A perfectly conducting metal plate is placed in $x-y$ plane in a right handed coordinate system. A charge of $+32\pi \epsilon _0\sqrt{2}$ columbs is placed at coordinate $(0, 0, 2)$. $\epsilon _0$ is the permittivity of free space. Assume $\hat{i}$,$\hat{j}$,$\hat{k}$ to be unit vectors along $x$, $y$ and $z$ axes respectively. At the coordinate $(\sqrt{2},\sqrt{2},0)$, the electric field vector $\overrightarrow{E} \text{(Newtons/Columb)}$ will be
- $2\sqrt{2}\hat{k}$
- $-2\hat{k}$
- $2\hat{k}$
- $-2\sqrt{2}\hat{k}$