We examine the thermal fluctuations of the local electric field E loc k and the dipole moment µ k in liquid water at T = 298 K between metal walls in electric field applied in the perpendicular direction. We use analytic theory and molecular dynamics simulation. In this situation, there is a global electrostatic coupling between the surface charges on the walls and the polarization in the bulk. Then, the correlation function of the polarization density pz(r) along the applied field contains a homogeneous part inversely proportional to the cell volume V . Accounting for the longrange dipolar interaction, we derive the Kirkwood-Fröhlich formula for the polarization fluctuations when the specimen volume v is much smaller than V . However, for not small v/V , the homogeneous part comes into play in dielectric relations. We also calculate the distribution of E loc k in applied field. As a unique feature of water, its magnitude |E loc k | obeys a Gaussian distribution with a large mean value E0 ∼ = 17 V/nm, which arises mainly from the surrounding hydrogen-bonded molecules. Since |µ k |E0 ∼ 30kBT , µ k becomes mostly parallel to E loc k . As a result, the orientation distributions of these two vectors nearly coincide, assuming the classical exponential form. In dynamics, the component of µ k (t) parallel to E loc k (t) changes on the timescale of the hydrogen bonds ∼ 5 ps, while its smaller perpendicular component undergoes librational motions on timescales of 0.01 ps.