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We have calculated in a closed form solution, in terms of modified Bessel function the first kind of order 0 and 1, for the motion of a positively charged particle in the magnetic field of an infinitely long, current-carrying wire in the nonrelativistic range. The orbits are not closed but exhibit a drift in the direction of the current with a speed that is independent of the launch angle. We found the drift velocity, drift displacement and the corresponding time, which we call the period. Keywords: Trajectory of a charged particle in magnetic field, Drift velocity, Drift displacement, Modified bessel function

We report on seven nights of optical observation taken over a two-week period, and the resultant analysis of the intermediate-frequency peaked BL Lac object (IBL), BL Lac itself, at redshift z = 0.069. The microvariable behavior can be confirmed over the course of minutes for each night. A relativistic beaming model was used in our analysis, to infer changes to the line of sight angles for the motion of the different relativistic components. This model has very few free parameters. The light curves we generated show both high and moderate frequency cadence to the variable behavior of BL Lac itself, in addition to the well documented long-term variability.

We report on the optical observations and analysis of the high-energy peaked BL Lac object (HBL), Mrk 501, at redshift z = 0.033. We can confirm microvariable behavior over the course of minutes on several occasions per night. As an alternative to the commonly understood dynamical model of random variations in intensity of the AGN, we develop a relativistic beaming model with a minimum of free parameters, which allows us to infer changes in the line of sight angles for the motion of the different relativistic components. We hope our methods can be used in future studies of beamed emission in other active microvariable sources, similar to the one we explored.

High-frequency coaxial waveguide measurements are used to evaluate composition- and frequency-dependent complex permittivities and permeabilities of polycrystalline ferroelectric and ferrimagnetic ceramics. Material dielectric and magnetic property measurements were performed on ferroelectric barium titanate (BaTiO3) and ferrimagnetic yttrium iron garnet (YIG), with the upper measurement frequency bound below gyromagnetic resonance of YIG. These polycrystalline materials were chosen because of their widespread use in voltage- and magnetic field-tunable devices. Wideband frequency material measurements were used to predict dielectric and magnetic properties of various two-phase composite media incorporating BaTiO3 and YIG. Two effective medium theories were used: an asymmetric, modified Maxwell-Garnett type and a symmetric Bruggeman model. The Bruggeman effective medium model is extended to include three-phases. The three-phase Bruggeman predictive model is employed when controlled porosity is introduced into the composite and when two component phases are combined with polytetrafluoroethylene.

The principal of least action is one of the fundamental ideas in physics. The path of the shortest time of a particle in the presence of gravity is an example of this principal. In this paper some methods are introduced to teach the optimal path in introductory physics courses. The optimal path (path of the shortest time) is calculated for a few families of paths. Finally a numerical method according to Snell’s law in a discrete medium is used to find the general optimal path and is compared with the brachistochrone path.