  Critical experimental tests of the time-dependent Abraham force in
phenomenological electrodynamics are scarce. In this paper we analyze the
possibility of making use of intensity-modulated whispering gallery modes in a
microresonator for this purpose. Systems of this kind appear attractive, as the
strong concentration of electromagnetic fields near the rim of the resonator
serves to enhance the Abraham torque exerted by the field. We analyze mainly
spherical resonators, although as an introductory step we consider also the
cylinder geometry. The order of magnitude of the Abraham torques are estimated
by inserting reasonable values for the various input parameters. As expected,
the predicted torques turn out to be very small, although probably not beyond
any reach experimentally. Our main idea is essentially a generalization of the
method used by G. B. Walker et al. [Can. J. Phys. 53, 2577] for low-frequency
fields, to the optical case.
