We place one

aluminum ring, with radius y $=5\mathrm{.}00$ cm and resistance R $=3\mathrm{.}00$ x $10\backslash$Omega $,$ around one end of a long tubular tube, with n $=1000$ turns

$1$

$$

per meter of radius r$2=3\mathrm{.}00$ cm$,$ at the core of which there is atmospheric air. Assume that the axial component of the magnetic field produced by the solenoid at its ends is half of the corresponding component at its center. Also, assume that the field produced by the solenoid outside its coils is negligible. The current in the solenoid increases at a rate of $270$ A$/$s$.($a$)$ What is the induced current in the ring? At the center of the ring, find $($b$)$ the magnitude and $($c$)$ the direction of the magnetic field produced by the induced ring current.