$$

Outside the shell: Vout$($r$)=$ V$0$R$2$cos$($$)/$r$2$

Inside the shell: Vin$($r$)=$ c r cos$($$)/$R$.$

$$

$($a$)$ Given the formula for Vout$($r$),$ tell me what c is$,$ and how you know. $(5$ points$)$

$($b$)$ Find the surface charge density $($$).(15$ points$)$

$($c$)$ What is the net charge of this charge distribution? $(10$ points$)$

$($d$)$ What is the dipole moment p of this charge distribution? $($For p$,$ give direction

and magnitude.$)$ As always, briefly but clearly explain reasoning. $(10$ points$)($c$)$ What is the net charge of this charge distribution? $(10$ points$)$

$($d$)$ What is the dipole moment p of this charge distribution? $($For p$,$ give direction

and magnitude.$)$ As always, briefly but clearly explain reasoning. $(10$ points$)$