Step 1

The charge located at the origin is given as,

\(\displaystyle{q}=-{12}{n}{C}\)

\(\displaystyle=-{12}{n}{C}\times{\frac{{{10}^{{-{9}}}{C}}}{{{1}{n}{C}}}}\)

\(\displaystyle=-{12}\times{10}^{{-{9}}}{C}\)

Step 2

(a)

The position at which electric field required is given as,

\(\displaystyle{\left({x},{y}\right)}={\left({0}{c}{m},{5}{c}{m}\right)}\)

The distance of the required position from the origin can be determined as,

\(\displaystyle{r}=\sqrt{{{x}^{{{2}}}+{y}^{{{2}}}}}\)

\(\displaystyle=\sqrt{{{\left({0}{c}{m}\right)}^{{{2}}}+{\left({5}{c}{m}\right)}^{{{2}}}}}\)

\(\displaystyle={5}{c}{m}\times{\frac{{{10}^{{-{2}}}{m}}}{{{1}{c}{m}}}}\)

\(\displaystyle={0.05}{c}{m}\)

The electric field strength at the required location can be determined as,

\(E=\frac{k\mid q\mid}{r^{2}}\)

\(=\frac{(9\times10^{9}N.m^{2}/C^{2})\mid-12\times10^{-9}C\mid}{(0.05m)^{2}}\)

\(\displaystyle={43200}\frac{{N}}{{C}}\)