What will be the magnitude of electric field at point O as shown in figure?

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Question:
What will be the magnitude of electric field at point O as shown in figure? Each side of the figure is l and perpendicular to each other?

$\frac{1}{4 \pi \varepsilon_{0}} \frac{q}{l^{2}}$
$\frac{1}{4 \pi \varepsilon_{0}} \frac{\mathrm{q}}{\left(2 l^{2}\right)}(2 \sqrt{2}-1)$
$\frac{\mathrm{q}}{4 \pi \varepsilon_{0}(2 l)^{2}}$
$\frac{1}{4 \pi \varepsilon_{0}} \frac{2 \mathrm{q}}{2 l^{2}}(\sqrt{2})$

Correct Option: , 2

Solution:

$\mathrm{E}_{1}=\frac{\mathrm{kq}}{\ell^{2}}=\mathrm{E}_{2}$

$\mathrm{E}_{3}=\frac{\mathrm{kq}}{(\sqrt{2} \ell)^{2}}=\frac{\mathrm{kq}}{2 \ell^{2}}$

$\mathrm{E}=\frac{\sqrt{2} \mathrm{kq}}{\ell^{2}}-\frac{\mathrm{kq}}{2 \ell^{2}}=\frac{\mathrm{kq}}{2 \ell^{2}}(2 \sqrt{2}-1)$

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