Q. Six charges are placed at the vertices of a rectangular hexagon as shown in the figure. The electric field on the line passing through point O and perpendicular to the plane of the figure as a function of distance x from point O is (*x* >> *a*)

(a)Zero

(b) $ \displaystyle \frac{Qa}{\pi\epsilon_0 x^3 } $

(c) $ \displaystyle \frac{2Qa}{\pi\epsilon_0 x^3 } $

(d) $ \displaystyle \frac{\sqrt3 Qa}{\pi\epsilon_0 x^3 } $

Ans: (b)

Electric Field due to dipole at a point on the axis passing through O is

$\displaystyle E = \frac{p}{4\pi \epsilon_0 x^3}$

Where p = Q × 2a

Net field is

$ \displaystyle E_{net} = 2E = \frac{2 \times Q \times 2 a}{4\pi \epsilon_0 x^3}$

$ \displaystyle = \frac{Q a}{\pi\epsilon_0 x^3 } $