A wall-engaging apparatus for microinductively investigating a characteristic of an earth formation traversed by a borehole comprises an antenna set mounted in an longitudinally elongated body adapted for a sliding engagement with the wall of the borehole. The antenna set includes a transmitter antenna mounted in the body for coupling electromagnetic energy into a formation; a receiver antenna for sensing a signal indicative of the characteristic; and at least one electroquasistatic shield element mounted coaxially with the magnetic dipole axis of the transmitter antenna. The electroquasistatic shield element comprises a sheet of conductive, non-magnetic material having a conductive center; a first annular band of narrow ray-like conductive segments, each of the conductive segments thereof integrally extending radially from the conductive center and being spaced from adjacent conductive segments by respective narrow radially-extending spaces originating in and traversing the first annular band; and preferably but not necessarily a second annular band of ray-like conductive segments, the conductive segments thereof integrally extending radially in pairs from a respective one of the conductive segment of the first annual band, and being spaced from adjacent pairs of conductive strips of the second annual band by respective longitudinal spaces originating in the first annular band and from one another by a narrow radially-extending space originating in and traversing the second annular band.