Three point charges $q_1,q_2,$ and $q_3$ are situated at three corners of a rectangle as shown in the diagram below. Here $q_1=+2\mathrm{.}00C,q_2=-2\mathrm{.}00C,q_3=+3\mathrm{.}00C.$

$13$

$($a$)$ What is the electric potential at the free corner where there is no charge?

$V$

$($b$)$ What charge should be placed at the free corner for the electric potential at the center of the rectangle to be zero? Include both magnitude and sign if applicable.

$C$