A water drop that is gently deposited on a very cold surface freezes into a pointy ice-drop with a very sharp tip. The formation of this singular shape originates from the reduction of mass density during the freezing process and can be explained using a simplified model for which the universal structure of the singularity is revealed in full detail. The combination of a relatively simple, static experiment, and the accessible asymptotic analysis makes this system an ideal introduction to the topic of singularities.

Surface charges play a major role in DC circuits because they help generate the electric field and potential distributions necessary to move the charges around the circuit. Unfortunately, it is generally regarded as a difficult task to determine the surface charge distribution for all but the simplest geometries. In this paper, we develop a graphical method for the approximate construction of surface charge distributions in DC circuits. This method allows us to determine (approximately) the location and the amount of surface charge for almost any circuit geometry. The accuracy of this semi-quantitative method is limited only by one’s ability to draw equipotential lines. We illustrate the method with several examples.

We re-examine the case of rare-earth magnets rolling down an inclined plane, presenting an approach to conducting quantitative investigations that results in high-quality experimental data connecting simple experiments to a handful of important applications of eddy currents. These include not only magnetic braking but also the characterization of conductive materials, measurement of the thickness of dielectric coatings, and nondestructive evaluation of conductive objects. The simplicity of the proposed experimental setups, which include the use of widely available smart phones to record video that can be post-processed with free software, makes these experiments appealing to high school and college physics students.