Answer
(a) $U = 1.1\times 10^{-7}~J$
(b) The energy density is $~0.70~J/m^3$
Work Step by Step
(a) We can find the energy:
$U = \frac{1}{2}C~(\Delta V)^2$
$U = \frac{(\epsilon_0~A)~(\Delta V)^2}{2~d}$
$U = \frac{(\epsilon_0~\pi~r^2)~(\Delta V)^2}{2~d}$
$U = \frac{(8.854\times 10^{-12}~F/m)~(\pi)~(0.010~m)^2~(200~V)^2}{(2)(0.50\times 10^{-3}~m)}$
$U = 1.1\times 10^{-7}~J$
(b) Let $V$ be the volume of the space between the plates.
We can find the energy density:
$\frac{U}{V} = \frac{1.1\times 10^{-7}~J}{(\pi)~(0.010~m)^2~(0.50\times 10^{-3}~m)} = 0.70~J/m^3$
