A proton moving at speed v $=1\mathrm{.}00$ x $106$ m$/$s enters a region in space where a magnetic fi eld given

by B $=(0\mathrm{.}500$ T$)$ z exists. The velocity vector of the proton is at an angle $=60\mathrm{.}0$ with respect to

the positive z$-$axis. a$)$ Analyze the motion of the proton and describe its trajectory $($in qualitative

terms only$).$ b$)$ Calculate the radius, r$,$ of the trajectory projected onto a plane perpendicular to the

magnetic fi eld $($in the xy$-$plane$).$ c$)$ Calculate the period, T$,$ and frequency, f$,$ of the motion in that

plane. d$)$ Calculate the pitch of the motion $($the distance traveled by the proton in the direction of

the magnetic fi eld in $1$ period$).$