If you want to maintain a potential difference of \(6000 \mathrm{~V}\) between the plates of a parallel-plate capacitor, what is the minimum value of the plate separation if the space between the plates is completely filled by \((a)\) a slab of mica and \((b)\) a slab of barium titanate? (c) What is the ratio of the maximum charges that could be put on a plate of the capacitor in part \(b\) to the capacitor in part \(a\).