One long wire carries current $38\mathrm{.}0$ A to the left along the x axis. A second long wire carries current $62\mathrm{.}0$ A to the right along the line $($y $=0\mathrm{.}280$ m$,$ z $=0).$

$($a$)$ Where in the plane of the two wires is the total magnetic field equal to zero?

y $=$ m

$($b$)$ A particle with a charge of $2\mathrm{.}00$C is moving with a velocity of $150$ Mm$/$s along the line $($y $=0\mathrm{.}100$ m$,$ z $=0).$Calculate the vector magnetic force acting on the particle. $($Ignore relativistic effects.$)$

$=$

N

$($c$)$ A uniform electric field is applied to allow this particle to pass through this region undeflected. Calculate the required vector electric field.

$=$

N$/$C