Physics - Elecrostatics Question with Solution | TestHub

We can replace $-Q$ charge at origin by $+Q$ and $-2Q.$

Now due to $+Q$ charge at every corner of cube. Electric field at center of cube is zero so now net electric field at center is only due to $-2\mathrm{Q}$ charge at origin.

$\overrightarrow{E}=\frac{kq\overrightarrow{r}}{r^3}=\frac{1\left(-2Q\right)\frac{a}{2}\left(\hat{x}+\hat{y}+\hat{z}\right)}{4\pi {\epsilon }_0{\left(\frac{a}{2}\sqrt{3}\right)}^3}$

$\overrightarrow{E}=\frac{-2Q\left(\hat{x}+\hat{y}+\hat{z}\right)}{3\sqrt{3}\pi a^2{\epsilon }_0}$