At time t $=0,$ an electron with kinetic energy $9\mathrm{.}7$ keV moves through x $=0$ in the positive direction of an x axis that is parallel to the horizontal component of Earth's magnetic field $.$ The field's vertical component is downward and has magnitude $45\mathrm{.}1$T$.$

$($a$)$ What is the magnitude of the electron's acceleration due to $?$

m$/$s$2$

$($b$)$ What is the electron's distance from the x axis itself, when the electron reaches coordinate x $=23\mathrm{.}0$ cm$?$