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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 $\vec{E}$ $(Newtons/Columb)$ will be

  1. $2\sqrt{2}\hat{k}$
  2. $-2\hat{k}$
  3. $2\hat{k}$
  4. $-2\sqrt{2}\hat{k}$
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