An Electromagnetic Thirring Problem

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Abstract
A neutral rotating mass shell surrounds a concentric stationary electrically charged insulating shell. The dipole-like magnetic field induced by (and proportional to) the rotation of the neutral shell is calculated on the basis of the coupled linearized Einstein-Maxwell field equations of general relativity. This field is apparently at variance with a conjecture made on Machian grounds, for which a possible explanation is suggested. The corresponding induced quadrupolar electric field is calculated for the region within the charged shell, and the potential is given for this field everywhere. Though understandable on mutually inconsistent elementary grounds, we regard this field as a useful example of a solution of linearized general relativity.