Two $1\mathrm{.}20m$ nonconducting rods meet at a right angle.Part A

Two small spheres, each carrying a net positive

charge, are separated by $0\mathrm{.}400m.$ You have been

asked to perform measurements that will allow you

to determine the charge on each sphere. You set

up a coordinate system with one sphere $($charge

$q_1)$ at the origin and the other sphere $($charge $q_2)$

at $x=+0\mathrm{.}400m.$ Available to you are a third

sphere with net charge $q_3=6\mathrm{.}00{10}^{-6}C$ and an

apparatus that can accurately measure the location

of this sphere and the net force on it$.$ First you

place the third sphere on the $x-$axis at

$x=0\mathrm{.}200m$; you measure the net force on it to be

$3\mathrm{.}50N$ in the $+x-$direction. Then you move the

third sphere to $x=+0\mathrm{.}600m$ and measure the net

force on it now to be $2\mathrm{.}50N$ in the $+x-$direction.

Calculate $q_1.$

Express your answer with the appropriate units.

$\{$:$q_1=,]$

Part B

Calculate $q_2.$

Express your answer with the appropriate units.

$q_2=$

One rod carries $+2\mathrm{.}50C$ of charge distributed uniformly

along its length, and the other carries $-2\mathrm{.}50C$

distributed uniformly along it $($Figure $1).$

Part A

Find the magnitude of the electric field these rods produce at point $P,$ which is $60\mathrm{.}0cm$ from each rod.

Express your answer with the appropriate units.

$E=$