#$1-$ Analyzing Capacitors $(10$ pts$)$

A coaxial capacitor is shown to the right. The inner conductor $(1)$ radius is $a=1\mathrm{.}5mm$ and the outer conductor radius $(2)$ is $b=2\mathrm{.}25mm.$ The coaxial capacitor's relative permittivity is $lo{n}_r=10.$

The inner conductor has radius a$,$ and the outer conductor has radius $b,$ as shown in the figure below, right.

Equal charges $+$Q and $-$Q are placed on the inner and outer conductors.

$($a$)$ Following the steps outlined in the course notes, determine the capacitance of the coaxial capacitor. Number the steps and show all the work. Assume an infinite length for the coaxial capacitor in this part.

$($b$)$ With the expression you found in part $($a$),$ calculate the capacitance of the coaxial capacitor with the dimensions shown above, and a length $L=10cm.$

Recall that the permittivity of free space is given by $lo{n}_o=8\mathrm{.}854{10}^{-12}\frac{F}{m}.$