Motion of a drop in a conducting liquid under the action of a variable electromagnetic field

The authors consider the MHD motion of a spherical drop having conductivity sigma1 is identical to 0 different from conductivity sigma2 of the carrier liquid filling a vertically placed long solenoid fed by an alternating current I cos omega t. The authors introduce a spherical system of coordinates attached to the center of the drop, in which polar angle theta is reckoned from the direction of the vertical. At small Reynolds numbers with negligible inertial effects and in the absence of gravitational force the MHD flow around the drop is described by a system of equations