$[1/2$ Points$]$

SERPSE$1028.$A$.$OP$\mathrm{.}032.$

PRACTICE ANOTHER

The figure below shows a proton $($mass of $1\mathrm{.}67{10}^{-27}kg),$ initially at the origin of a coordinate system with an initial velocity vec$(v)$ in the $xy-$plane. The initial speed is $5\mathrm{.}20{10}^6\frac{m}{s}$ at an angle of $=70\mathrm{.}0$ with the $x-$axis. The proton moves in the presence of a uniform magnetic field vec$(B)$ in the positive $x$ direction with a magnitude of $0\mathrm{.}158$ T and makes a helical path. The pitch $p$ of the helix, shown on the figure, is the distance between successive complete turns of the helix, measured along the helix axis.

$$

$($a$)$ What is the pitch $p($in m $)$ of the trajectory as defined in the figure?

$$ What is the angular speed of the circular motion of the particle in the $yz$ plane? How is it related to the period? Does the $x-$component of the velocity change during the motion? How can you relate it and the period to the pitch? $m$

$($b$)$ What is the radius $r($in m $)$ of the trajectory as defined in the figure?

$$ m