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Find the electric field at point \( P \) (as shown in figure) on the perpendicular bisector of a uniformly charged thin wire of length \( L \) carrying a charge \( Q \). The distance of the point from the center of the rod is \( a=\frac{\sqrt{3}}{2} L \).
(a) \( \frac{Q}{2 \sqrt{3} \pi \in_{0} L^{2}} \)
(b) \( \frac{\sqrt{3} Q}{4 \pi \in_{0} L^{2}} \)
(c) \( \frac{Q}{3 \pi \in_{0} L^{2}} \)
(d) \( \frac{Q}{4 \pi \in_{0} L^{2}} \)
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