Volume 70, Issue 11, November 2002
 PAPERS


The training, careers, and work of Ph.D. physical scientists: Not simply academic
View Description Hide DescriptionWe present an indepth portrait of the training, careers, and work of recent Ph.D. physical scientists. Use of specialized training varies widely, with about half often using knowledge of their Ph.D. specialty area in their jobs. The use of specialized training does not, however, correlate with job satisfaction. In this and other important measures, there are relatively few differences between “academics” and “nonacademics.” Important job skills for all employment sectors include writing, oral presentation, management,data analysis, designing projects, critical thinking, and working in an interdisciplinary context. Rankings given by respondents of graduate training in some of these skill areas were significantly lower than the importance of these skills in the workplace. We also found that the rated quality of graduate training varies relatively little by department or advisor. Finally, although nonacademic aspirations among graduate students are fairly common, these do not appear to be well supported while in graduate school.

Gripslip behavior of a bouncing ball
View Description Hide DescriptionMeasurements of the normal reaction force and the friction force acting on an obliquely bouncing ball were made to determine whether the friction force acting on the ball is due to sliding, rolling, or static friction. At low angles of incidence to the horizontal, a ball incident without spin will slide throughout the bounce. At higher angles of incidence, elementary bounce models predict that the ball will start to slide, but will then commence to roll if the point of contact on the circumference of the ball momentarily comes to rest on the surface. Measurements of the friction force and ball spin show that real balls do not roll when they bounce. Instead, the deformation of the contact region allows a ball to grip the surface when the bottom of the ball comes to rest on the surface. As a result the ball vibrates in the horizontal direction causing the friction force to reverse direction during the bounce. The spin of the ball was found to be larger than that due to the friction force alone, a result that can be explained if the normal reaction force acts vertically through a point behind the center of the ball.

When physical intuition fails
View Description Hide DescriptionWe analyze the problemsolving strategies of physics professors in a case where their physical intuition fails. A nonintuitive introductorylevel problem was identified and posed to twenty physics professors. The problem placed the professors in a situation often encountered by students, and their response highlights the importance of intuition and experience in problem solving. Although professors had difficulty in solving the problem under the time constraint, they initially employed a systematic approach, for example, visualizing the problem, considering various conservation laws, and examining limiting cases. After finding that familiar techniques were not fruitful, they made incorrect predictions based on one of two equally important factors. In contrast, other more familiar problems that require the consideration of two important principles (for example, conservation of both energy and momentum for a ballistic pendulum) were quickly solved by the same professors. The responses of students who were given the same problem reflected no overarching strategies or systematic approaches, and a much wider variety of incorrect responses were given. This investigation highlights the importance of teaching effective problemsolving heuristics, and suggests that instructors assess the difficulty of a problem from the perspective of beginning students.

Tunneling through arbitrary potential barriers and the apparent barrier height
View Description Hide DescriptionA simple matrix formalism is presented that allows the tunneling current between two planar electrodes with an arbitrary barrier potential to be calculated conveniently. This formalism is a straightforward extension of the usual textbook example for tunneling through a rectangular barrier and can be easily implemented on a personal computer. A first principles derivation of the tunneling current based on freeelectron electrodes is given that is useful for the teaching of solidstate physics. Examples showing the utility of the method are the transmission through a tunnel barrier modified by the image potential and tunneling via intermediate states (resonances). These issues are interesting topics in scanning tunneling microscopy where both phenomena are believed to contribute to the image formation.

Demonstration of negative group delays in a simple electronic circuit
View Description Hide DescriptionWe present a simple electronic circuit that produces negative delays. When a pulse is sent to the circuit as input, the output is a pulse with a similar wave form that is shifted forward in time. The advance time or negative delay can be increased to the order of seconds so that we can observe the advance with the naked eye by observing two light emitting diodes that are connected to the input and the output. The negative group delay in the electronic circuit shares the same mechanism with superluminal light propagation, where the group velocity exceeds the speed of light or even becomes negative.

Series capacitors and the inverse sum rule
View Description Hide DescriptionAn exact solution for the capacitance of a three plate system is obtained and is used to quantify the error made by the inverse sum rule. Three finite, parallel disks are arranged as two capacitors in series. By treating the system as an electrostaticboundary value problem,exact solutions for the potential and capacitance are derived for the total system and for each pair of plates. The inverse sum rule is then applied to the two constituent capacitors and compared to the exact solution for the total system. Also provided are analyses of the equal plate charge hypothesis typically assumed for series capacitors, relations for the coefficients of capacitance for the system, a capacitive maximum, repulsive plate forces, charge migration on the inner plate, and plots of the field lines for the three plate system.

Electromagnetic conic sections
View Description Hide DescriptionCertain orthogonal coordinate systems naturally correspond to basis vectors which are both curlfree and divergencefree, and hence solve Maxwell’s equations. After first comparing several different traditional approaches to computing div, grad, and curl in curvilinear coordinates, we present a new approach, based on these “electromagnetic” basis vectors, which combines geometry and physics. Not only is our approach tied to a physical interpretation in terms of the electromagnetic field, it is also a useful way to remember the formulas themselves. We give several important examples of coordinate systems in which this approach is valid, in each case discussing the electromagnetic interpretation of the basis. We also give a general condition for when an electromagnetic interpretation is possible.

The exponential of the curl: Application to Maxwell fields
View Description Hide DescriptionThe operation of the exponential of the curl on a general vector field is studied. It is nonlocal, and it is shown that the resultant field may be written as the sum of integrals over all space. The formal solutions of the timedependent Maxwell’sequations for an arbitrary current density are first written in terms of the curl, and explicit expressions for the electric and magnetic fields are given in terms of the source current densities loaded with these kernels. This method of deriving the fields obviates the introduction of electromagnetic potentials. The wellknown expressions for the fields are derived for a fixed oscillating dipole and a charge in arbitrary motion. For a moving dipole the source current includes, in addition to the polarization current, a coupling of the polarization to the velocity of the dipole known as the Röntgen current. The magnetic field due to this current is given.

Efficiency of nonideal Carnot engines with friction and heat losses
View Description Hide DescriptionIn nonideal thermodynamic engines the efficiency is well below the Carnot efficiency In 1975 an expression for the efficiency of a nonideal Carnot engine with heat losses was derived, yielding at maximum power output. In this paper, a corresponding relation is obtained for more general nonideal Carnot engines. If there are friction losses only, the result is If friction and heat losses are both included, the efficiency at maximum power depends on a dimensionless parameter that takes into account the effects of friction and heat conduction, and can vary between the values obtained for friction and heat losses separately, A general relation between efficiency and power output is established, and it is shown that an appreciable gain in efficiency can be obtained at a power output only slightly below its maximum.

Experimental estimation of the band gap in silicon and germanium from the temperature–voltage curve of diode thermometers
View Description Hide DescriptionSemiconductor diodes, in conjunction with a constant current source, are sometimes used as thermometers. It has been observed experimentally that, within a certain temperature range, the relation between temperature and voltage is almost linear. We show that this linearity is a direct consequence of the constancy of the current flowing through the diode, and that the parameters resulting from a leastsquares fit to the experimental data can be used to determine the band gapenergy of the semiconductor. We test the validity of our model by comparing our results to measurements on diodes made of germanium and silicon. If we take into account the simplifications used in our model, the results agree well with known values of the energy gaps.

Sonic band structure and localized modes in a densitymodulated system: Experiment and theory
View Description Hide DescriptionThe sonic passing bands and stopping gaps of a quasionedimensional air tube with modulated mass density were studied experimentally and theoretically. Some gap modes whose wave functions are strongly localized near the ends of the air tube were also found. The simple experiment can be used as a demonstration of band structure in an upperdivision physics course.

Measuring the angular solar diameter using two pinholes
View Description Hide DescriptionAt the turn of the sixteenth century Tycho Brahe and Johannes Kepler made single pinhole measurements of the solar diameter. Their accuracy was limited by diffraction (unknown to them) and the motion of the image on the screen. We discuss how two pinholes built on the same mask can be used to bypass all the problems inherent in the single pinhole approach. The distance at which the two images of the Sun are in contact is the only measurement needed, and the experimental accuracy is much better than measuring the diameter of a single moving image. We obtained 0.5% accuracy, sufficient to follow the angular variations of the solar diameter due to the motion of the Earth in its orbit.
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 NOTES AND DISCUSSIONS



A remarkable mathematical property of the Landé factor in quantum mechanics
View Description Hide DescriptionWe show that the Landé factor can, in principle, attain any positive or negative rational number.

Comment on “The Thomas rotation,” by John P. Costella et al. [Am. J. Phys. 69 (8), 837–847 (2001)]
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 BOOK REVIEWS


A Guide to FirstPassage Processes
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The Atmospheric Environment: Effects of Human Activity
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