that the magnetic force is a good deal more complicated than the electric force.
The connection between the magnetic properties of an electric current and a lodestone or magnet is easily made by considering the atomic structure of a magnet. All atoms, because of their electrons orbiting the nucleus, have equivalent electric currents which can exert magnetic forces. Since the orientation of atoms in matter is so completely random, the effects of each individual atom's magnetism cancel. In certain very select materials, such as lodestones, the atoms are oriented in such a way that the magnetic forces exerted by individual atoms can add up constructively to create a rather strong magnetic force.
This explains why a magnet loses its magnetism if it is dropped or heated since, in both of these cases, the special orientation of the magnet's atoms are destroyed. This also explains why the north pole of one magnet attracts the south pole of another since it is in this position that the internal currents of the atoms are parallel and hence, attractive. When one of the magnets is rotated so that now two north poles are facing each other or two south poles, then the internal currents are anti-parallel and the two magnets repel each other.
Both the electric and magnetic interactions of charged particles discussed above have a magical quality about them in the sense that the charged particles interact with each other at a distance without any apparent phyical connection between them. With the exception of the gravitational force, which also has this magical property of action at a distance, all the other forces between bodies require some kind of physics contact. The concept of action at a distance is very difficult to comprehend. Try conceiving of how you personally could move some object without coming into physical contact with it. This is the work of a magician. Yet every proton, every electron, is a magician since they excert forces on each other through a vacuum with absolutely nothing between them. How can one account for this?
Michael Faraday invented the concept of the electric and magnetic field in an attempt to understand this mystery. According to his idea, each charged particle created an electric field about it. If the particle is in motion, then, in addition to the electric field, it also creates a magnetic field. This electric and magnetic field spread through all space. The field, at any given point in space, is inversely proportional to the square of the distance from the charged particle generating the field. Some charged particle finding itself in the electric field generated by another charged particle will experience and electric force according to the strength of the electric field and its own charge. If this particle is in motion then it will experience a magnetic force proportional to its charge, its velocity and the strength of the magnetic field.
While the concept of the electric and magnetic field might solve the mystery of action at a distance, it leaves us with a new mystery to wit; how does a charge dparticle create an electric or magnetic field at some distance from it without a connecting medium. Faraday and his successor actually believed in the existence of an invisible medium which they called aether which, according to them, filled up all of space. This concept survived until the advent of the theory of relativity when Einstein showed that the existence of an aether was inconsistent with experimental facts. The electric and magnetic field, as far as I am concerned, do not really exist in the same sense that charged particles exist. The field concept is an abstraction, a pictorial description of the electric and magnetic forces. It is, nevertheless, a conceptual construction which is very useful. The conept of electric and magnetic fields will help us to understand the phenomenon of electrical induction. It will also help to explain the creation, absorption and propogation of light as an electromagnetic phenomenon.
The phenomenon of electrical induction was first discovered by Faraday, who observed that an electric current momentarily within a loop of wire into which a magnet has been thrust as is illustrated in the above diagram. The current flows only while the magnet is in motion either being inserted into the loop or being withdrawn from it. It was not just the presence of the magnet but its motion that induced an electric current. Faraday discovered that a current could also be induced by moving the loop of wire with respect to the magnet. In other words, it is the relative motion of the magnet and the loop which induces a current. If the current flows in a clockwise direction when the magnet is inserted, then it flows counter-clockwise when the magnet is removed. Furthermore, if the opposite pole of the magnet is inserted into the loop, then the current also changes direction.
An understanding of the mechanism of induction can be made by recalling that it is the relative motion of the magnet and the loop of wire which causes a current to flow. Let us consider a loop of wire moving with respect to the magnet. The motion of the loop creates an effective current out of every electron in the wire. The direction of this current is not along the wire but perpendicular to it i.e. in the direction of its motion. Each of these individual currents is acted upon by the magnetic field of the magnet which exerts a force perpendicular to the direction of motion. It is this force which causes the current to flow in the looped wire. The same effect occurs when the magnet is moving and the wire is at rest since it is only the relative motion of the two which matters.
Electrical induction also operates with two loops of wire facing each other. If an electric current flowing in the first loop changes in any way, it causes a momentary current to flow in the second loop. The principle is the same as that of electrical induction caused by a moving magnet. When the current in the first loop of wire changes, the magnetic field generated by this current changes at the position of the second loop. In the case of induction involving the relative motion of the loop of wire and the magnet, the magnetic field at the loop of wire is also changing.
It is clear from these two cases that the induced electrical current is caused by a changing magnetic field. Since the induced electrical current is caused by an electric field, the phenomenon of induction can be expressed totally interms of fields. A changing magnetic field induces an electric field. Faraday's law states that the strength of the induced electrical field produced is proportional to the rate of change of the magnetic field and acts perpendicular to the direction in which the magnetic field is changing.
Faraday's concept of the electric and magnetic field was a great aid to his experimental work. Faradya's field concept, however, was absolutely crucial to the mathematical and theoretical work of James Clerk Maxwell. Maxwell was able to express all the laws of electricity and magnetism in terms of four very simple equations which relate the electric and magnetic fields and show their intimate connection. In fact, from the symmmetry of his equations, he predicted that, in analogy to Faraday's law of electric induction in which a changing magnetic field creates an electric field, that a changing electric field would create a magnetic field. This prediction of magnetic induction was immediately confirmed by experimental work and verified the validity of Maxwell's equations.
Maxweill was able to obtain still a more significant insight into electromagnetic phenomenon from the study of his equations. He discovered the existence of a solution to his equaitons in which there is an absence of charge and in which the electric and magnetic fields behave like a wave. He associated this solution with the phenomenon of light which he recognized as electromagnetic radiation. As a result of this insight, he was able to explain the emission, absorption and propogation of light.
The concept of an electromagnetic wave is easy to understand once its relation to electric and magnetic induction is realized. Consider an electric field oscillating at some point in space. Then, by magnetic induction, (or since a changing electric field produces a magnetic field) the oscillating electric field creates a magnetic field perpendicular to itself in its immediate neighborhood. This oscillating magnetic field, as a result of electric induction, then creates an oscillating electric field which, in turn, induces an osicllating magnetic field which, in turn, induces an oscillating electric field and so on and so forth. In this way, an electromagnetic wave propogates through empty space at the velocity of light which is 186,000 miles per second or 3 x 108 meters per second.
The production of electromagnetic radiation can be achieved by causing a charged particle to oscillate back and forth since this casues the electric field associated with the charged particle to also oscillate. This is precisely how radio waves, another form of electromagnetic radiation, are produced in a radio antenns. A current of electrons is made to oscillate up and down in the antenna at a given frequency in order to broadcast radio waves. The absorption of electromagnetic radiation occurs as a result of charged particles interacting with the oscillating electric and magnetic fields of the radiation. For example, the eye detects visible light when the electrons in the retina become activated by the electric and magnetic fields of the light ray.
Electromagnetic radiation comes in a variety of different forms such as microwaves, radio waves, infra-red (heat) radiation, visible light, ultra-violet radiation, X rays and gamma rays. All of these forms of electromagnetic radiation are identical in the sense that they are oscillating electric and magnetic fields which all propogate at the velocity of light. They differ only in that each one represents a different range of frequencies and hence, wavelengths. The frequency of a wave is the number of times per second that the electric and magnetic fields oscillate back and forth. The wavelength is the distance between successive maximums of the fields and is inversely proportional to the frequency. A list of the frequency and wavelength of the various forms of electromagnetic radiation is given in the accompanying table.
The range of frequencies of visible light and the range of frequencies that the sun radiates with maximum intensity exactly overlap. Apparantly, the eye has been biologically adapted so as to detect the electromagnetic radiation of the sun. If human life had developed on a planet orbiting a star which emitted principally infra-red radiation then, through the process of evolution, one would expect visible light for these people to be in the infra-red range. The visual detection of objects using infra-red radiation has actually been achieved by the military. They have developed a photographic film sensitive to infra-red rays which they have used for aerial photo reconnaissance at night.
In addition to perceiving electromagnetic radiation, the ey is also sensitive to the different frequencies in the visible light range. This accounts for our colour vision. Each colour corresponds to a different range of frequency in the visible range as is listed in the above table. The order of the colours in the list is exactly the same as the rainbow. This is no coincidence. The sun radiates visible light of all frequencies and hence, all colours. White light is merely a combination of all the colours. When white light or sunlight propogates through water such as a raindrop or glass such as a prism, the light ray is bent both upon entering and leaving the medium of water or glass. The amount of bending a ray of light experiences depends on the frequency of the ray; the greater the frequency, the more it is bent. The different colours that compose light are therefore separated when they propogate through a medium like water or glass and hence, one observes a rainbow.
The knowledge that sunlight is composed of all the colours helps us to understand why the sky is blue and why sunsets and sunrises are red. When one looks up at the sky on a cloudless day, one observes blue light. This light is sunlight which has been absorbed by air molecules in the upper atmosphere and reradiated towards earth. Because the amount of light reradiated at any one particular frequency is proportional to the fourth power of the frequency, more blue light than red is reradiated towards earth and hence, the sky appears blue. At sunset or sunrise, light arriving from the sun has a thicker envelope of air to travel through in order to reach us as is illustrated above. Since more blue light than red has been absorbed out of the beam of sunlight as it travels through the atmosphere, the light reaching us during a sunset or sunrise appears red.
Maxwell's identification of light with oscillations of the electric and magnetic fields explains the wave nature of light. Long before Maxwell's identification, it was realized that light behaves as a wave. The wave nature of light was first suggested by Christian Huyghens, a contemporary of Newton. In fact, he and Newton had a long standing controversy concerning the nature of light. Newton adopted the position that light was a beam of particles and hence, could not display wave behaviour. Huyghens had a difficult time convincing the scientific world of the wave nature of light because of the formidable reputation of his scientific foe. After the results of a number of experiments corroborating Huyghens point of view became known, however, the science community finally adopted the wave picture of light.
By an ironic twist of fate, however, experiments performed in the past century have revealed that, although light behaves in many situations as a wave, there are instances when it also behaves like a beam of particles. So, there is a sense in which Newton was correct. However, from the point of view of the experimental evidence that was available to Huyghens and Newton, it was Huyghens who made the more accurate interpretation of the data.
We will defer our discussion of the wave-particle duality of light to the time when we discuss atomic physics, and turn our attention instead to the wave nature of light. Let us first consider the nature of wave behaviour in general by discussing a more familiar example, namely, the waves of the sea. When one looks at the surface of the ocean on a windy day, one sees alternate rows of crests and troughs as are schematically shown in the above figure. As one observes the movement of the water, one observes that the crests and troughs are moving toward the shore. One might conclude that the water is moving towards the shore but, in fact, the water composing the wave is actually moving up and down. It is oscillating in the direction perpendicular to the direction in which the wave is moving. This can be easily verified by watching a buoy bobbing up and down in the water. At the shore, it is true that at certain moments water moves toward the shore, but it is also true that, at other moments, an equal amount of water moves away from the shore as the wave washes back into the sea.
One should not confuse the two different types of motion one encounters in wave behaviour. One motion is the motion of the wave or really, the wave form which is continuous and unidirectional. The other motion is the actual movement of the medium which is always an oscillatory motion. In the example of waves upon the ocean, the oscillatory motion of the medium is perpendicular to the motion of the wave form. This type of wave is called a transverse wave and is differentiated from a longitudinal wave in which the medium oscillates back and forth in the same direction in which the wave moves.
Perhaps the best known example of a longitudinal wave is a sound wave. A sound wave requires the existence of transmitting medium. Most of the sound waves with which we come in contact propogate through the atmosphere although sound waves can also propogate through solids and liquids. There are no sound waves on the surface of the moon however, because there is no atmosphere.
Let us consider the production and propogation of sound waves in our atmosphere. A sound wave is produced as a result of the rapid vibration of some object, like a violin string for example, which cuases the molecules of air surrounding it to move back and forth like the vibrating string. This causes alternate condensations and rarefications of the air molecules as is illustrated in the accompanying diagram. As the string moves to the right, it pushes the air molecules together creating a condensation; as it moves back to the other direction, it leaves a rarefication. The motion of the air molecules back and forth is in the same direction as the motion of the vibrating string. The vibrating column of air adjacent to the string will, in turn, cause the column of air adjacent to it to vibrate and then, this column of air will act on the column adjacent to it and so on and so forth and in this way, the sound wave will propogate through the air. Each column of air will vibrate back and forth and hence, there will be no net displacement of the air as the sound wave propogates from the vibrating string to the ears of some listener.
The air molecules that are contact with with violin strings will not come in contact with the listener's ear. The vibration of these air moleculaes will propogate through the air to the listener's ear, however, as a consequence of contact the air molecules make with each other through collisions. The vibrations of the final column of air adjacent to the eardrum of the listener will cause his eardrum to vibrate with the same frequency of the original violin string. The vibrations of the eardrum are transmitted through tiny bones to a cavity containing a fluid where they activate nerve cells which transmit the information to the brain. The human ear is capable of detecting frequencies in the range from sixteen vibrations per second to twenty thousand. The greater the frequency of the sound wave, the higher the pitch that we detect. The loudness of the sound wave depends on the strength of the vibrations or on the distance through which the string vibrates. The harder the string is struck, the greater is the amplitude of its vibration and hence, the louder the sound. The frequency of the string does not depend on the strength with wich it is struck but rather on the length of the string, its thickness and the amount of tension with which it is strung.
We have now considered both transverse waves, (waves on the ocean) and longitudinal waves (sound waves). In both cases, the wave is transmitted as the result of oscillatory motion of a physical medium. In the case of ocean waves, the water was osicllating up and down in the direction transverse to the propogation of the wave. In the case of the sound wave, the air molecules were oscillating back and forth in the direction longitudinal to the wave motion. We encounter a somewhat different situation when we consider electromagnetic radiation since no medium is required to propogate the wave motion. Instead of the oscillation of some physical medium, electromagnetic waves involve the oscillation of the electric and magnetic fields. The oscillation of these fields are transverse to the direction of the wave propogation and hence, light is a tranverse wave.
We are still left with the mystery of how a wave is able to propogate through empty space. This mystery is related to the mystery of action at a distance discussed earlier in connection with electric and magnetic forces. The solution to these two related mysteries, provided by Faraday and Maxwell, is the concept of a field. Later in this book, after we have studied more about elementary particles and their basic interactions, we shall return to this mysterious question and consider another possible solution.
Although it is more difficult to conceive the wave nature of light than that of the ocean because of the absence of a concrete medium, light, nevertheless, displays exactly the same wave behaviour characteristic of waves on the water. Let us consider two phenomena characteristic of waves, namely, linear super-position and interference. If I drop a stone into a quiet pond of water, a wavefront with a circular shape will propogate from the point where the stone enters the water. If two stones are dropped into the water a short distance apart, two circular waveforms will propogate as is illustrated in the sequences of figures shown below.
The two waves will flow through each other without affecting each other, that is, after passing each other the two waves are exactly the same as they were before, i.e., they retain their circular form. In the region where they meet, however, they interfere with each other. The motion of the water up and down due to the two waves will either add together or subtract depending on whetehr or not two crests arrived at the same point or a crest and a trough. If two crests arrive at the same place, then, the waves add such that a crest of twice the height of a single wave is created. If, on the other hand, the crest from one wave arrives at the trough of another, then, the two waves can momentarily cancel so that it appears there is no disturbance of the water at all at this point. However, an instant later, as the two waves propogate past each other, one observes the two waves again. The two cases of constructive and destructive interferences are illustrated for a linear wave of one pulse in the figure below.
Light also can interfere constructively or destructively with itself just like water waves. Let us consider light from the same source shining through two slits of some opaque material. This situation is analogous to the dropping of two stones since spherical light waves will emanate from each of the two slits. If we now observe the light from these two slits projected on a screen, we will observe a pattern of alternating illuminated and dark patches. Those positions which are illuminated are the places where the light from the two sources arrived in phase and the dark points where the two beams of light arrived out of phase. It was the two slit interference experiment first performed in 1789 by Thomas Young which finally settled the controversy between Newton and Huyghens concerning the wave or particle nature of light.
