$($a$)$ Given a coaxial capacitor with the length of $L$ which has two coaxial conductors with radius a and $b$ for inner and outer conductor, respectively. The inner conductor carries the total charge of $-$Q C whilst the outer carries $+$Q C$.$ Show that the capacitance as:

$C=\frac{2L}{ln(\frac{b}{a})}$

$[2$ marks$]$

$($b$)$ If the length of the coaxial, $L=100m,$ the inner radius $a=1cm$ and the outer radius $b=4cm$ and the coaxial is filled with the lossy Teflon $({}_r=2\mathrm{.}2$ and $=4S{m}^{-1}),$ determine:

i$.$ The capacitance

$[2$ marks$]$

ii$.$ The resistance across the Teflon

$[2$ marks$]$

iii. Potential difference between $r=3cm$ and $r=6cm$

$[2$ marks$]$

iv$.,$ Energy in region $a$

$[2$ marks$]$