$(a)\;zero\qquad(b)\;\large\frac{Qa}{\pi \in_{0}x^3}\qquad(c)\;\large\frac{2Qa}{\pi\in_{0}x^3}\qquad(d)\;\large\frac{\sqrt{3}Qa}{\pi\in_{0}x^3} $

Answer : (a) $\;\large\frac{Qa}{\pi\in_{0}x^3}$

Explanation :

Consider the charges at opposite sides of O . They form a dipole with dipole moment p=2Qa

Electrical field due to a dipole on its axis is $E=\large\frac{k\;p}{x^3}=\large\frac{Qa}{2\pi \in_{0} x^3}$

Now three fields exists as shown in figure :

Net electric field :

$|E_{net}|=2|E|$

$=\large\frac{2Qa}{2 \pi \in_{0} x^3}=\large\frac{Qa}{\pi \in_{0}x^3}$

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