A parallel-plate capacitor with plate area \(A\) and plate separation \(d\) is completely filled with an insulating liquid of dielectric constant \(\kappa > 1\) and connected to an ideal battery maintaining a constant potential difference \(V_0\). While remaining connected to the battery, the liquid is drained from the space between the plates without altering the plate separation. In terms of the given quantities and fundamental constants, what is the final electric field magnitude \(E\) between the plates, and what is the work \(W_{\text{battery}}\) done by the battery during the draining process?