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 } $