A square wire loop of size $2$a x $2$a lies in the xy plane with its center at the origin and sides parallel to the x and y axes. A counterclockwise current $1$ runs around the loop. $($a$)$ Find the magnetic field on the z axis. $[$Answer: Bz $($z$)=2$ltOl a$2/[]!\text{'}($a$2+$ z$2)(2$a$2+$ z$2)1/2]]($b$)$ Show that for z$/$a $$ I the field becomes that of a magnetic dipole, and find the magnetic moment. $($See $(8\mathrm{.}78)$ and $(8\mathrm{.}80).)($c$)$ Compare the field at the center of this square loop with that at the center of a circular loop of diameter $2$a$.$