In a reference system $,$ there exists a homogeneous electric field E $=$ E$\_$x and a homogeneous magnetic field B $=$ B$\_$z$,$ where B $=$ E$\_0/(2$c$)($c is the speed of light$).$ A charge q $>0$ enters the space of this EM field with velocity $($relative to $)$ v $=0\mathrm{.}8$cx$.$

Questions:

$($a$)$ Calculate the four$-$force exerted by the field on the charge q$.$

$($b$)$ Examine whether there exists a reference system in which the electric or magnetic field is zero, and find the velocity of this system relative to $.$