Measuring the diameter of your blind spot

A simple experiment to determine the diameter of the blind spot is described. Students are divided into groups of three and work together to perform the experiment. The procedure takes about 15 minutes and seems to be quite enjoyable to the class

How Spherical Is a Cube (Gravitationally)?

An important concept that is presented in the discussion of Newton\u27s law of universal gravitation is that the gravitational effect external to a spherically symmetric mass distribution is the same as if all of the mass of the distribution were concentrated at the center.1,2 By integrating over ring elements of a spherical shell, we show that the gravitational force on a point mass outside the shell is the same as that of a particle with the same mass as the shell at its center. This derivation works for objects with spherical symmetry while depending on the fact that the gravitational force between two point masses varies inversely as the square of their separation.3 If these conditions are not met, then the problem becomes more difficult. In this paper, we remove the condition of spherical symmetry and examine the gravitational force between two uniform cubes

The Biot-Savart Law: From Infinitesimal to Infinite

In this paper, we discuss a simple apparatus and accompanying class activity that we have developed to illustrate the Biot-Savart law. Since students in introductory electricity and magnetism courses often find this law a mathematical mystery, we feel that a simple experiment such as this will provide the students a better understanding of the concepts introduced. By collecting data from several finite segment lengths, students are able to infer the 1/r2 distance dependence of the magnetic field for infinitesimal segments and the 1/r dependence for infinite wires

Measurements of orbit-lattice coupling of Er and Dy impurities in Ag and Al hosts

The magnetic resonance of dilute Dy and Er impurities has been observed in thin polycrystalline Al and Ag films on two different substrates. The films are deposited at room temperature, and the measurements are made at liquid-helium temperatures. During cooling, the difference in thermal contraction between film and substrate produces an effectively uniaxial strain in the film. This results in an anisotropic g value, which we have used to obtain lower limits on the orbit-lattice coupling coefficient for these systems. We find values for V ( Γ 3g, 2 ) from 600 to 2000 cm − 1 , somewhat smaller than observed in insulators, but of the same order of magnitude. Measurements on substrates with different thermal contractions indicate that all of the expected strain is present in these films, contrary to previous measurements on Ag: Er films grown on NaCl surfaces

A statistical study of transient event motion at geosynchronous orbit

The geosynchronous GOES 5 and GOES 6 satellites frequently observe transient events marked by magnetic field strength increases and bipolar magnetic field signatures lasting several minutes. In this study we report a survey of 87 events observed simultaneously by both GOES spacecraft (for a total of 174 individual observations) from August to December 1984. Events detected in the prenoon sector outnumbered those in the postnoon sector by about a 3 to 1 ratio. The distribution of the events versus local time exhibited a significant prenoon peak like the distribution of magnetic impulse events observed in high-latitude ground magnetometers. A cross-correlation analysis of the two GOES data sets indicated lags that range from 0 to over 2 min, with the majority of the events moving antisunward. The short lags correspond to azimuthal speeds of hundreds of kilometers per second, greater than flow speeds in the magnetosheath, but less than fast mode waves. The short lags may indicate that the events move primarily latitudinally and/or that transient events are seldom localized, but rather occur over extended, if not global, regions. Investigations of event occurrence versus interplanetary magnetic field (IMF) Bz, event motion versus IMF By, and correspondence between upstream plasma data and the events all indicate that pressure pulses are the likely source of many of the events. About 27% of the events with simultaneous solar wind data were preceded by sharp reversals in one or more IMF components, and nearly all of this particular group of events occurred in the dawn sector. This suggests that the pressure pulses may be commonly generated in the foreshock/bow shock region, since the prenoon magnetopause lies generally behind the quasi-parallel bow shock where such pulses are thought to be triggered by IMF discontinuities. Finally, several events in the data set were also observed by the AMPTE/CCE. These are presented as case studies

ESR and spin-lattice relaxation of Nd3+ in a metallic host: LaRh2

We report the first ESR observation of Nd3+ in a metal: cubic LaRh2. The resonance arises from a Γ6 ground state and exhibits hyperfine splitting at low temperature, allowing for positive identification. Above about 12 K, the ESR linewidth increases exponentially with temperature. We attribute this increase to the resonance phonon relaxation process involving the first excited state at 125±10 K

A statistical study of the magnetic signatures of FTEs near the dayside magnetopause

During magnetopause crossings, the AMPTE CCE satellite frequently observed flux transfer events (FTEs) characterized by fluctuations in the magnetic field strength (B) and bipolar signatures in the field component (BN) normal to the nominal magnetopause. In this study, we survey 110 events observed from October to December 1984 and during January 1986. Nearly all events exhibited increases in B, and although the majority of events exhibited a symmetric bipolar signature in BN, a significant number (31 of 110) had asymmetric bipolar signatures in which the trailing pulse was dominant. Most of the asymmetric events were observed near the magnetic equator. This is consistent with an explanation in which FTEs form via merging along a single subsolar X line with strongly asymmetric signatures but that these signatures evolve into the familiar symmetric bipolar form with distance from the merging line

Low-temperature magnetic properties of submetallic phosphorous-doped silicon

Measurements of the electron-spin-resonance properties of Si:P with dopant concentration of n=2.05×1018 cm−3 (somewhat below the metal-insulating transition) at low temperatures (0.035 to 4.2 K) and low frequencies (11.5-58.2 MHz) are reported. They show a substantial deviation from Curie-law behavior for the susceptibility, in agreement with previous static experiments. An internal field is observed to develop as the temperature is lowered. At 35 mK, the internal field has a magnitude of 2.1 Oe and is directed opposite to the externally applied field. The buildup of the internal field is accompanied by an increase in the resonance linewidth. Both the linewidth and the internal field can be fitted with a power-law divergence that suggests critical behavior relative to a phase transition at zero temperature. At all temperatures investigated the relaxation time of the magnetization is observed to be less than 1 ms, and is interpreted as relaxation of the Zeeman reservoir to the exchange reservoir