Answer
(a) $B_3\lt B_1\lt B_2$
(b) $B_1$ out of the page; $B_2$ into the page; $B_3$ out of the page
Work Step by Step
(a) We know that $r=\frac{mv}{qB}$. This equation shows that larger the radius, the smaller will be the magnetic field strength and vice versa. Thus, we can rank the fields in increasing order as $B_3\lt B_1\lt B_2$.
(b) We know that in the magnetic field regions $B_1$ and $B_3$, the direction of the proton is towards the right and the magnetic force is in the downward direction. Thus, according to the right hand rule, the magnetic fields should be directed out of the page. On the other hand, in the magnetic field region $B_2$, the direction of the proton is towards the left and the magnetic force is in the downward direction. Thus, the magnetic field should be directed into the page.
