$(20$ pts$)$ Three charges are placed at the corners of a square as shown below, where qo and $d$ are fixed parameters and $q_2$ is unknown.

$q_1=-2q_0$

${}^2+de{l}^2=c^2$

$4+n=c^2$

a$.$ If $q_0=3\mathrm{.}00C$ and $d=5\mathrm{.}00cm,$ what charge $q_2$ is required to produce zero acceleration on an electron placed at the bottom$-$right corner of the square?

$ma=\frac{k{q}_2{q}_e}{\sqrt[\phantom{2}]{8}}$

$=\frac{\frac{n{q}_2{q}_e}{\sqrt[\phantom{2}]{8}}}{m_e}$

$i\frac{1\text{m}\text{e}\text{q}+q}{\sqrt[\phantom{2}]{8}}$

$120$

b$.$ What is the potential energy of the electron placed at the bottom$-$right corner of the square $($if we choose to set the potential energy at infinity equal to zero$)?$