A parallel-plate capacitor with plate separation \(d\) is connected to an ideal battery that maintains a constant potential difference \(V_0\). With air between the plates, the electric field magnitude between the plates is \(E_0\). While the capacitor remains connected to the battery, a dielectric slab with dielectric constant \(\kappa\) is inserted, completely filling the space between the plates. What is the ratio of the new electric field magnitude \(E\) to the initial electric field magnitude \(E_0\)?