The geometry of the Fabry-Perot cavity makes it difficult to use for measuring the Stark effect. A "Stark cage" is described which generates an electric field suitable for this purpose. The cage is used to measure first and second order Stark splittings of several low-J transitions of the benzene-water dimer previously reported [Gutowsky, Emilsson, and Arunan, J. Chem. Phys. 99, 4883 (1993)]. The dipole moment is found to depend somewhat on rotational state, ranging from 1.65 to 2.00 Debye for both ground m=0 and first excited m=1 internal rotation states of the dimer. Additional m=1 transitions are reported, including the previously missing downshifted line of a k=0(') doublet. Its presence and various Stark effects require reassignment of the m=1 spectrum. The results demonstrate that each J --> J+1 spectrum consists of three distinct components which arise from the H2O in an unusual way. In addition to the k-doublets, there are two progressions; a set of (J+1) negative k's running from -J to 0, and a set of (J-1) positive k's with somewhat smaller spacings, running from +2 to +(J-1). It is proposed that each of the three components is associated primarily with one of the three 1(01), 1(11), and 1(10) rotor states of the water. These "patches" are attributed to the potential energy surface (PES). Molecular mechanics for clusters (MMC) calculations indicate barriers of 300-600 cm(-1) to internal rotation of the water about any of its inertial axes and nearly free rotation about an axis parallel to the benzene C-6 axis. This novel PES leads to unusual internal motions; asymmetric top rotations of the water about the benzene C-6 axis instead of the usual rotation about an inertial axis of the water.