Quadrupole Electromagnetic Radiation of a Charged Drop Oscillating in the Superposition of Collinear Gravitational and Electrostatic Fields

The analytical expression for the quadrupole moment of a charged conducting droplet caused by the presence of the self- and induced charges on the droplet surface is obtained. The droplet is assumed to be motionless in the superposition of gravitational and electrostatic fields. The analytical calculations are carried out in the first order in the dimensionless oscillation amplitude of the droplet. The intensity of electromagnetic radiation of the droplet generated by time variation in its quadrupole moment is estimated in the second order of smallness with respect to the square of the ratio of the characteristic linear droplet size to the length of emitted wave.