A parallel plate capacitor is to be designed using barium titanate $($BaTiO$3$ or BTO$),$ a common

dielectric material used in high voltage capacitors. The design calls for a $1\mathrm{.}88$ nF capacitor, in

which the dielectric layer of BTO separates two parallel metal plates each having an area of

$9$ cm$2.$ Using a dielectric constant of $6,000$ for BTO,

$($a$)$ Determine the length, l$,$ in mm$,$ separating the two parallel plates $(10$ points$)$

$($b$)$ The application calls for a $1$ kV electric field to be applied to the capacitor. Under this field,

what will the polarization, P$,$ be$?$