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In 1968, F.L. Shapiro published the suggestion that one could search for anelectron EDM by applying a strong electric field to a substance that has anunpaired electron spin; at low temperature, the EDM interaction would lead to anet sample magnetization that can be detected with a SQUID magnetometer. Oneexperimental EDM search based on this technique was published, and for a numberof reasons including high sample conductivity, high operating temperature, andlimited SQUID technology, the result was not particularly sensitive compared toother experiments in the late 1970's.  Advances in SQUID and conventional magnetometery had led us to reconsiderthis type of experiment, which can be extended to searches and tests other thanEDMs (e.g., test of Lorentz invariance). In addition, the complementarymeasurement of an EDM-induced sample electric polarization due to applicationof a magnetic field to a paramagnetic sample might be effective using modernultrasensitive charge measurement techniques. A possible paramagnetic materialis Gd-substituted YIG which has very low conductivity and a net enhancement(atomic enhancement times crystal screening) of order unity. Use of areasonable volume (100's of cc) sample of this material at 50 mK and 10 kV/cmmight yield an electron EDM sensitivity of $10^{-33}$ e cm or better, a factorof $10^6$ improvement over current experimental limits.Comment: 6 pages. Prepared for ITAMP workshop on fundamental physics that was  to be held Sept 20-22 2001 in Cambride, MA, but was canceled due to terrorist  attack on U.S New version incorporates a number of small changes, most  notably the scaling of the sensitivity of the Faraday magnetometer with  linewidth is now treated in a saner fashion. The possibility of operating at  an even lower temperarture, say 10 microkelvin, is also discusse

Solid-state systems for the electron electric dipole moment and other fundamental measurements