The Cavendish Experiment in General Relativity
Solutions of Einstein’s equations are discussed in which the “gravitational force” is balanced by an electrical force, and which can serve as models for the Cavendish experiment.
Equilibrium of charged dust in general relativity
Equilibrium of charged dust is studied in both the classical and relativistic theories. It is already known that the configuration of the dust is arbitrary if the ratio of the charge to mass densities,σ/ρ, is everywhere ± 1 (in relativistic units). I show here that there are equilibrium configurations for certain other valuesσ/ρ, including nonuniform ones. The solutions in these cases are arbitrary up to the choice of a harmonic function and a function of the electrostatic potential. In general they contain singularities.
Slotted Waveguide Antenna With Two Radiation Nulls
A design of a linear array antenna having two radiation nulls and otherwise omnidirectional radiation pattern is reported. A new configuration of a waveguide broad wall longitudinal slot doublet with positive and negative offsets with respect to the waveguide center line is used to design the array. This type of doublet produces two radiation nulls. Each of the null directions can be shifted at least up to plusmn25deg by proper choice of slot offset. Resonance and radiation characteristics of the proposed doublet are also presented. Finally, one linear array antenna consisting of seven doublets has been fabricated. Measurements show that the 15 dB null widths are 14.2deg and the null depths are at least 24.8 dB. Maximum gain ripple in the omnidirectional region is 1.75 dB.