Coulombs law

Charles Coulomb (1736-1806) is credited with the definitive verification of the hypothesis of Priestley and Cavendish, and showed that the force between two electrically charged spheres varies inversely as the square of the distance separating them. He designed a very sensitive torsion balance which could measure forces as small as 'a ten thousandth part of a grain'.f He established the expression, which bears his name, for the law of force between two stationary electric charges of magnitude...

The Galilean transformation

The mathematical method of comparing how things appear to observers in different frames of reference is called a transformation of coordinates from a set of axes centred in one frame of reference to another. The Galilean transformation is the 'normal', classical transformation between two inertial frames, such as a ship which is stationary at the dockside, or a ship which is moving with a speed v in the x direction. The Galilean transformation merely involves the addition of a term to the x...

The journey of a photon

In the example of our perception of the countryside, the story begins about 8 minutes earlier, when light is born on the surface of the sun. It does not matter, for the moment, what we mean by saying 'light is born'. We will just picture light as a tiny particle (a photon), which suddenly materialises at the surface of the sun. Countless photons leave the sun every second and go out into the universe in all directions. They travel through space with a speed of 3 x 108 ms-1 for billions of...

The invariant interval

Is there anything on which all observers agree Going back to Equation 15.3, we recall that x2 + y2 + z2 - c2t2 0 represented the special case of an interval between two events, which happened to be connected by the passage of a light signal. Event 1 was the emission of a light signal from the origin of both frames as the two frames coincided. Event 2 was the same signal arriving at a certain point in space and time. The coordinates of that second event were x, y, z, t in frame S and x', y', z',...

Ampres discovery

In 1820, Andr Marie Amp re made the surprising discovery that moving charges produce a new force which is not there when the charges are stationary. This force manifested itself in a very simple experiment where two electric currents were running parallel to each other. Amp re noticed that two current-carrying wires attract each other when the currents are running in the same direction and repel each other when their directions are opposite There is no force before the currents are switched on,...

The quantum hypothesis

Perhaps there is a law of nature which forbids some high frequency modes of vibration. This law must be such that the number of modes is limited by the condition to form stationary waves, but as the wavelength gets shorter and the frequency increases, this number increases rapidly. As we have seen in Section 11.2.5, this leads to the ultraviolet catastrophe. Something prohibits higher frequencies. higher the frequency, the more modes are forbidden. Then only a fraction of the high frequency...

Mathematics of the Compton effect

Collision of a photon with a stationary electron deriving the Compton formula relating change in wavelength to scattering angle of the photon When a photon of a given momentum is scattered elastically through an angle d, the energy loss is uniquely defined. Assume the incoming photon has energy E hf and momentum p hf c, the scattered photon has energy E' hf' and momentum p' hf ' c, and pe is the momentum of the recoil electron. From the cosine rule and multiplying across by c2, pi c2 (hf )2 +...

What happens to light as it passes through a polaroid

In this simple model we represent the polariser by a thin slit. The incoming light has its electric field vectors scattered all over the plane perpendicular to the direction of propagation. The vectors which are parallel to the slit get through unscathed. For the remainder, as illustrated in Figure 8.21, only the component parallel to the slit emerges. These vibrations emerge polarised in the direction of the slit and reduced in size. Let us consider a light wave which is already polarised when...

The branches of optics

We can approach the study of light from any of its aspects Geometrical optics the path of light is represented by a ray without reference to either waves or particles. Physical optics emphasis on the wave nature of light. Newton firmly believed that light was carried by particles (corpuscles). He published his theory of light in the book Optiks (1704). It is ironic that Newton, the firm devotee of the corpuscular theory of light, was the first person known to have observed Newton's rings, which...

The return of photographic emulsion

In the 1970s, nuclear emulsions were very much 'old' technology. There were much more efficient ways of detecting sub-nuclear particles. The reaction products from every pulse of an accelerator could be monitored by electronic counters particle tracks were made visible as they passed through spark chambers bubble chamber photographs provided beautiful pictures of interactions as they occurred. However, nuclear emulsions had one very important advantage over all other techniques at that time...

Charm

In August 1964, a paper was published by James Bjorken (1956-) and Sheldon Lee Glashow (1932-), two American theorists working at the University of Copenhagen. It suggested the existence of a wider symmetry named SU(4), of which SU(3) was a sub-group. Despite the fact that it pointed towards a basic unification of weak and electromagnetic interactions, it attracted little attention at the time. This new symmetry implied that there should be a fourth quark. The authors even suggested the name...

Propagation of sound in open and confined spaces

Perfect reproduction of sound in an open space In open spaces, the sound waves travel directly from the source to the listener, who hears an almost perfect reproduction of the sound, as illustrated in Figure 7.11. The loudness of the sound Figure 7.11 Comparison of words 'spoken' and 'heard' in an open space. depends on the separation of the musician and the listener (except when the two are close together). As the listener moves away from the source, the loud-ness decreases. In confined...

Resonance a part of life

We make use of resonant behaviour in many ways. For example, resonance chambers are used to amplify sound in acoustic instruments resonant behaviour of electrical circuits is used in the transmission and reception of the wireless communications of radio, television and cellphones lasers operate on the principle of resonance. Resonant systems can sometimes create situations over which we have no control. There have been some devastating consequences of uncontrolled resonant oscillations. 6.6.1...

The Doppler effect

Sound from the siren of a vehicle rushing to the scene of an emergency may appear to have a higher frequency as the vehicle approaches the scene and a lower frequency as it leaves the scene. This apparent change in the frequency of sound, which can be due to motion of the source or the observer, is called the Doppler effect. The Doppler effect is named after the Austrian physicist Christian Johann Doppler (1803-1853), who developed formulae to express the change in frequency as a function of...

Wiens displacement law

Wien's displacement law could also be derived from the same model. Wilhelm Carl Wien (1864-1928) noticed that the shape of the black-body radiation spectrum bore a remarkable resemblance to the distribution of speeds of the molecules in a gas. This, he thought, may not be a coincidence since if the molecules of the blackbody are thermally agitated, then their velocities and accelerations may be related to the molecular velocities of a gas which is also thermally agitated. The radiation which...

Amperes law

When Amp re heard of Oersted's discovery, he immediately returned to his work on electric currents, and devoted his attention to developing a mathematical theory of magnetic phenomena. Magnetic field lines surrounding a current are quite different from electric field lines, in that magnetic lines form a closed loop with no beginning and no end, whereas electric lines always begin and end on electric charges. As we saw above, there was no evidence for single isolated magnetic poles acting as...

Timing the ferry

The principle of the Michelson-Morley experiment can be understood by taking the analogy of two identical ferries which bring tourists on river trips. One ferry makes return trips across a wide river and the other makes return trips along the same river (Figure 15.3). Both ferries start from and return to the same jetty. There is a current flowing in the river with velocity v from left to right, as illustrated below. Each ferry is capable of the same speed, V, relative to still water and...

A historical interlude Galileo Galilei 15641642

Galileo was born in Pisa on February 15, 1564 (the same year as William Shakespeare). His family was of noble ancestry, but modest means. His father, Vincenzio, was a musician who made a number of discoveries about stringed instruments, which Galileo was later to incorporate into his own work. It was the wish of his father that he embark on a 'real' career as a doctor, rather than pursue his interest in mathematics, so the young Galileo enrolled in medical school at the University of Pisa. He...

The electrostatic force

The ancient Greeks discovered that amber rubbed with fur attracts little pieces of straw. This phenomenon we now call electrification, derived from e EKipov, the Greek word for 'amber'. The Greeks could hardly have realised what they were seeing was a tiny clue to a hidden force of enormous dimensions. The source of this force we call electric charge. This force also acts at a distance. It is much stronger than gravitation in fact, stronger by a factor of about 1036 * A major difference between...

Oersteds discovery

At about the same time as Coulomb was making his discoveries, a Danish scientist, Hans Christian Oersted (1777-1851), was also experimenting with electrical currents. Oersted gave a public lecture in April 1820 in which he demonstrated that an electric current could be produced in a wire by means of a battery. The wire began to glow as its temperature increased, showing that the current was generating heat and light. As he was giving the lecture, it struck him that there might be some magnetic...

Quantum electrodynamics

Quantum electrodynamics (QED) was not a new theory, it was initially developed in 1929 to describe the interaction of light and matter. In particular, light photons interact not with matter as such, but with electrons, which are fundamental carriers of electric charge. In 1929, Paul Dirac incorporated the theory of special relativity into quantum mechanics, and developed a relativistic theory of the electron. The theory says that the electron has a magnetic moment, which means that it behaves...

Putting the size of an atom into perspective

We could fit 108 atoms along each side. This would mean 1024 atoms squashed into the tube. Compare that with the Pacific Ocean 10,000 km x 10,000 km x 1 km volume 108 km3 1023 cm3. Thus there are 10 times as many atoms of hydrogen in a 1 cc box as there are cubic centimetres of water in the Pacific Ocean

Reconstructing the past

The laws of physics can be used to predict how a system will develop in the future. Equally, they can be used to reconstruct the past. By observing the universe as it is now, one can form models of what it was like in the distant past. This is a fascinating exercise, an epic detective story based on clues we observe around us. In the middle of the 20th century, there were two conflicting theories on the origin of the universe. 5.4.1 The steady state cosmological model Originally put forward by...

A reactionary hypothesis

Suddenly the smug belief that all basic concepts in natural philosophy were well understood, and only some loose ends remained to be tied up, had suffered a major blow. The idea that natural processes come in 'jumps' and are not continuous was completely foreign to most physicists, including Planck. Atomicity of matter' was one thing it was well established since it had been originally proposed by the Greeks. Atomicity of energy' was quite another story. Planck himself was at first reluctant to...

The planets 441 The wanderers

The Greeks and other ancient cultures observed certain heavenly bodies which looked like very bright stars and seemed to wander across the heavens (as shown in Figure 4.11), unlike the normal fixed stars which exactly keep their positions relative to one another. The fixed stars remain in patterns we now call constellations while these bright objects move along paths which are certainly not straight lines or curves, and to the Greeks they were quite puzzling. They called them planets, from the...

Relativistic analysis of the beta decay of bismuth 210

83Bi210 84Po210 + e- + v e- end-point energy 1.16 MeV A feature of beta decay is that there are three particles present after the decay the emitted electron, the recoil nucleus and a neutrino (a 'three-body final state'). As a result, the energy of any of these decay products is not unique. We consider here the special case in which the neutrino takes a negligible part of the energy available. The process can then be considered as a simple projectile-recoil 'two-body final state', with the...

Optical pyrometers

A non-contact method of measuring high temperature is to match the brightness of a tungsten lamp filament with the brightness of a hot object. Instruments which use this technique, called optical pyrometers, are used to measure temperatures, such as those of hot furnaces, molten glass, nuclear blasts and the surface of the sun. The advantage of tungsten is that its melting point is 3700 K, much higher than that of iron ( 1800 K) or copper ( 1350 K). The brightness of the source is reduced by a...

Terrestrial measurement

In 1849, the French physicist Hyppolyte Fizeau (1819-1896) made the first terrestrial measurement of the speed of light, in a simple but ingenious way. A beam of light was passed through one of 720 notches around the edge of a rotating wheel, was reflected by a mirror and retraced its path, as shown in Figure 1.3. When the returning light passed through a notch, an observer could detect it if it hit the disc between notches, the light was eclipsed. The 'round-trip' distance from the open Figure...

A table top experiment with polaroids

We have discussed the polarisation of light in Section 8.12 from the wave theory point of view, representing the polaroids material schematically as a 'slit' which allows only the component of vibrations parallel to it to get through. The emerging light is then represented as consisting of electric field oscillations only in the direction of the slit. If the light then comes to a second polaroid with its axis inclined at an angle 0 to the first, the intensity of the light emerging is reduced by...

E me2 the most famous result of all

So far our discussion on relativity seems to have brought us no nearer to the ultimate relation, E mc2, for which Einstein is best known. The reason for this is that we have been dealing exclusively with kinematics, the study of motion without reference to force. We will now turn our attention to dynamics, the study which encompasses force, energy and momentum. In this context we are interested in how these dynamical variables appear in different frames of reference in particular, frames which...

Pythagoras revisited Measuring distance on a map

On the map in Figure 15.9(a), the x and y axes of the S coordinate frame are drawn in the east-west and south-north directions. (The sides of the grid squares are approximately 100 km and we are assuming that the map is flat, i.e. ignoring the earth's curvature.) In Figure 15.9(b) a coordinate frame has Figure 15.9 Invariant interval in space-time. Figure 15.9 Invariant interval in space-time. been chosen (S' frame) which has been rotated and displaced by an arbitrary amount. The distance...

Newtons rings

Newton demonstrated interference in the film of air between a convex lens and a flat glass plate. Light reflected at the lower surface of the lens interferes with light reflected at the glass plate, producing a set of alternately bright and dark rings centred on the point of contact between the lens and the glass, as illustrated in Figure 8.12. Newton's measurements showed that the depth of air between the lens and the glass is related to the spacing of the rings. He attempted to explain the...

An important extension to Amperes law

Maxwell soon realised that one of the laws, namely Ampere's law, as given by equation (10.1), is incomplete. This equation correctly quantifies the magnetic field produced by an electric current, i.e. by moving electric charges. Maxwell pointed out that it is also possible to have a magnetic field without physically moving electric charges. We can most easily understand why this is so by looking at what happens during the process of charging an electrical capacitor A capacitor is a device which...

The demise of determinism

The idea that an electron should drop from a higher to a lower energy state was, in itself, not unreasonable. However, applying Newton's mechanics one would expect some reason to cause it to jump at a particular instant. There should be some inner mechanism, perhaps difficult or impossible to observe, to trigger the transition. According to the thinking of that time, quantum jumps were quite mysterious. There was no evidence to suggest that there was any direct cause and effect in the process....

A historical interlude Richard Feynman 19181988

Richard Feynman was born in a small town near the outskirts of New York called Far Rockaway. He never lost his unpretentious manner and his strong Brooklyn accent, and disliked pomp and ceremony of any kind. Even when his contribution to quantum electro-dynamics earned him the Nobel Prize in 1965, he accepted it graciously but somewhat reluctantly. He was not interested in prizes 'I already had the prize the discovery of such a wonderful law of Nature.' Feynman lived in Rockaway until he was 17...

Geometrical Optics Refraction

Providing more than one quickest route When light crosses the boundary between two media, it changes direction. This phenomenon is called refraction. In this chapter we study the rules and applications of refraction. The basic rule is the same as always it is Fermat's principle of least time. We show that the principle leads to the experimentally established Snell's law of diffraction. Lenses are the most common example of the application of the laws of refraction. In making a lens, the trick...

The gamma factor

For relative velocities which are small compared to the speed of light, the relativistic gamma factor y 1. The Lorentz transformation becomes the Galilean transformation and relativistic effects become negligible. In practice, astronauts travelling in satellites in orbit around the earth or space vehicles to the moon never reach speeds even remotely close to relativistic speeds. Concorde was a supersonic aircraft, by far the fastest means of travel for fare-paying passengers, with the...

Dimensions of energy

Dimensions of force Mass x acceleration M L T -2 Dimensions of work Dimensions of energy force x distance M L 2 T -2 M L T -1 L T -1 M L 2 T -2 As one would expect, the dimensions of classical energy and of mass-energy are identical. In using SI units, relativis-tic energy will come out in joules and the units and dimensions of momentum, speed, kinetic energy and mass will be consistent. It is more usual and numerically less cumbersome to use units based on the electron-volt. An electron-volt...

Sound as a tool

Lithotripters Internal Composition

Sound waves are reflected from obstacles. This is used to great effect in remote sensing, where the location, composition and motion of an object can be determined from large distances. Detailed analysis of the intensities and frequencies of reflected sounds forms the basis for a whole range of imaging techniques. In most applications the sound is emitted as a series of pulses. The distance between the source and the reflecting surface is calculated from the time between the emission of a pulse...