A parallel-plate capacitor has air between its plates, which are $6.0\ \text{mm}$ apart. It is charged to $90\ \text{V}$ and then taken off the battery. Two flat pieces are now slid into the gap, parallel to the plates, as in the figure. One is a slab of dielectric constant $3.0$ and thickness $3.0\ \text{mm}$. The other is an uncharged metal sheet of thickness $1.5\ \text{mm}$. They do not touch each other or the plates, and they cover the plates fully. Ignore the effects at the edges. What is the potential difference between the plates now?

Fig. 1: Side view of a parallel-plate capacitor with its plates 6.0 mm apart. Inside, parallel to the plates and not touching them or each other, are a dielectric slab 3.0 mm thick with dielectric constant 3.0 and a metal sheet 1.5 mm thick. The capacitor is not joined to anything.