A wafer of titanium dioxide $(\kappa=173)$ of area 1.00 $\mathrm{cm}^{2}$ has a thickness of 0.100 $\mathrm{mm}$ . Aluminum is evaporated on the parallel faces to form a parallel-plate capacitor. (a) Calculate the capacitance. (b) When the capacitor is charged with a $12.0-\mathrm{V}$ battery, what is the magnitude of charge delivered to each plate? (c) For the situation in part $(\mathrm{b}),$ what are the free and induced surface charge densities? (d) What is the magnitude of the electric field?