B$-$Field from a Rotating Disk $(25$ points$)$

$($a$)$ Compute the magnetic field $$ B$(0,0,$ z$)$ on the axis of a circular ring

of radius R carrying a current I. The ring is in the xy$-$plane and

is centered on the origin.

$($b$)$ Earlier we considered a CD of radius R with a fixed, constant,

uniform surface electric charge density everywhere on its top

surface. It was spinning at angular velocity $$z about its center

$($the origin$).$ You found the current density $$ K at a distance r from

the center. Use that result to find the magnetic field $$ B$(0,0,$ z$)$ at

any distance z directly above the origin. Does your answer seem

reasonable? Check its limiting behaviors $($e$.$g$.$ what do you expect

if R $0?$ z $$ $?$ $0?$ Slightly less obvious, but also worth

checking$/$thinking about, what about z $0?)$