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In this chapter, we want to show that electric and magnetic fields depend upon the frame of reference from which they are observed. This fact will lead us to a deeper understanding of induction in moving conductors, as already described in Chap. 5 in the groups 2 and 3.

In our whole discussion of image formation and optical instruments, the details of lens fabrication and ray diagrams have not been emphasized; instead, we have used the limiting boundaries of light beams as an explanatory principle. This decisive point will also lead us to an understanding of energy transport by radiation, whether or not it is accompanied by image formation.

We return to the first experiment (in group 1) of Sect. 5.2, and reconsider induction in the simplest possible case: An induction coil with only one turn, i.e. an induction loop, is supposed to enclose a time-dependent magnetic field of flux density B along some arbitrary curve s with a cross-sectional area A (Fig. 6.1). Then at the ends of the loop, we observe the induced voltage (without taking its sign into account): $$\displaystyle U=\,\dot{\!B}\,A\,. $$ This experimental result can be interpreted in a more profound sense as follows: The conductor, the single loop of wire, is quite unimportant and insignificant. The actual phenomenon does not depend on the accidental presence of the wire loop. It consists of the appearance of electric field lines along closed paths around the time-dependent magnetic field (Fig. 6.2). Electric field lines in the form of closed circles are something quite new and completely unexpected. Up to now, we have encountered only electric field lines with ends; at their ends were electric charges.

Some black night in your darkened bedroom, stick your head under the covers and press on the corner of your eye. Then you will see a bright light, in the form of a colored, yellow, shining ring. The words printed here in italics are used by our natural language to describe sensory perceptions. Every involvement with light and its measurement (photometry, see Chap. 29), and every investigation of colors and brilliance do not belong in the realm of physics; they are the jurisdiction of psychology and physiology. Taking this fundamental fact into account from the outset can avoid many fruitless discussions and diversions.

Textbooks on mechanics usually begin with the concepts of length, time, and mass. The measurement apparatus which has been tried and tested in everyday life is described, i.e. rulers, clocks and balances, and they are immediately put to use. No one uses a sundial or a water clock for the first experiments, or even a slave who is beating time. No one begins by considering the entire historical evolution of the unit ‘second’. We all make use of a modern stopwatch or digital clock. We can all use clocks, even if we are not aware of the details of their construction or of their historical development.

Physics is and remains an empirical science. In optics, as in other areas, observations and experiments have to provide the starting points for concepts and physical laws. It is reasonable to begin our treatment of optics, as in other fields, with the simplest experiences from daily life.

In 1676, Olaf Romer, a Dane, at that time tutor to the royal princes at the court of Louis XIV in Paris, discovered the finite propagation velocity of light. Based on astronomical observations, he obtained a value which is of the correct order of magnitude, namely \(c=2.3\cdot 10^{8}\) m/s. He used light signals from one of the moons of Jupiter at the moment when it emerged from the shadow of the planet. The delay between successive signals was found to be 42.5 h, i.e. equal to the time required for one orbital passage of the Jupiter moon. He carried out the measurements when Jupiter was at its closest approach to the earth and when it was furthest away, that is at opposite points along the earth’s orbit around the sun, separated by the diameter of the orbit (the diameter of earth’s orbit is \(3\cdot 10^{11}\) m). At the most distant point on the orbit, the signal showed an additional delay of 1320 s. From this, he was able to calculate the above value of the velocity of light.

Figure 9.1 serves to illustrate the general definition of the term current source or generator. A pair of condenser plates or “electrodes” A and C are connected through an ammeter. Between these electrodes are charges of both signs; we can think of them as localized on charge carriers. Two of them, a charge-carrier pair, are sketched in Fig. 9.1. The distance between the positive and the negative charges, measured along a horizontal line between the electrodes, can be increased by some sort of charge-separation forces. During their motion (not only when the charges reach the electrodes!), the ammeter indicates the flow of a current. In order to move the charges, the charge-separation forces must perform work. It is taken from a reservoir of mechanical, thermal or chemical energy.

Thus far, we have dealt only with electric fields in empty space. The presence of air molecules could be neglected in our considerations; their influence is felt only in the fourth decimal place by 6 digits. However, when we consider fields in insulating materials – dielectrics – with a dense packing of atoms or molecules, that is liquids and solids, the situation becomes different. Such a dielectric between the plates of a condenser increases its capacitance. Thus, in Sect. 2.17, we proposed a definition of the dielectric constant:C13.1 $$\displaystyle\varepsilon=\frac{\text{Capacitance\ }C_{\text{m}}\text{\ of a\leavevmode\nobreak\ condenser which is filled with matter}}{\text{Capacitance\ }C_{0}\text{\ of the empty condenser}}\,. $$ C m is larger than C 0, so that \(\varepsilon\) is always a number greater than one.

Thus far, we have considered magnetic fields only in empty space (the presence of air molecules had a negligible effect on our results. The influence of the air changes only the 6th place after the decimal by 4 units). Some of the current-carrying conductors that we considered, in particular coils, were not self-supporting, but rather were wound on coil forms or spools, e.g. thin-walled cardboard or wooden tubes covered with an insulating layer of shellac. The effects of these spools was also negligible within the precision needed for our demonstration experiments.

From our detailed consideration of induction in moving conductors, we became aware of the existence of the Lorentz force $$\displaystyle\boldsymbol{{F}}=Q(\boldsymbol{{u}}\times\boldsymbol{{B}}) $$ (F for example in newton (=1 N), B in V s/m2 (=1 T), u in m/s, Q in A s).

The purpose of the first chapter in this book was summarized in Sect. 1.1. It was intended to provide a brief overview of the most important measuring instruments for electric current and voltage (potential difference). To this end, we introduced some of the basic concepts of electromagnetism. Now, making use of these concepts, we want to give a systematic treatment of the field of electromagnetism, essentially following its historical development. We start with the concepts of the electric field and electric charge.

The eye, like our other sensory organs, has been the object of much physiological and psychological research. Nevertheless, physicists must also be aware of the more important properties of their sense of visual perception.

Self-inductance refers to a special form of induction processes. Knowledge of this phenomenon is of great importance for a modern understanding of electromagnetism.

1. In every physics laboratory for research or teaching, one can find an assortment of instruments for measuring time, length, mass, and temperature as well as for electric current, voltage, capacitance and various other electric quantities. However, force meters are to be found, if at all, only rarely and then mostly in teaching labs. If an investigation requires the measurement of a force, one generally compares that force to the force that we call weight (unit newton). In general, forces are not measured directly, but rather are computed from other quantities.

The refractive index n depends on the wavelength λ of the radiation; it exhibits “dispersion”. Dispersion is closely related to the absorption of radiation, and it, in turn, depends strongly on the wavelength. In the following Sects. 27.2 through 27.5, we will consider the empirical evidence relating dispersion and absorption. Then we will treat quantitatively the wavelength dependence of refraction and absorption. This will show close ties to our quantitative treatment of scattering in Chap. 26. C27.1. This chapter goes well beyond the topic of optics and deals with many particular details from solid-state physics. These are intended to illustrate general applications of the optical concepts dispersion and absorption, which is the goal of this chapter.

For image formation, basically only one condition needs to be fulfilled: The rays which originate at “object points” must be limited to a small spatial opening angle ω by passing through an aperture (Sect. 16.1) on their way to the image plane (e.g. a projection screen or a photographic plate). In Fig. 17.1a, the aperture B is a small round opening (pinhole camera!); in Fig. 17.1b, it is a small planar mirror. In both cases, as a suitable object to be imaged, we have chosen an arrow or letter made with small light bulbs.

Wir haben schon zweimal Diffusionsvorgange behandelt, und zwar beide Mal im Zusammenhang mit dem molekularen Bild der Warmebewegung (Abschn. 16.1). In diesem Kapitel soll einiges uber die quantitative Behandlung der Diffusion gebracht werden, und im Anschluss daran etwas uber die verwandten Probleme der Warmeleitung und des Warmetransports. – Anfanger werden manches uberschlagen. Es handelt sich zwar um praktisch bedeutsame Probleme, aber ihre quantitative Erfassung ist noch wenig befriedigend.

Motion refers to a change in the location of an object with time, as seen from a fixed, rigid frame, the “frame of reference”. This supplementary specification is quite essential. We can see this from a randomly-chosen example: A bicyclist looks down at her feet and sees them moving in circular paths with the pedals. An observer standing on the sidewalk sees a very different picture of the motion of the bicyclist’s feet; for her or him, the feet follow a wavelike path, namely the cycloids which are sketched in Fig. 2.1. Open image in new window

Mithilfe der Grundgleichung und des Satzes „actio gleich reactio“ kann man samtliche Bewegungen quantitativ behandeln. Viele Bewegungen sind sehr kompliziert. Man denke an die Bewegungen von Maschinen und an die Bewegungen unseres Korpers und seiner Gliedmasen. In solchen Fallen kommt man nur mit einem grosen Aufwand an Rechenarbeit zum Ziel. Dieser lasst sich oft durch weitere geschickt gebildete Begriffe erheblich vermindern. Es sind dies Arbeit, Energie und Impuls. Diese Begriffe werden nicht etwa aufgrund bisher nicht berucksichtigter Erfahrungstatsachen hergeleitet, sondern mithilfe der Grundgleichung eingefuhrt. Wir beginnen mit dem Begriff Arbeit.

Unser nachstes Ziel ist die quantitative Erfassung des Satzes von der Erhaltung der Energie, also des ersten Hauptsatzes. Dieser und der folgende Abschnitt dienen der Vorbereitung.

Die Technik hat die Warmekraftmaschine geschaffen, um Temperaturdifferenzen zur Gewinnung von Arbeit auszunutzen. Die wichtigsten Ausfuhrungsformen, die Dampfmaschinen und die Verbrennungsmotoren, sind heute jedermann bekannt. Alle Warmekraftmaschinen vermitteln mit einem stromenden Arbeitsstoff den Ubergang von Warme von einem heisen zu einem kalten Korper und wiederholen diesen Vorgang in periodischer Folge. Der Anfangszustand der Maschine wird in periodischer Folge wiederhergestellt, vermindert wird nur der Brennstoffvorrat.

The tunneling model has enjoyed considerable success in describing the low temperature properties of glasses. However, departures from the tunneling model have been noted in experiments at very low temperatures (below 100 mK). We have measured the change in the sound speed ΔV/V 0 between 1 and 40 mK in an amorphous silica double paddle oscillator oscillating at 14 kHz. Most importantly, the sound speed displayed the logarithmic temperature dependence predicted by the tunneling model to a lower temperature than in previous experiments on amorphous silica. Below 3 mK the sound speed departed from the logarithmic temperature dependence and began to level off. The leveling off can be explained by either an intrinsic effect or thermal decoupling of the sample from the thermometer. By heating the oscillator with a gamma source to determine the thermal resistance of the oscillator, it was found that a relatively large stray heat input (9×10−4 nW) would be needed to cause the leveling off. Further work will be needed to determine whether the leveling off is due to stray heat or intrinsic physics.

We measured the low temperature internal friction of a variety of hydrogenated amorphous, nanocrystalline, polycrystalline, and epitaxial silicon thin films. Most of the films studied are prepared either by hot-wire chemical-vapor deposition (HWCVD) or by plasma-enhanced chemical-vapor deposition (PECVD). We show that structural changes with varying modes of deposition can be monitored by the internal friction measurements, which are a sensitive probe to structural disorder resulted from atomic tunneling states below 10 K. For hydrogenated amorphous silicon films, the measurements are also sensitive to the content of atomic hydrogen and bulk molecular hydrogen trapped in the films. With H2 dilution of the silane during deposition, a transition from amorphous to nanocrystalline phase takes place as H2 dilution increases. We show that with increasing volume of nanocrystallinity, the internal friction increases in contrast to our common expectation. The results suggest a large structural disorder in the nanocrystalline phase that is at least comparable to that of amorphous phase exists. The observation of internal friction peaks in amorphous HWCVD films and in nanocrystalline PECVD films indicates that the microstructures of the HWCVD and PECVD films are different.

Using a sensitive silicon paddle oscillator technique, we measured the internal friction of single-crystalline silicon substrate implanted with As+, Si+, B+, and H+ ions with a dose of ∼ 1 0 19 m−2. A distinct internal friction peak at about 48 K is observed in all cases. The overall internal friction from 0.4 K to room temperature is also similar for the different species of ions used. The peak shifts to lower temperature at a reduced resonance frequency, characteristic of a thermally activated relaxation. The insensitivity of the peak to the ion species indicates that it is caused by a vacancy-type defect. Isochronal annealing study shows that the peak anneals away at a temperature between 200 and 300 ° C, and that is consistent with divacancy defects. By plasma etching the substrate layer by layer, we have identified that the defects are concentrated at a damaged crystalline layer right underneath the top amorphized layer in the Si+ implanted sample. The exact mechanism that caused the relaxation peak is still not clear, although our quantitative analysis points to an electronic origin.

Measurements of the thermal conductivity of glasses have led to a model of their lattice vibrations. They are not described as waves, as they are in crystals, but as uncorrelated harmonic motions of individual atoms. The lattice vibrations of fully cerammed, crystalline glass ceramics have been found to be either waves, as in crystals, or vibrations of individual atoms, as in glasses. The understanding of the cause for this different behavior has been aided by studies of systematically doped crystals.

We report on the acoustic and thermal behavior of a Stycast 1266 - quartz composite torsional oscillator below 100 mK. The epoxy exhibits heat release manifested by a strong time dependence of the sound velocity below 10 mK. Also, the Stycast sample is sensitive to both γ and μ radiation, displaying transients superposed on the resonant response of the composite oscillator, as well as heating when exposed to a 22Na source. The long thermal relaxation time of the tunneling states together with the high thermal resistance limits the lowest achievable temperature in this insulating amorphous material.

We measured the spectrum of energies deposited by γ-radiation, emanating from radioactive materials in the laboratory that houses our mK cryostat, and by cosmic ray muons. This allows us to quantify the heat input that adversely affects the lowest temperature accessible in sub-mK experiments. We use our nuclear stage, stage plate and experimental cell as a prototype “model” system, and calculate the power deposited due to low energy (below 2.65 MeV) background radiation γ quanta (~20 pW). This is significantly less than the power (~120 pW) deposited in the nuclear and experimental stages by muons. Installation of a 5 cm thick lead wall around the cryostat reduced the energy due to the flux of γ quanta by a factor of ~10 to ~2 pW, and the number of γ quanta by a factor of ~20. The lower energy, “soft” cosmic ray component was also affected by introducing the same thickness of lead, reducing the overall count of cosmic ray derived particles by ~15% and the heat leak to ~100 pW.

We have studied the acoustic behavior of an a-SiO2 composite torsional oscillator in the temperature range between 1 and 100 mK. At higher temperatures, the acoustic properties of amorphous solids are well described by the ‘tunneling model’. However, below 10 mK it was found that the resonance exhibited a non-Lorentzian shape and was highly distorted by random ‘noise’. We attribute this stochastic noise—‘transients’ to interactions of a-SiO2 with ambient γ quanta present in the laboratory. By shielding the cryostat with a 5 cm thick lead wall we were able to reduce the number of transients. On the other hand, a deliberately introduced 6.1μCi 22Na source of γ radiation caused the opposite effect. We interpret the transients in the framework of local heating caused by the interaction between photons and amorphous SiO2 which changes the elastic properties of the oscillator. Our findings have potential applications for particle detection.