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 (assume x>>>a)

Explanation

This is basically a problem of finding the electric field due to three dipoles. The dipole moment of each dipole is P = Q(2a) Electric field due to each dipole will be `E= (KP)/(x^(3))`

The direction of electric field due to each dipole is as shown below:
`E_("net") = E + 2E cos 60^(@)= 2E`
`=2 ((1)/(4pi epsi_(0))) (2Qa)/(x^(3))= (Qa)/(pi epsi_(0)x^(3))`