A solid insulating sphere of radius r$1=$ a has a total charge, NON$-$uniformly distributed, of $2$Q$.$ The sphere is

surrounded cocentrically by a conducting spherical shell of inner radius r$2=$ b and outer radius r$3=$ c$,$ and

contains a total charge of $-$Q$.$ All your answers should some or all of the following variables$/$constants: a$,$ b$,$ c$,$

Q$,$ K$,$ o$,$

a$)$ If the charge density function of the insulating sphere is given by $=$ D

r$2$

$,$ use Gauss's law to derive an

expression for the Electric field as a function of distance r for r $<$ a$.$ b$)$ Use Gauss's law to derive an expression for the Electric field as a function of distance r for a $<$ r $<$ b

$3$

c$)$What is the charge on the inner surface of the conducting shell at r $=$ b$?$

d$)$ What is the charge on the outer surface of the conducting shell at r $=$ c$?$

e$)$ Derive an expression for the Electric field as a function of distance r for r $>$ c$.$